Levy flights and nonlocal quantum dynamics

We develop a fully fledged theory of quantum dynamical patterns of behavior that are nonlocally induced. To this end we generalize the standard Laplacian-based framework of the Schr\"{o}dinger picture quantum evolution to that employing nonlocal (pseudodifferential) operators. Special attention is paid to the Salpeter (here, $m\geq 0$) quasirelativistic equation and the evolution of various wave packets, in particular to their radial expansion in 3D. Foldy's synthesis of "covariant particle equations" is extended to encompass free Maxwell theory, which however is devoid of any "particle" content. Links with the photon wave mechanics are explored.

Influence of semiconducting electrodes on properties of thin ferroelectric films

The influence of semiconducting electrodes on the properties of thin ferroelectric films is considered within the framework of the phenomenological Ginzburg-Landau theory. The contribution of the electric field produced by charges in the electrodes allowing for the screening length of the carriers is included in the functional of the free energy and so in the Euler-Lagrange equation for the film's polarization. Application of the variational method to the solution of this equation allows the transformation of the free energy functional into a conventional type of free energy with renormalized coefficients. The obtained dependence of the coefficients on the film thickness, temperature, elect…

The influence of topological phase transition on the superfluid density of overdoped copper oxides

We show that a topological quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bo\^zovi\'c, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. We demonstrate that 1) at temperature $T=0$, the superfluid density $n_s$ turns out to be considerably smaller than the total electron density; 2) the critical temperature $T_c$ is controlled by $n_s$ rather than by doping, and is a linear function of the $n_s$…

Electric field driven domain wall transfer in hybrid structures

Domain wall (DW) motion devices attracts much interest with their prospective logic and memory applications[1][2]. Present on-chip DW manipulations by a magnetic field of electric currents or electron spin torque raise the problem of high Ohmic energy losses. We show that such a difficulty can be avoided by applying an exchange field H eff to the magnetic layer from the proximate graphene (Gr), instead of using an actual magnetic field. H eff is shown to be dependent on carrier density gradient in Gr, which is easily manipulated with a gate voltage. A novel memory device implementing this concept is designed and modeled, demonstrating switching power well below femto-Joule while maintaining…

The behavior of the 180° domain walls in disordered dielectrics like KTaO3 : Li and KTaO3 : Nb

We calculate the structure of 180° domain wall in disordered ferroelectrics with random site electric dipoles (i.e. those like K 1-x Li x TaO 3 , KTa 1-x Nb x O 3 , where Li + or Nb 5+ are off-center ions forming impurity dipoles). The calculation is performed on the base of the free energy functional of disordered dielectrics derived earlier [M. D. Glinchuk et al., Phase Transit., 2003 (to be published)] within the framework of a random field method. We obtain the domain wall thickness as a function of impurity dipole concentration n and temperature T. It is shown that in disordered ferroelectrics the domain wall is usually broader than in their ordered counterparts. The thickness increase…

Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.

The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …

Universal low-temperature behavior of the CePd_{1-x}Rh_x ferromagnet

The heavy-fermion metal CePd_{1-x}Rh_x evolves from ferromagnetism at x=0 to a non-magnetic state at some critical concentration x_c. Utilizing the quasiparticle picture and the concept of fermion condensation quantum phase transition (FCQPT), we address the question about non-Fermi liquid (NFL) behavior of ferromagnet CePd_{1-x}Rh_x and show that it coincides with that of both antiferromagnet YbRh_2(Si_{0.95}Ge_{0.05})_2 and paramagnet CeRu_2Si_2 and CeNi_2Ge_2. We conclude that the NFL behavior being independent of the peculiarities of specific alloy, is universal, while numerous quantum critical points assumed to be responsible for the NFL behavior of different HF metals can be well redu…

The manifestation of dipoles clustering in paraelectric phase of disordered ferroelectrics

Abstract We predict the existence of Griffiths phase in the dielectrics with concentrational crossover between dipole glass (electric analog of spin glass) and ferroelectricity. The peculiar representatives of above substances are KTaO3: Li, Nb, Na or relaxor ferroelectrics like Pb1−xLaxZr0.65Ti0.35O3. Since this phase exists above ferroelectric phase transition temperature (but below that temperature for ordered substance), we call it “para-glass phase”. We assert that the difference between paraelectric and para-glass phase of above substances is the existence of clusters (inherent to “ordinary” Griffiths phase in Ising magnets) of correlated dipoles. We show that randomness play a decisi…

The Topological Phase Transitions Related to Fermion Condensate

In this chapter, we consider so-called topological phase transitions, taking place in normal Fermi liquid. In other words, here we are dealing with different instabilities of normal Fermi liquids relative to several kinds of perturbations of initial quasiparticle spectrum \(\varepsilon (p)\) and occupation numbers \(n(p)\) associated with the emergence of a multi-connected Fermi surface. Depending on the parameters and analytical properties of the Landau interaction, such instabilities lead to several possible types of restructuring of initial Landau Fermi liquid ground state. This restructuring generates topologically distinct phases. One of them is the FC discussed above, another one belo…

On the theory of domain structure in ferromagnetic phase of diluted magnetic semiconductors

Abstract We present a comprehensive analysis of domain structure formation in ferromagnetic phase of diluted magnetic semiconductors (DMS) of p-type. Our analysis is carried out on the base of effective magnetic free energy of DMS calculated by us earlier [Yu.G. Semenov, V.A. Stephanovich, Phys. Rev. B 67 (2003) 195203]. This free energy, substituting DMS (a disordered magnet) by effective ordered substance, permits to apply the standard phenomenological approach to domain structure calculation. Using coupled system of Maxwell equations with those obtained by minimization of above free energy functional, we show the existence of critical ratio ν cr of concentration of charge carriers and ma…

Energy scales and magnetoresistance at a quantum critical point

The magnetoresistance (MR) of CeCoIn_5 is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization etc) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the abov…

Levy flights in confining environments: Random paths and their statistics

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…

Synthesis of Nanoferroics

The Chapter covers the technological aspects of many chemical and physico-chemical nanofabrication methods relevant to making nanoferroic materials and composites. First, the classification of relevant synthesis methods of nanoferroics has been presented. Synthesis of particular nanoferroics with different chemical bonding like metallic, oxide and non-oxide compounds is considered in details. Among the methods, the mechanochemical, sonochemical, hydrothermal, co-precipitation, emulsion, thermal decomposition of unstable precursors have been analyzed. The competition between new phase nucleation and nuclei growth has been revealed to be controlled using feedback between reaction rate and tem…

Asymmetrical tunneling in heavy fermion metals as a possible probe for their non-Fermi liquid peculiarities

Tunneling conductivity and point contact spectroscopy between heavy fermion metal and a simple metallic point contact may serve as a convenient probing tool for non-Fermi liquid behavior. Landau Fermi liquid theory predicts that the differential conductivity is a symmetric function of voltage bias. This symmetry, in fact, holds if so called particle–hole symmetry is preserved. Here, we show that the situation can be different when one of the two metals is a heavy fermion one whose electronic system is a heavy fermion liquid. When the heavy fermion liquid undergoes fermion condensation quantum phase transition, the particle–hole symmetry in the excitation spectra is violated making both the …

Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review

In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits t…

The enhancement of ferromagnetism in uniaxially stressed diluted magnetic semiconductors

We predict a new mechanism of enhancement of ferromagnetic phase transition temperature $T_c$ in uniaxially stressed diluted magnetic semiconductors (DMS) of p-type. Our prediction is based on comparative studies of both Heisenberg (inherent to undistorted DMS with cubic lattice) and Ising (which can be applied to strongly enough stressed DMS) models in a random field approximation permitting to take into account the spatial inhomogeneity of spin-spin interaction. Our calculations of phase diagrams show that area of parameters for existence of DMS-ferromagnetism in Ising model is much larger than that in Heisenberg model.

On the Theory of Domain Structure of Disordered Ferroelectrics

We present a comprehensive analysis of domain structure formation in ferroelectric phase of incipient ferroelectrics with off-center dipole impurities like KTaO 3 :Li, Nb,Na. Our analysis is carried out on the base of effective free energy of disordered ferroelectrics, derived by us earlier. This free energy permits to apply the standard approach to domain structure calculation. Using coupled system of Maxwell equations with those obtained by minimization of above free energy, we calculate the physical characteristics of domain structure as functions of impurity dipoles concentration n. Our theory can be easily generalized for arbitrary temperature and crystal shape including thin films.

Energy-level repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to non-integrability of the system and hints on the possibility of quantum chaos emerging. Such a behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization…

Magnetic-field-induced reentrance of Fermi-liquid behavior and spin-lattice relaxation rates in

Abstract A strong departure from Landau–Fermi liquid (LFL) behavior have been recently revealed in observed anomalies in both the magnetic susceptibility χ and the muon and 63Cu nuclear spin-lattice relaxation rates 1 / T 1 of YbCu 5 − x Au x ( x = 0.6 ). We show that the above anomalies along with magnetic-field-induced reentrance of LFL properties are indeed determined by the dependence of the quasiparticle effective mass M ∗ on magnetic field B and temperature T and demonstrate that violations of the Korringa law also come from M ∗ ( B , T ) dependence. We obtain this dependence theoretically utilizing our approach based on fermion condensation quantum phase transition (FCQPT) notion. Ou…

Flat bands and strongly correlated Fermi systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermiliquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle-hole (C) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity dI/dV, where I is the current and V the bias voltage, is a symmetric function of V. Thus, it has been predicted that the conductivity becomes asymmetric …

Baryon Asymmetry Resulting from FCQPT in the Early Universe

This Chapter does not follow the main line of the book that is the theory of HF compounds but illustrates how the ideas of FC may be applicable to describe a very dissimilar system. Namely, here we consider a novel mechanism for explaining the matter-antimatter asymmetry of the universe. We assume that the universe starts from completely symmetric state and then, as it cools down, it undergoes a quantum phase transition, which in turn causes an asymmetry between matter and anti-matter. As we shall see the quantum phase transition is represented by FCQPT. The mechanism does not require the baryon number violating interactions or \({\textit{CP}}\) violation at a microscopic level. The state F…

Thermodynamic, dynamic and transport properties of quantum spin liquid in herbertsmithite from experimental and theoretical point of view

In our review we focus on the quantum spin liquid, defining the thermodynamic, transport and relaxation properties of geometrically frustrated magnets (insulators) represented by herbertsmithite $\rm ZnCu_{3}(OH)_6Cl_2$.

Magnetoelectric effect in mixed valency oxides mediated by charge carriers

We show that the presence of free carriers in a substance can generate the multiferroic behavior. Namely, if the substance has mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, all three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperature. The physical origin of the effect is that charge carriers can mediate the multiferroic behavior via spin - spin (RKKY), dipole-dipole and dipole - spin interactions. Our estimate of the interaction magnitude shows that there exist an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of spin-spin RKKY…

Cluster superconductivity in the magnetoelectric Pb(Fe1/2Sb1/2)O3 ceramics

We report the observation of cluster (local) superconductivity in the magnetoelectric Pb(Fe1/2Sb1/2)O3 ceramics prepared at a hydrostatic pressure of 6 GPa and temperatures 1200-1800 K to stabilize the perovskite phase. The superconductivity is manifested by an abrupt drop of the magnetic susceptibility at the critical temperature TC 7 K. Both the magnitude of this drop and TC decrease with magnetic field increase. Similarly, the low-field paramagnetic absorption measured by EPR spectrometer drops significantly below TC as well. The observed effects and their critical magnetic field dependence are interpreted as manifestation of the superconductivity and Meissner effect in metallic Pb nanoc…

Ultrafast dynamics of indirect exchange interaction and transient spin current generation in a two-dimensional electron gas

We predict that a driven localized magnetic moment coupled to mobile carriers of a metal or semiconductor surface or interface generates a specific dynamics of the carrier spin density as well as a transient spin current. Numerical results illustrate the time-dependent Friedel oscillations and the associated ultrafast Ruderman-Kittel- Kasuya-Yosida (RKKY) interaction as well as the spin current generated by the impurity spin flipping. Retardation effects of the indirect exchange interaction of the impurity spins via the conduction electrons are found and discussed. Our results point to an alternative way of controlling the local magnetization on a subpicosecond time scale via appropriate tu…

The exact solution of the diffusion trapping model of defect profiling with variable energy positrons

We report an exact analytical solution of so-called positron diffusion trapping model. This model have been widely used for the treatment of the experimental data for defect profiling of the adjoin surface layer using the variable energy positron (VEP) beam technique. Hovewer, up to now this model could be treated only numerically with so-called VEPFIT program. The explicit form of the solutions is obtained for the realistic cases when defect profile is described by a discreet step-like function and continuous exponential-like function. Our solutions allow to derive the analytical expressions for typical positron annihilation characteristics including the positron lifetime spectrum. Latter …

Continuous theory of switching in geometrically confined ferroelectrics

A theory of ferroelectric switching in geometrically confined samples like thin films and multilayers with domain structure has been proposed. For that we use Landau–Khalatnikov (LK) equations with free energy functional being dependent on polarization gradients. In this case, the consistent theory can be developed as for thin ferroelectric films and multilayers the domain structure reduces to Fourier series in ferroelectric polarization. The specific calculations are presented for thin film ferroelectric with dead layers and ferro-/paraelectric multilayer. Our theory is generalizable to ferroelectrics and multiferroics with other geometries.

Two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ inteface with a potential barrier

We present a tight binding description of electronic properties of the interface between LaAlO$_3$ (LAO) and SrTiO$_3$ (STO). The description assumes LAO and STO perovskites as sets of atomic layers in the $x$-$y$ plane, which are weakly coupled by an interlayer hopping term along the $z$ axis. The interface is described by an additional potential, $U_0$, which simulates a planar defect. Physically, the interfacial potential can result from either a mechanical stress at the interface or other structural imperfections. We show that depending on the potential strength, charge carriers (electrons or holes) may form an energy band which is localized at the interface and is within the band gaps …

Photoinduced magnetization wave in diluted magnetic semiconductors

We derive an evolutional equation incorporating the processes of spin-polarization transfer from an electron to a magnetic ion subsystem of a diluted magnetic semiconductor along with spin-lattice relaxation and spatial spin diffusion. Above equation has been obtained for nonequilibrium magnetization due to exchange scattering of photoexcited charge carriers by magnetic ions. We show that the mechanism of a band gap narrowing due to exchange scattering requires relatively low optical power to reach an optical bistability for pump frequency range close to crystal band gap. In a bulk crystal, only relatively small local area with essential magnetization enhancement can absorb optical power, t…

Lévy flights in an infinite potential well as a hypersingular Fredholm problem.

We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schr\"odinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numer…

Highly Correlated Fermi Liquid in Heavy-Fermion Metals: Magnetic Properties

In this chapter we show how the FCQPT theory works, when describing the behavior of HF metals under the application of magnetic field. We show that a large body of experimental data regarding the thermodynamic, transport and relaxation properties collected in measurements on HF metals can be well explained. It is demonstrated that the experimental data exhibit the scaling behavior.

Properties of Thin Ferroelectric Film with Different Electrodes

The influence of different metallic and semiconducting electrodes on the properties of thin ferroelectric films is considered within the framework of the phenomenological Ginzburg-Landau theory. Allowing for the effect of charge screening in metals and semiconductors, the contribution of electric field produced by charges in the electrodes is included into the functional of free energy and, hence, to the Euler-Lagrange equation for film polarization. Application of variational method to this equation solution permitted the transformation of the free energy functional into a conventional type free energy with a renormalized coefficient before P 2 , the coefficient being dependent on the both…

Quantum critical point in high-temperature superconductors

Recently, in high-T_c superconductors (HTSC), exciting measurements have been performed revealing their physics in superconducting and pseudogap states and in normal one induced by the application of magnetic field, when the transition from non-Fermi liquid to Landau Fermi liquid behavior occurs. We employ a theory, based on fermion condensation quantum phase transition which is able to explain facts obtained in the measurements. We also show, that in spite of very different microscopic nature of HTSC, heavy-fermion metals and 2D 3He, the physical properties of these three classes of substances are similar to each other.

The Peculiar Physical Properties of Nanosized Ferroics (Nanoferroics)

This Chapter contains the experimental facts about size effects in nanoferroics. They include ferroelectric, ferroelastic, magnetic and multiferroic nanostructured materials. The main peculiar feature of nanoferroics is the geometric confinement originating from their surfaces and interfaces. This is in contrast to the ordinary bulk ferroics, where the sample surface plays a minor role. In particular, in nanoferroics, the surface generates the physical properties gradients in the normal (to the surface) direction. This fact yields strong size effects and spatial inhomogeneity of the nanoferroics properties, which should be taken into account to get their adequate physical description. We re…

Macroscopic description of the two-dimensionalLaAlO3/SrTiO3interface

We propose a simple analytical model to explain the possible appearance of the metallic conductivity in the two-dimensional (2D) ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ interface. Our model considers the interface within a macroscopic approach, which is usual for semiconductor heterojunctions and is based on drift-diffusion equations. The solution of these equations allows us to obtain the positions of band edges as a function of distances from the interface. We show that for the 2D metallic conductivity to appear at the interface, the constituting substances should have the same type (either electronic or hole) of conductivity; in the opposite case the possible transition to metallic p…

Theory of Heavy-Fermion Compounds : Theory of Strongly Correlated Fermi-Systems

Domain-Enhanced Interlayer Coupling in Ferroelectric/Paraelectric Superlattices

We investigate the ferroelectric phase transition and domain formation in a periodic superlattice consisting of alternate ferroelectric (FE) and paraelectric (PE) layers of nanometric thickness. We find that the polarization domains formed in the different FE layers can interact with each other via the PE layers. By coupling the electrostatic equations with those obtained by minimizing the Ginzburg-Landau functional we calculate the critical temperature of transition Tc as a function of the FE/PE superlattice wavelength and quantitatively explain the recent experimental observation of a thickness dependence of the ferroelectric transition temperature in KTaO3/KNbO3 strained-layer superlatti…

Landau Fermi Liquid Theory and Beyond

In this chapter we consider the Landau theory of the Fermi liquid that has a long history and remarkable results in describing a numerous properties of the electron liquid in ordinary metals and Fermi liquids of the \(^3\)He type. The theory is based on the assumption that elementary excitations determine the physics at low temperatures, resembling that of weakly interacting Fermi gas. These excitations behave as quasiparticles with a certain effective mass. The effective mass \(M^*\) exhibits a simple universal behavior, for it is independent of the temperature, pressure, and magnetic field strength and is a parameter of the theory. Microscopically deriving the equation determining the eff…

True Nanoferroics with the Properties Absent in Corresponding Bulk Samples

The Chapter covers the theoretical and experimental approaches to the investigations of the physical properties, which are inherent in ferroics of nanosize and absent in corresponding bulk materials. Namely, the strong surface influence along with other effects of geometrical confinement generates number of physical effects, which do not occur in bulk ferroics samples. One example of such phenomena is room-temperature ferromagnetism in nanoparticles and thin films of undoped CeO2, HfO2, SnO2, Al2O3 and other nonmagnetic (in bulk samples) oxides. Theo other striking example is appearance of so-called spontaneous flexoeffects (i.e. flexoelectric, flexomagnetic, flexoelastic) in ferroic nanosa…

Quantum Criticality of Heavy-Fermion Compounds

Chapter 17 is devoted to the quantum criticality of quantum spin liquids. In this chapter we continue to consider the nature of quantum criticality in HF compounds. The quantum criticality induced by the fermion condensation quantum phase transition extends over a wide range in the \(T-B\) phase diagram. As we shall see, the quantum criticality in all such different HF compounds, as high-\(T_c\) superconductors, HF metals, compounds with quantum spin liquids, quasicrystals, and 2D quantum liquids, is of the same nature. This challenging similarity between different HF compounds expresses universal physics that transcends the microscopic details of the compounds. This uniform behavior, induc…

The depolarization field effect on the thin ferroelectric films properties

Abstract The calculation of the spontaneous polarization (Ps), dielectric susceptibility (χ) and pyroelectric coefficient (Π) of the ferroelectric films has been performed in the phenomenological theory framework. Euler–Lagrange equation was solved analytically under the boundary conditions with different extrapolation lengths at two surfaces, respectively. The depolarization field contribution was taken into account in the model of short-circuited mono domain ferroelectric film, treated as perfect insulator. The detailed analysis of the aforementioned quantities’ space distribution and their average values in two cases with and without depolarization field was carried out. It was shown tha…

Universal behavior of two-dimensional 3He at low temperatures.

On the example of two-dimensional (2D) 3He we demonstrate that the main universal features of its experimental temperature T - density x phase diagram [see M. Neumann, J. Ny\'{e}ki, J. Saunders, Science 317, 1356 (2007)] look like those in the heavy-fermion metals. Our comprehensive theoretical analysis of experimental situation in 2D 3He allows us to propose a simple expression for effective mass M^*(T,x), describing all diverse experimental facts in 2D 3He in unified manner and demonstrating that the universal behavior of M^*(T,x) coincides with that observed in HF metals.

Depolarization Field and Properties of Thin Ferroelectric Films with Inclusion of the Electrode Effect

The influence of metallic electrodes on the properties of thin ferroelectric films is considered in the framework of the Ginzburg-Landau phenomenological theory. The contribution of the electrodes with different screening lengths l s of carriers in the electrode material is included in the free-energy functional. The critical temperature T cl , the critical thickness of the film, and the critical screening length of the electrode at which the ferroelectric phase transforms into the paraelectric phase are calculated. The Euler-Lagrange equation for the polarization P is solved by the direct variational method. The results demonstrate that the film properties can be calculated by minimizing t…

Theoretical Description of Primary Nanoferroics. Comparison of the Theory with Experiment

This Chapter is devoted primarily to the theoretical description of the physical properties of nanoferroics. The theoretical approach that has been successful in describing the size- and shape-dependent effects observed experimentally in nanoferroics is Landau – Ginzburg – Devonshire phenomenological theory, operating on nanoferroics symmetry and order parameters. Our analysis of this theory applicability shows that it can be safely applied down to the sample sizes of few nanometers. The main peculiarity of theoretical description of nanoferroics is that the boundary conditions and terms containing gradients of order parameters cannot be omitted and play the vital role in the description of…

Role of quasiparticles in universal low-temperature properties of

Abstract We demonstrate that the main universal features of the low temperature magnetic field-temperature experimental phase diagram of CeCoIn 5 and other heavy-fermion metals can be well explained within the concept of quasiparticles and fermion condensation quantum phase transition. We analyze dynamic conductance recently obtained in measurements on CeCoIn 5 and show that the particle–hole symmetry is violated in this metal making dynamic conductance asymmetric as a function of applied voltage V .

Time-resolved buildup of twisted indirect exchange interaction in two-dimensional systems

We study theoretically the time-domain dynamics of the spin-dependent Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between driven magnetic impurities localized in a spin-orbit-coupled two-dimensional system. Particular attention is given to the influence of the spin-orbit coupling (SOC) on the system's dynamical response to a time-dependent precessional motion of the localized magnetic moment. We show that, via the RKKY mechanism, a flip of the spin $z$ component of one localized moment affects all $x,\phantom{\rule{4pt}{0ex}}y$, and $z$ spin components of the other localized moment. The Friedel oscillations and the transient spin current triggered by the time-varying localized spin dep…

FERMION CONDENSATION, T -LINEAR RESISTIVITY AND PLANCKIAN LIMIT

We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT). We emphasize that so - called Planckian limit, widely used to explain the above universal scatteri…

Quasiparticles and quantum phase transition in universal low-temperature properties of heavy-fermion metals

We demonstrate, that the main universal features of the low temperature experimental $H-T$ phase diagram of CeCoIn5 and other heavy-fermion metals can be well explained using Landau paradigm of quasiparticles. The main point of our theory is that above quasiparticles form so-called fermion-condensate state, achieved by a fermion condensation quantum phase transition (FCQPT). When a heavy fermion liquid undergoes FCQPT, the fluctuations accompanying above quantum critical point are strongly suppressed and cannot destroy the quasiparticles. The comparison of our theoretical results with experimental data on CeCoIn5 have shown that the electronic system of above substance provides a unique opp…

The influence of intergranular interaction on the magnetization of the ensemble of oriented Stoner-Wohlfarth nanoparticles

We consider the influence of interparticle interaction on the magnetization reversal in the oriented Stoner-Wohlfarth nanoparticles ensemble. To do so, we solve a kinetic equation for the relaxation of the overall ensemble magnetization to its equilibrium value in some effective mean field. Latter field consists of external magnetic field and interaction mean field proportional to the instantaneous value of above magnetization. We show that the interparticle interaction influences the temperature dependence of a coercive field. This influence manifests itself in the noticeable coercivity at $T>T_{b}$ ($T_{b}$ is so-called blocking temperature). The above interaction can also lead to a forma…

Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling

We demonstrate that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, we study the conditions of chaos emergence and report the dynamics both in the regular and chaotic regimes. {We observe the critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions …

Suppression of carrier induced ferromagnetism by composition and spin fluctuations in diluted magnetic semiconductors

We suggest an approach to account for spatial (composition) and thermal fluctuations in "disordered" magnetic models (e.g. Heisenberg, Ising) with given spatial dependence of magnetic spin-spin interaction. Our approach is based on introduction of fluctuating molecular field (rather than mean field) acting between the spins. The distribution function of the above field is derived self-consistently. In general case this function is not Gaussian, latter asymptotics occurs only at sufficiently large spins (magnetic ions) concentrations $n_i$. Our approach permits to derive the equation for a critical temperature $T_c$ of ferromagnetic phase transition with respect to the above fluctuations. We…

Spontaneous magnon decays in planar ferromagnet

We predict that spin-waves in an easy-plane ferromagnet have a finite lifetime at zero temperature due to spontaneous decays. In zero field the damping is determined by three-magnon decay processes, whereas decays in the two-particle channel dominate in a transverse magnetic field. Explicit calculations of the magnon damping are performed in the framework of the spin-wave theory for the $XXZ$ square-lattice ferromagnet with an anisotropy parameter $\lambda<1$. In zero magnetic field the decays occur for $\lambda^*<\lambda<1$ with $\lambda^*\approx 1/7$. We also discuss possibility of experimental observation of the predicted effect in a number of ferromagnetic insulators.

Asymmetric Conductivity of Strongly Correlated Compounds

In this chapter, we show that the FC solutions for distribution function \(n_0(\mathbf{p})\) generate NFL behavior, and violate the particle-hole symmetry inherent in LFL. This, in turn, yields dramatic changes in transport properties of HF metals, particularly, the differential conductivity becomes asymmetric. As it is demonstrated in Sect. 3.1, Fermi quasiparticles can behave as Bose one. Such a state is viewed as possessing the supersymmetry (SUSY) that interchanges bosons and fermions eliminating the difference between them. In the case of asymmetrical conductivity it is the emerging SUSY that violates the time invariance symmetry. Thus, restoring one important symmetry, the FC state vi…

Exact and Variational Treatment of Ferroelectric Thin Films with Different Materials of Electrodes

We trace the influence of metallic electrodes on the properties of thin ferroelectric films. This has been done in the framework of the phenomenological Landau theory. We present both exact analytical solution of the problem in terms of Weierstrass elliptic functions and the variational solution. We calculate polarization, dielectric susceptibility, pyroelectric coefficient and depolarization field. We have shown that the ferroelectric phase of the film can be destroyed by the choice of material of electrodes with screening length exceeding some critical value. This demonstrates that we can control the physical properties of thin ferroelectric films by the proper choice of the electrode mat…

The influence of quantum fluctuations on phase transition temperature in disordered ferroelectrics

We consider the disordered ferroelectric, where the impurity dipoles interact via quantum optical phonons. We show that quantum fluctuations are amplified by the effects of disorder so that they can be important up to the ferroelectric phase transition temperature. In this paper, we calculate the ferroelectric phase transition temperature as a function of impurity dipole concentration. We show that quantum effects change the character of concentrational dependence of . Namely, they cause the discontinuity in so that the critical concentration is reached abruptly. We have shown that quantum effects inhibit the ferroelectricity so that larger (than that in purely classical disordered ferroele…

Superspin glass phase and hierarchy of interactions in multiferroic PbFe1/2Sb1/2O3: an analog of ferroelectric relaxors?

We have fabricated new perovskite multiferroic PbFeSbO3 with a high degree (up to 0.9) of chemical ordering and unexpectedly high-temperature magnetic relaxor properties, which can barely be described within concepts of conventional spin glass physics. Notably, we found that the field-temperature phase diagram of this material, in the extremely wide temperature interval, contains the de Almeida–Thouless-type critical line, which has been the subject of long debates regarding its possible experimental realization. We explain our findings by the creation, at high temperatures of not less than 250 K, of giant superspins (SSs), owing, curiously enough, to the antiferromagnetic superexchange int…

&lt;title&gt;Correlation effects in the disordered ferroelectrics&lt;/title&gt;

ABSTRACT The calculation of the correlation radius distribution function is performed for the cases of undamped and overdamped softmode dispersion laws. Taking into account the correlation radius dependence on the random field and this field distribution function we carried out the theoretical calculation of the correlation radius distribution function dependence ontemperature, damping coefficient and random field distribution function parameters. It was shown that at temperaturehigher than Burns temperature Td the most probable value of the correlation radius is equal to its maximal valueindependently on the system disorder, while in the dipole glass state it is close to the minimal value …

Violation of the Wiedemann-Franz Law in HF Metals

Experimental observations of the much-studied compounds CeCoIn\(_5\) and YbRh\(_2\)Si\(_2\) at vanishing temperatures carefully probe the nature of their magnetic-field-tuned QCPs. The violation of Wiedemann-Franz (WF) law, along with jumps revealed both in the residual resistivity \(\rho _0\) and the Hall resistivity \(R_H\), provide vital clues to the origin of their non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with FC forming flat bands.

High Magnetic Fields Thermodynamics of Heavy Fermion Metals

In this chapter, we present the comprehensive theoretical analysis of thermodynamics of HF compounds at high magnetic fields. Such analysis permits to gain a deeper insight into the interplay of high magnetic field and temperature in suppressing and retrieving the Landau Fermi liquid state in these substances. Our analysis shows that although high magnetic fields and temperatures alter the properties of ordinary Landau quasiparticles, they survive, generating the experimentally observable anomalies in the thermodynamical quantities of HF compounds. We illustrate our theoretical findings by the example of the HF compound \(\mathrm{{YbRh_2Si_2}}\).

Lévy flights in confining potentials.

We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are considered: those driven by Langevin equation with L\'{e}vy noise and those, named by us topological L\'{e}vy processes (occurring in systems with topological complexity like folded polymers or complex networks and generically in inhomogeneous media), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary (eventually asymptotic) probability densit…

Heavy-tailed targets and (ab)normal asymptotics in diffusive motion

We investigate temporal behavior of probability density functions (pdfs) of paradigmatic jump-type and continuous processes that, under confining regimes, share common heavy-tailed asymptotic (target) pdfs. Namely, we have shown that under suitable confinement conditions, the ordinary Fokker-Planck equation may generate non-Gaussian heavy-tailed pdfs (like e.g. Cauchy or more general L\'evy stable distribution) in its long time asymptotics. For diffusion-type processes, our main focus is on their transient regimes and specifically the crossover features, when initially infinite number of the pdf moments drops down to a few or none at all. The time-dependence of the variance (if in existence…

Thermalization of Random Motion in Weakly Confining Potentials

We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approa…

On the theory of domain switching kinetics in ferroelectrics

Abstract We investigate theoretically the polarization switching kinetics in ferroelectrics, both bulk and thin films samples. In such substances, the domain walls are pinned by (usually dipole) defects, which are present also in ordered samples as technologically unavoidable impurities. This random interaction with dipole pinning centers results, in particular, in exponentially broad distribution of switching times. Under supposition of low pinning centers concentration, we derive the distribution function of switching times showing that it is not simply Lorentzian (as it was first suggested by Tagantsev et al. [Phys. Rev. B 66 (2002) 214109]), but is a “square of Lorentzian”, which is due…

Asymmetric Tunneling Conductance and the non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the nonFermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau– Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V . This is because the particle-hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle-hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V . Th…

The influence of disorder on the exciton spectra in two-dimensional structures

We study the role of disorder in the exciton spectra in two-dimensional (2D) semiconductors. These can be heterostructures, thin films and multilayers (so-called van der Waals structures) of organometallic perovskites, transition metal dichalcogenides and other semiconductors for optoelectronic applications. We model the disorder by introduction of a fractional Laplacian (with Le´vy index m, defining the degree of disorder) to the Scro¨dinger equation with 2D Coulomb potential. Combining analytical and numerical methods, we observe that the exciton exists only for m 4 1, while the point m = 1 (strongest disorder) corresponds to the exciton collapse. We show also that in the fractional (diso…

Conductivity of the two-dimensional electron gas atLaAlO3/SrTiO3interface

We propose an analytical theory of metallic conductivity in the two-dimensional (2D) ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ (LAO/STO) interface. For that we consider the electron-phonon interaction at the interface. The electronic part is taken from our previous work [Phys. Chem. Chem. Phys. 18, 2104 (2016)], considering the conditions for the interfacial charge carrier (electron or hole) to become itinerant. The second ingredient deals with the atomic oscillations localized near the interface and decaying rapidly at its both sides, which can be regarded as 2D acoustic phonons. The dispersion of such phonons depends on the characteristics of phonon spectra of LAO and STO. Calculating t…

Ultrarelativistic (Cauchy) spectral problem in the infinite well

We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$ and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of $|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while passing from $R$ to a bounded spatial domain $D\subset R$.

Metals with a Strongly Correlated Electron Liquid

In this chapter, we consider the main properties of strongly correlated Fermi systems, which are formed by the fermion condensate leading to the emergence of flat bands. Namely, we consider the residual entropy \(S_0\) related to the flat bands that leads to the violation of the quasiparticle—hole symmetry. The presence of \(S_0\) has a profound impact on the universality of second order phase transitions. In that case under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point, thus leading to a violation of the critical universality of the fluctuation theory. We demonstrate that a jump in t…

Flat Bands and Salient Experimental Features Supporting the Fermion Condensation Theory of Strongly Correlated Fermi

The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence…

The Lineshape of Inelastic Neutron Scattering in Relaxor Ferroelectrics

We show that a microscopic reason for the steep drop of the optical phonon branch into an acoustic one (the so-called waterfall effect) in relaxor ferroelectrics may be the coupling of phonons with defects and impurities of different kinds, which is always present in relaxors. Namely, we do not specify the type of impurities but rather represent them as an ensemble of so-called two-level systems (TLS). This approach makes it possible to trace the evolution of the “waterfall” with temperature and the TLS concentration. To facilitate the planning of experiments on inelastic neutron scattering, we present a modification of the so-called Latin hypercube sampling method, which, based on some sig…

Magnetoelectric effect in antiferromagnetic multiferroic Pb(Fe1/2Nb1/2)O3 and its solid solutions with PbTiO3

Antiferromagnets (AFMs) are presently considered as promising materials for applications in spintronics and random access memories due to the robustness of information stored in the AFM state against perturbing magnetic fields. In this respect, AFM multiferroics may be attractive alternatives for conventional AFMs as the coupling of magnetism with ferroelectricity (magnetoelectric effect) offers an elegant possibility of electric-field control and switching of AFM domains. Here we report the results of comprehensive experimental and theoretical investigations of the quadratic magnetoelectric (ME) effect in single crystals and highly resistive ceramics of $\mathrm{Pb}(\mathrm{F}{\mathrm{e}}_…

Levy targeting and the principle of detailed balance

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …

Thickness Dependence of Random Field Distribution in Thin Films Made of Disordered Ferroelectrics

Abstract We present the calculation of first moment E 0 and variance ΔE of distribution function of random fields in a ferroelectric of finite size. Specific calculations have been performed for the case of slab-shaped ferroelectric thin film. We have shown that E 0 and ΔE can be expressed through the integrals from first and second degree of Green's function of ferroelectric in k-space. To obtain the Green's function, we solve the differential equation minimizing Landau free energy of a ferroelectric with respect to the boundary conditions on its surfaces. We show that both E 0 and ΔE depend on film thickness L.

Highly Correlated Fermi Liquid in Heavy-Fermion Metals: The Scaling Behavior

In this chapter we show how the FCQPT theory works. We do that on the base of experimentally relevant examples. Namely, as noted in the Introduction (Chap. 1), the challenge for the theories is to explain the scaling behavior of the normalized effective mass \(M^*_N(y)\) displayed in Fig. 1.3. The theories analyzing only the critical exponents characterizing \(M^*_N(y)\) at \(y\gg 1\) consider only a part of the problem. In this section we analyze and derive the scaling behavior of the normalized effective mass near QCP as reported in Fig. 1.3. We start with describing magnetic field dependence of the quasiparticle effective mass in Sect. 6.1. Quasiparticle damping and the temperature depen…

Size effects of static and dynamic polarization in ferroelectric thin film multilayers

Abstract A thermodynamic theory for the calculation of static and dynamic polarization profiles of ferroelectric thin film multilayers is developed. The free energy functional is written down using a multilayer model in which c-domain layers of the ferroelectric material alternate with a-domain layers of a second ferroelectric materials. We assume that the interfaces are perfectly sharp and that the polarization at these boundaries is zero. The equilibrium polarization profile, its temperature and thickness dependencies were determined from the solutions of the Euler-Lagrange equations. A thickness induced ferroelectric phase transition is shown to exist and its transition temperature and c…

Physical properties of ferroelectric film with continuous space charge distribution

We present a theory of ferroelectric phase transitions in a film with a homogeneously distributed space charge leading to the so-called built-in polarization. On the base of our complete solution of the problem of continuous space charge distribution in a ferroelectric film, we calculate the ferroelectric phase transition temperature , spatial polarization distribution in paraelectric and ferroelectric phases as well as hysteresis loop in the ferroelectric phase. We have shown that the presence of continuous space charge in a film inhibits the ferroelectricity in it: it lowers the ferroelectric phase transition temperature and coercive field. Our estimates of these differences show that the…

Quasi-classical Physics Within Quantum Criticality in HF Compounds

In this chapter, we explore how the fermion condensation paves the road for quasi-classical physics in HF compounds. This means simply that systems with FC admit partly the quasi-classical description of their thermodynamic and transport properties. This, in turn, simplifies a lot not only of their description but permits to gain more insights both in the puzzling NFL physics of HF compounds and of the physics of FC itself. The quasi-classical physics starts to be applicable near FCQPT, at which FC generates flat bands and quantum criticality, and makes the density of electron states in strongly correlated metals diverge. As we shall see, due to the formation of flat bands the strongly corr…

Free Charge Carriers in Mixed Valency Oxides as Possible Mediators of Magnetoelectric Effect

We show, that in a substance with mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperatures. The origin of the effect is that free charge carriers can mediate the multiferroic behavior via spin – spin (RKKY), dipole-dipole and dipole - spin interactions. We show that there is an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of RKKY interaction. Our analysis shows that disorder and finite conductivity in the above substances does not suppress multiferroic effects.

Trajectory Statistics of Confined L\'evy Flights and Boltzmann-type Equilibria

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of t…

Confinement of Lévy flights in a parabolic potential and fractional quantum oscillator

We study L\'evy flights confined in a parabolic potential. This has to do with a fractional generalization of an ordinary quantum-mechanical oscillator problem. To solve the spectral problem for the fractional quantum oscillator, we pass to the momentum space, where we apply the variational method. This permits one to obtain approximate analytical expressions for eigenvalues and eigenfunctions with very good accuracy. The latter fact has been checked by a numerical solution to the problem. We point to the realistic physical systems ranging from multiferroics and oxide heterostructures to quantum chaotic excitons, where obtained results can be used.

Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes

We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function $\rho (x,t)$. Our main goal is to demonstrate a compatibility of a {\it direct} solution method (an explicit, albeit numerically assisted, integration of the master equation) with an {\it indirect} path-wise procedure, recently proposed in [Physica {\bf A 392}, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large…

Identification of strongly correlated spin liquid in herbertsmithite

Exotic quantum spin liquid (QSL) is formed with such hypothetic particles as fermionic spinons carrying spin 1/2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental properties of QSL, forming strongly correlated Fermi system located at a fermion condensation quantum phase transition. These are in a good agreement with experimental data and allow us to detect the behavior of QSL as that observed in heavy fermion metals. We predict that the thermal resistivity of QSL under the application of magnetic fields at fixed temperature demonstrates a very specific behavior. The key features of our findings are the presence of spin-char…

Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: a review

The exotic substances have exotic properties. One class of such substances is geometrically frustrated magnets, where correlated spins reside in the sites of triangular or kagome lattice. In some cases, such magnet would not have long-range magnetic order. Rather, its spins tend to form kind of pairs, called valence bonds. At $$T \rightarrow 0$$ these highly entangled quantum objects condense in the form of a liquid, called quantum spin liquid (QSL). The observation of a gapless QSL in actual materials is of fundamental significance both theoretically and technologically, as it could open a path to creation of topologically protected states for quantum information processing and computation…

Magnetoresistance in the HF Metal at Zero Temperature

In this chapter we consider the paradoxical behavior of the residual resistivity \(\rho _0\) of HF metals in magnetic fields and under pressure. Our consideration is based on the idea of flattening of the single-particle spectrum \(\varepsilon (\mathbf{p})\) that profoundly effects on the specific heat \(C\), thermal expansion coefficient \(\alpha \) and magnetic susceptibility \(\chi \) in the normal state, the jump of \(C\) at the point of superconducting phase transition etc. We show that FC associated with flat bands contributes to the residual resistivity \(\rho _0\), while the application of the magnetic field or pressure to the system with a flat band removes the flat band and leads …

Chaotization of internal motion of excitons in ultrathin layers by spin–orbit coupling

We show that Rashba spin-orbit coupling (SOC) can generate chaotic behavior of excitons in two-dimensional semiconductor structures. To model this chaos, we study a Kepler system with spin-orbit coupling and numerically obtain a transition to chaos at a sufficiently strong coupling. The chaos emerges since the SOC reduces the number of integrals of motion as compared to the number of degrees of freedom. Dynamically, the dependence of the exciton energy on the spin orientation in the presence of SOC produces an anomalous spin-dependent velocity resulting in chaotic motion. We observe numerically the critical dependence of the dynamics on the initial conditions, where the system can return to…

The peculiarities of the phase diagram of heavy fermion metal CeCoIn5

We analyze the low temperature experimental magnetic field–temperature H–T phase diagram of CeCoIn5. We demonstrate that its main features can be well explained within Landau quasiparticle picture incorporating the fact that quasiparticles form so-called fermion-condensate (FC) state emerging behind the fermion condensation quantum phase transition (FCQPT). We show that near FCQPT, the fluctuations are strongly suppressed while FC by itself is “protected” from above fluctuations by the first order phase transition. We demonstrate that the electronic system of CeCoIn5 can be shifted from the ordered towards disordered side of FCQPT by the application of magnetic field therefore giving a uniq…

Quantum critical point in ferromagnet

Abstract The heavy-fermion metal CePd 1 - x Rh x can be tuned from ferromagnetism at x = 0 to non-magnetic state at the critical concentration x c . The non-Fermi liquid behavior at x ≃ x c is recognized by power law dependence of the specific heat C ( T ) given by the electronic contribution, susceptibility χ ( T ) and volume expansion coefficient α ( T ) at low temperatures: C / T ∝ χ ( T ) ∝ α ( T ) / T ∝ 1 / T . We show that this alloy exhibits a universal thermodynamic non-Fermi liquid behavior independent of magnetic ground state. This can be well understood utilizing the quasiparticle picture and the concept of fermion condensation quantum phase transition at the density ρ = p F 3 / …

Fermion Condensation in Finite Systems

Here we consider another example of systems, in which fermion condensation takes place. These are what is called finite Fermi systems, i.e. systems with finite number of fermions, contrary to a solid, where the number of electrons is practically infinite. An example of a finite Fermi system is an atomic nucleus, having finite number of nucleons, protons and neutrons, which are fermions. Here we show that the fermion condensation manifests itself in finite Fermi systems as a forced merger of all, discreet for finite systems, single-particle levels, lying near the Fermi surface. On the first sight, this merger contradicts the standard Landau quasiparticle picture. Nevertheless, similar to inf…

New state of matter: heavy-fermion systems, quantum spin liquids, quasicrystals, cold gases, and high temperature superconductors

We report on a new state of matter manifested by strongly correlated Fermi systems including various heavy-fermion (HF) metals, two-dimensional quantum liquids such as $\rm ^3He$ films, certain quasicrystals, and systems behaving as quantum spin liquids. Generically, these systems can be viewed as HF systems or HF compounds, in that they exhibit typical behavior of HF metals. At zero temperature, such systems can experience a so-called fermion-condensation quantum phase transition (FCQPT). Combining analytical considerations with arguments based entirely on experimental grounds we argue and demonstrate that the class of HF systems is characterized by universal scaling behavior of their ther…

Zero Temperature Magnetoresistance of the HF Metal: Enigma of $$\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}$$

To understand the nature of field-tuned metamagnetic quantum criticality in the ruthenate \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) is one of the significant challenges in the condensed matter physics. It is established experimentally that the entropy has a peak in the ordered phase. It is unexpectedly higher than that outside latter phase, while the magnetoresistivity varies abruptly near the ordered phase boundary. We demonstrate unexpected similarity between \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) and HF metals expressing universal physics that transcends microscopic details. Our \(T-B\) phase diagram of \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) explains main featu…

Fermi Liquid with Fermion Condensate

Here we discuss the general properties of FCQPT leading to the emergence of FC. We present a microscopic derivation of the main equations of FC, and show that Fermi systems with FC form an entirely new class of Fermi liquids with its own topological structure, protecting the FC state. We construct the phase diagram, and explore the order parameter of these systems. We show that the fermion condensate has a strong impact on the observable physical properties of systems, where it is realized, up to relatively high temperatures of a few tens kelvin. Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state, related to the divergence of the …

Carrier-induced ferromagnetism in two-dimensional magnetically doped semiconductor structures

We show theoretically that the magnetic ions, randomly distributed in a two-dimensional (2D) semiconductor system, can generate a ferromagnetic long-range order via the RKKY interaction. The main physical reason is the discrete (rather than continuous) symmetry of the 2D Ising model of the spin-spin interaction mediated by the spin-orbit coupling of 2D free carriers, which precludes the validity of the Mermin-Wagner theorem. Further, the analysis clearly illustrates the crucial role of the molecular field fluctuations as opposed to the mean field. The developed theoretical model describes the desired magnetization and phase-transition temperature ${T}_{c}$ in terms of a single parameter, na…

Lévy distributions and disorder in excitonic spectra.

We study analytically the spectrum of excitons in disordered semiconductors like transition metal dichalcogenides, which are important for photovoltaic and spintronic applications. We show that ambient disorder exerts a strong influence on the exciton spectra. For example, in such a case, the wellknown degeneracy of the hydrogenic problem (related to Runge–Lenz vector conservation) is lifted so that the exciton energy starts to depend on both the principal quantum number n and orbital l. We model the disorder phenomenologically substituting the ordinary Laplacian in the corresponding Schro¨dinger equation by the fractional one with Le´vy index m, characterizing the degree of disorder. Our v…

Heavy fermion spin liquid in herbertsmithite

We analyze recent heat capacity measurements in herbertsmithite $\rm ZnCu_3(OH)_6Cl_2$ single crystal samples subjected to strong magnetic fields. We show that the temperature dependence of specific heat $C_{mag}$ formed by quantum spin liquid at different magnetic fields $B$ resembles the electronic heat capacity $C_{el}$ of the HF metal $\rm YbRh_2Si_2$. We demonstrate that the spinon effective mass $M^*_{mag}\propto C_{mag}/T$ exhibits a scaling behavior like that of $C_{el}/T$. We also show that the recent measurements of $C_{mag}$ are compatible with those obtained on powder samples. These observations allow us to conclude that $\rm ZnCu_3(OH)_6Cl_2$ holds a stable strongly correlated …

Quasi-one-dimensional quantum spin liquid in the $\rm {Cu(C_4H_4N_2)(NO_3)_2}$ insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-one dimensional insulator Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic $T-H$ (temperature---magnetic field…

Experimental Manifestations of Fermion Condensation in Strongly Correlated Fermi Systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which the Landau–Fermi liquid theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle– hole (C) invariance. Here we consider two most recent experimental puzzles, which cannot be explained neither within the Landau–Fermi liquid picture nor can they be made intelligible by the approaches like the Hubbard model and/or the Kondo effect, which are commonly used to spell out the typical non-Fermi-liquid behavior. The first experimental puzzle is the asymmetric (with…

Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite

We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transiti…

Magnetic quantum criticality in quasi-one-dimensional Heisenberg antiferromagnet Cu (C4H4N2)( NO 3)2

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C4H4N2)(NO3)2 (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so-called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitativ…

Depolarization Field in Thin Ferroelectric Films With Account of Semiconductor Electrodes

Within the framework of the phenomenological Ginzburg-Landau theory influence of semiconductor electrodes on the properties of thin ferroelectric films is considered. The contribution of the semiconductor electrodes with different Debye screening length of carriers is included in the functional of free energy. The influence of highly doped semiconductor electrodes on the depolarization field and the film properties was shown to be great.

Appearance of Fermion-Condensation Quantum Phase Transition in Fermi Systems

As high-\(T_c\) superconductors are represented primarily by 2D layered structures, in Sect. 5.1 we discuss the superconducting state of a 2D liquid of heavy electrons, and within the framework of Gor’kov microscopic equations construct the Green functions of the FC state. On the other hand, our study can easily be generalized to the 3D case. To show that there is no fundamental difference between the 2D and 3D cases, we derive Green’s functions for the 3D case in Sect. 5.1.1. In Sect. 5.2, we consider the dispersion law and lineshape of single-particle excitations. Section 5.3 is devoted to the behavior of heavy-electron liquid with FC in magnetic field. In Sect. 5.4, we analyze conditions…

Chemical disorder and Pb207 hyperfine fields in the magnetoelectric multiferroic Pb(Fe1/2Sb1/2)O3 and its solid solution with Pb(Fe1/2Nb1/2)O3

We report on the results of magnetic susceptibility, electron paramagnetic resonance, and $^{207}\mathrm{Pb}$ nuclear magnetic resonance (NMR) studies of the magnetoelectric multiferroic $\mathrm{Pb}(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{S}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ (PFS) ceramic, as well as its solid solution with $\mathrm{Pb}(\mathrm{F}{\mathrm{e}}_{1/2}\mathrm{N}{\mathrm{b}}_{1/2}){\mathrm{O}}_{3}$ (PFN) of different degrees of the 1:1 ordering of magnetic $\mathrm{F}{\mathrm{e}}^{3+}$ and nonmagnetic $\mathrm{S}{\mathrm{b}}^{5+}$ ions. The ordering has been studied by x-ray diffraction (XRD) and NMR methods. In particular, two spectral lines, originating from the ordered and dis…

Tetragonal tungsten bronze compounds: relaxor versus mixed ferroelectric-dipole glass behavior.

We demonstrate that recent experimental data (E. Castel et al J.Phys. Cond. Mat. {\bf 21} (2009), 452201) on tungsten bronze compound (TBC) Ba$_2$Pr$_x$Nd$_{1-x}$FeNb$_4$O$_{15}$ can be well explained in our model predicting a crossover from ferroelectric ($x=0$) to orientational (dipole) glass ($x=1$), rather then relaxor, behavior. We show, that since a "classical" perovskite relaxor like Pb(Mn$_{1/3}$ Nb$_{2/3}$)O$_3$ is never a ferroelectric, the presence of ferroelectric hysteresis loops in TBC shows that this substance actually transits from ferroelectric to orientational glass phase with $x$ growth. To describe the above crossover theoretically, we use the simple replica-symmetric so…

L\'{e}vy flights in inhomogeneous environments

We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It turns out that the semigroup modeling provides much stronger confining properties than the standard Langevin one. Since contractive semigroups set a link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian systems, we can use the latter to control the long - time asymptotics of the pertinent pdfs. To do so, we need to impose suitable restrictions upon the Hamiltonian and its potential. That provides verifiable criteria for an invarian…

Quantum Criticality of Spin Liquids in Novel Insulators and Magnets

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still under consideration. Quantum spin liquids are a promising new phases, where exotic quantum states of matter could be realized. Exotic quantum spin liquid (QSL) made of such hypothetic particles as fermionic spinons which carry spin \(1/2\) and no charge are considered in this chapter. Magnetic insulators with geometrical frustration produce important experimental facts shedding light on the nature of quantum spin liquid composed of spinons. We present a theory of the thermodynamic properties of quantum spin liquids, elucidating how their properties…

Enhanced ferroelectric phase-transition temperature in perovskite-based solid solutions

We explain how the phenomena of ferroelectric phase transition temperature ${T}_{c}$ enhancement beyond the end members in perovskite solid solution such as $\mathrm{Bi}M{\mathrm{O}}_{3}\text{\ensuremath{-}}{\mathrm{PbTiO}}_{3}$ ($M=\mathrm{Sc}$, In, etc.) is related to nonlinear and spatial correlation effects. The explanation is based on the calculation of ${T}_{c}$ in the framework of our random field theory with additional account for nonlinear effects in the above substances. We show that the maximum of ${T}_{c}$ for certain ${\mathrm{PbTiO}}_{3}$ content takes place when coefficient of nonlinearity is positive, the value of this coefficient is found from best fit between theory and ex…

Griffiths phase manifestation in disordered dielectrics

We predict the existence of Griffith phase in the dielectrics with concentrational crossover between dipole glass (electric analog of spin glass) and ferroelectricity. The peculiar representatives of above substances are $KTaO_3:Li$, $Nb$, $Na$ or relaxor ferroelectrics like $Pb_{1-x}La_xZr_{0.65}Ti_{0.35}O_3$. Since this phase exists above ferroelectric phase transition temperature (but below that temperature for ordered substance), we call it "para-glass phase". We assert that the difference between paraelectric and para-glass phase of above substances is the existence of clusters (inherent to "ordinary" Griffiths phase in Ising magnets) of correlated dipoles. We show that randomness play…