Persistent Currents in Small, Imperfect Hubbard Rings

We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show, that the imperfection, whether localized or not, nearly always decrease, but can also \emph{increase} the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.

Beyond ideal two-dimensional metals: Edges, vacancies, and polarizabilities

Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously…

Electromechanics of graphene spirals

Among the most fascinating nanostructure morphologies are spirals, hybrids of somewhat obscure topology and dimensionality with technologically attractive properties. Here, we investigate mechanical and electromechanical properties of graphene spirals upon elongation by using density-functional tight-binding, continuum elasticity theory, and classical force field molecular dynamics. It turns out that electronic properties are governed by interlayer interactions as opposed to strain effects. The structural behavior is governed by van der Waals interaction: in its absence spirals unfold with equidistant layer spacings, ripple formation at spiral perimeter, and steadily increasing axial force;…

Yliopistofysiikkaa laatuaikaoppimalla : teknologiset työkalut yhteisöllisen tutkivan oppimisen tukena

Understanding the microscopic processes that govern the charge-induced deformation of carbon nanotubes

While carbon nanotubes have technological potential as actuators, the underlying actuation mechanisms remain poorly understood. We calculate charge-induced stresses and strains for electrochemical actuation of carbon nanotubes with different chiralities and defects, using density-functional theory and various tight-binding models. For a given deformation mode the concept of bonding and antibonding orbitals can be redefined depending on the sign of a differential band-structure stress. We use this theoretical framework to analyze orbital contributions to the actuation. These show charge asymmetric behavior which is due to next-nearest-neighbor hopping while Coulombic contributions account fo…

Approximate modeling of spherical membranes

Spherical symmetry is ubiquitous in nature. It is therefore unfortunate that simulation of spherical systems is so hard and require complete spheres with millions of interacting particles. Here, we introduce a method to model spherical systems using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single-layer and multilayer graphene. The method works with any interaction (ab initio, classical interactions), with any approach (mol…

Graphene Cardboard: from Ripples to Tunable Metamaterial

Recently graphene was introduced with tunable ripple texturing, a nanofabric enabled by graphene's remarkable elastic properties. However, one can further envision sandwiching the ripples, thus constructing composite nanomaterial, graphene cardboard. Here the basic mechanical properties of such structures are investigated computationally. It turns out that graphene cardboard is highly tunable material, for its elastic figures of merit vary orders of magnitude, with Poisson ratio tunable from 10 to -0.5 as one example. These trends set a foundation to guide the design and usage of metamaterials made of rippled van der Waals solids.

Atlas for the properties of elemental two-dimensional metals

Common two-dimensional (2D) materials have a layered three-dimensional (3D) structure with covalently bonded, atomically thin layers held together by weak van der Waals forces. However, in a recent transmission electron microscopy experiment, atomically thin 2D patches of iron were discovered inside a graphene nanopore. Motivated by this discovery, we perform a systematic density-functional study on atomically thin elemental 2D metal films, using 45 metals in three lattice structures. Cohesive energies, equilibrium distances, and bulk moduli in 2D are found to be linearly correlated to the corresponding 3D bulk properties, enabling the quick estimation of these values for a given 2D metal a…

Primetime learning: collaborative and technology-enhanced studying with genuine teacher presence.

Background Productive learning processes and good learning outcomes can be attained by applying the basic elements of active learning. The basic elements include fostering discussions and disputations, facing alternative conceptions, and focusing on conceptual understanding. However, in the face of poor course retention and high dropout rates, even learning outcomes can become of secondary importance. To address these challenges, we developed a research-based instructional strategy, the primetime learning model. We devised the model by organizing the basic elements of active learning into a theory-based four-step study process. The model is based on collaborative and technology-enhanced lea…

Growth of two-dimensional Au patches in graphene pores: A density-functional study

Inspired by recent studies of various two-dimensional (2D) metals such as Au, Fe and Ag, we study the growth of two-dimensional gold patches in graphene pores by density-functional theory. We find that at room temperature gold atoms diffuse readily on top of both graphene and two-dimensional gold with energy barriers less than $0.5$ eV. Furthermore, gold atoms move without barriers from the top of graphene to its edge and from the top of 2D gold to its edge. The energy barriers are absent even at the interface of 2D gold and graphene, so that the gold atoms move effortlessly across the interface. We hope our demonstration for the propensity of diffusing gold atoms to grow 2D gold patches in…

Making Graphene Luminescent by Direct Laser Writing

Graphene is not intrinsically luminescent, due to a lack of bandgap, and methods for its creation are tricky for device fabrication. In this study, we create luminescent graphene patterns by a simple direct laser writing method. We analyze the graphene using Raman spectroscopy and find that the laser writing leads to generation of line defects after initial formation of point defects. This Raman data enables us to create a model that explains the luminescence by a formation of small domains due to confinement of graphene by line defects, which is conceptually similar to the mechanism of luminescence in graphene quantum dots. peerReviewed

Electron quantization in arbitrarily shaped gold islands on MgO thin films

Low-temperature scanning tunneling microscopy has been employed to analyze the formation of quantum well states (QWS) in two-dimensional gold islands, containing between 50 and 200 atoms, on MgO thin films. The energy position and symmetry of the eigenstates are revealed from conductance spectroscopy and imaging. The majority of the QWS originates from overlapping Au 6p orbitals in the individual atoms and is unoccupied. Their characteristic is already reproduced with simple particle-in-a-box models that account for the symmetry of the islands (rectangular, triangular, or linear). However, better agreement is achieved when considering the true atomic structure of the aggregates via a densit…

Free-standing 2D metals from binary metal alloys

Recent experiment demonstrated the formation of free-standing Au monolayers by exposing Au-Ag alloy to electron beam irradiation. Inspired by this discovery, we used semi-empirical effective medium theory simulations to investigate monolayer formation in 30 different binary metal alloys composed of late d-series metals Ni, Cu, Pd, Ag, Pt, and Au. In qualitative agreement with the experiment, we find that the beam energy required to dealloy Ag atoms from Au-Ag alloy is smaller than the energy required to break the dealloyed Au monolayer. Our simulations suggest that similar method could also be used to form Au monolayers from Au-Cu alloy and Pt monolayers from Pt-Cu, Pt-Ni, and Pt-Pd alloys.

Electron quantization in arbitrarily shaped Au islands on MgO thin films

Low-temperature scanning tunneling microscopy has been employed to analyze the formation of quantum well states (QWS) in two-dimensional gold islands, containing between 50 and 200 atoms, on MgO thin films. The energy position and symmetry of the eigenstates are revealed from conductance spectroscopy and imaging. The majority of the QWS originates from overlapping Au 6p orbitals in the individual atoms and is unoccupied. Their characteristic is already reproduced with simple particle-in-a-box models that account for the symmetry of the islands (rectangular, triangular, or linear). However, better agreement is achieved when considering the true atomic structure of the aggregates via a densit…

Evidence for Graphene Edges Beyond Zigzag and Armchair

The edges of nanoscopic objects determine most of their properties. For this reason the edges of honeycomb carbon--always considered either zigzag- or armchair-like--need special attention. In this report we provide experimental evidence confirming a previous unexpected prediction: zigzag is a metastable edge, as its planar reconstruction lowers energy and forms the most stable graphene edge. Our evidence is based on re-analyzing a recent experiment. Since the reconstructed edge, along with other unconventional edges we discuss, has distinct chemical properties, this discovery urges for care in experiments and theory--we must enter the realm beyond zigzag and armchair.

Energy spectrum, persistent current and electron localization in quantum rings

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body system can be described with a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the …

Stability limits of elemental 2D metals in graphene pores

Two-dimensional (2D) materials can be used as stabilizing templates for exotic nanostructures, including pore-stabilized, free-standing patches of elemental metal monolayers. Although these patches represent metal clusters under extreme conditions and are thus bound for investigations, they are poorly understood as their energetic stability trends and the most promising elements remain unknown. Here, using density-functional theory simulations and liquid drop model to explore the properties of 45 elemental metal candidates, we identify metals that enable the largest and most stable patches. Simulations show that pores can stabilize patches up to $\sim 8$ nm$^2$ areas and that the most promi…

Correction to “Self-Consistent Charge Density-Functional Tight-Binding Parameterization for Pt–Ru Alloys”

Bright Beaches of Nanoscale Potassium Islands on Graphite in STM Imaging

We demonstrate, via scanning tunneling microscopy (STM) measurements performed at 48 K, the existence of "bright beaches" at the edges of K islands (diameter approximately 5-500 nm) on the graphite surface. The enhanced tunneling current is only observed in monolayer-high islands on graphite, and not in islands of similar geometry on top of a K monolayer film. First-principles density functional calculations and STM simulations suggest that this is an STM field effect, which appears as the positive tip attracts donated electrons back to the metallic K islands. The restored charge accumulates preferentially at the island edges.

The focus and timing of gaze matters : Investigating collaborative knowledge construction in a simulation-based environment by combined video and eye tracking

Although eye tracking has been successfully used in science education research, exploiting its potential in collaborative knowledge construction has remained sporadic. This article presents a novel approach for studying collaborative knowledge construction in a simulation-based environment by combining both the spatial and temporal dimensions of eye-tracking data with video data. For this purpose, we have investigated two undergraduate physics student pairs solving an electrostatics problem in a simulation-based environment via Zoom. The analysis of the video data of the students’ conversations focused on the different collaborative knowledge construction levels (new idea, explication, eval…

What do we do when we analyse the temporal aspects of computer-supported collaborative learning? A systematic literature review

To better understand the premises for successful computer-supported collaborative learning (CSCL), several studies over the last 10 years have analysed the temporal aspects of CSCL. We broadly define the temporal aspects of CSCL as focusing on the characteristics of or interrelations between events over time. The analysis of these aspects, however, has been loosely defined, creating challenges regarding the comparability and commensurability of studies. To address these challenges, we conducted a systematic literature review to define the temporal analysis procedure for CSCL using 78 journal papers published from 2003 to 2019. After identifying the key operations to be included in the proce…

Electronic structure trends of Möbius graphene nanoribbons from minimal-cell simulations

Investigating topological effects in materials requires often the modeling of material systems as a whole. Such modeling restricts system sizes, and makes it hard to extract systematic trends. Here, we investigate the effect of M\"obius topology in the electronic structures of armchair graphene nanoribbons. Using density-functional tight-binding method and minimum-cell simulations through revised periodic boundary conditions, we extract electronic trends merely by changing cells' symmetry operations and respective quantum number samplings. It turns out that for a minimum cell calculation, once geometric and magnetic contributions are ignored, the effect of the global topology is unexpectedl…

The potential of temporal analysis: Combining log data and lag sequential analysis to investigate temporal differences between scaffolded and non-scaffolded group inquiry-based learning processes

This paper contributes to the ongoing discussion about analysing the temporal aspects of learning processes in the educational technology research field. Our main aim was to advance methods for analysing temporal aspects of technology-enhanced learning (TEL) processes by introducing the temporal lag sequential analysis (TLSA) technique and by combining TLSA with temporal log data analysis (TLDA). Our secondary aim was to illustrate the potential of these two analysis techniques to reveal the differences between the face-to-face technology-enhanced collaborative inquiry-based learning (CIBL) processes of three different conditions (non-scaffolded, writing scaffolded and script scaffolded gro…

Fractional Periodicity of Persistent Currents: A Signature of Broken Internal Symmetry

We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin Hamiltonian holds the explanation to this transition. Numerical diagonalizations are performed to show this explicitely. Persistent currents therefore, provide an easy way to experimentally verify broken internal symmetry in electronic systems.

Real-space Wigner-Seitz Cells Imaging of Potassium on Graphite via Elastic Atomic Manipulation

Atomic manipulation in the scanning tunnelling microscopy, conventionally a tool to build nanostructures one atom at a time, is here employed to enable the atomic-scale imaging of a model low-dimensional system. Specifically, we use low-temperature STM to investigate an ultra thin film (4 atomic layers) of potassium created by epitaxial growth on a graphite substrate. The STM images display an unexpected honeycomb feature, which corresponds to a real-space visualization of the Wigner-Seitz cells of the close-packed surface K atoms. Density functional simulations indicate that this behaviour arises from the elastic, tip-induced vertical manipulation of potassium atoms during imaging, i.e. el…

Density-Functional Tight-Binding Simulations of Curvature-Controlled Layer Decoupling and Band-Gap Tuning in Bilayer MoS2

Monolayer transition-metal dichalcogenides (TMDCs) display valley-selective circular dichroism due to the presence of time-reversal symmetry and the absence of inversion symmetry, making them promising candidates for valleytronics. In contrast, in bilayer TMDCs both symmetries are present and these desirable valley-selective properties are lost. Here, by using density-functional tight-binding electronic structure simulations and revised periodic boundary conditions, we show that bending of bilayer MoS2 sheets breaks band degeneracies and localizes states on separate layers due to bendinginduced strain gradients across the sheets. We propose a strategy for employing bending deformations in b…

Optically Forged Diffraction-Unlimited Ripples in Graphene

In nanofabrication, just as in any other craft, the scale of spatial details is limited by the dimensions of the tool at hand. For example, the smallest details for direct laser writing with far-field light are set by the diffraction limit, which is approximately half of the used wavelength. In this work, we overcome this universal assertion by optically forging graphene ripples that show features with dimensions unlimited by diffraction. Thin sheet elasticity simulations suggest that the scaled-down ripples originate from the interplay between substrate adhesion, in-plane strain, and circular symmetry. The optical forging technique thus offers an accurate way to modify and shape two-dimens…

Liquid-liquid phase coexistence in gold clusters. 2D or not 2D?

The thermodynamics of gold cluster anions (${\mathrm{Au}}_{N}^{\ensuremath{-}}$, $N=11,\dots{},14$) is investigated using quantum molecular dynamics. Our simulations suggest that ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ may exhibit a novel, freestanding planar liquid phase which dynamically coexists with a normal three-dimensional liquid. Upon cooling with experimentally realizable cooling rates, the entropy-favored three-dimensional liquid clusters often supercool and solidify into the ``wrong'' dimensionality. This indicates that experimental validation of theoretically predicted ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ ground states might be more complicated than hitherto expected.

Characterizing low-coordinated atoms at the periphery of MgO-supported Au islands using scanning tunneling microscopy and electronic structure calculations

The perimeter of oxide-supported metal particles is suggested to be of pivotal importance for various catalytic processes. To elucidate the underlying effects, the electronic properties of edge and corner atoms of planar Au clusters on MgO/Ag(001) thin films have been analyzed with scanning tunneling microscopy and electronic structure calculations. The low-coordinated perimeter atoms are characterized by a high density of $s$-derived states at the Fermi level. Those states accommodate transfer electrons from the MgO/Ag substrate, which render the perimeter atoms negatively charged. In contrast, the inner atoms of the island are not affected by the charge transfer and remain neutral. This c…

Atlas for the properties of elemental 2D metals

Common two-dimensional (2D) materials have a layered 3D structure with covalently bonded, atomically thin layers held together by weak van der Waals forces. However, in a recent transmission electron microscopy experiment, atomically thin 2D patches of iron were discovered inside a graphene nanopore. Motivated by this discovery, we perform a systematic density-functional study on atomically thin elemental 2D metal films, using 45 metals in three lattice structures. Cohesive energies, equilibrium distances, and bulk moduli in 2D are found to be linearly correlated to the corresponding 3D bulk properties, enabling the quick estimation of these values for a given 2D metal and lattice structure…

Models for quantum dots and rings

Curvature in graphene nanoribbons generates temporally and spatially focused electric currents

Today graphene nanoribbons and other graphene-based nanostructures can be synthesized with atomic precision. But while investigations have concentrated on straight graphene ribbons of fixed crystal orientation, ribbons with intrinsic curvature have remained mainly unexplored. Here, we investigate electronic transport in intrinsically curved graphene nanoribbons coupled to straight leads using two computational approaches. Stationary approach shows how transport gaps are affected both by the straight leads and by the degree of edge asymmetry in the curved ribbons. An advanced time-dependent approach shows that behind the façade of calm stationary transport the currents run violently: curvatu…

A Self-Consistent Charge Density-Functional Tight-Binding Parameterization for Pt-Ru Alloys

We present a self-consistent charge density-functional tight-binding (SCC-DFTB) parametrization for PtRu alloys, which is developed by employing a training set of alloy cluster energies and forces obtained from Kohn–Sham density-functional theory (DFT) calculations. Extensive simulations of a testing set of PtRu alloy nanoclusters show that this SCC-DFTB scheme is capable of capturing cluster formation energies with high accuracy relative to DFT calculations. The new SCC-DFTB parametrization is employed within a genetic algorithm to search for global minima of PtRu clusters in the range of 13–81 atoms and the emergence of Ru-core/Pt-shell structures at intermediate alloy compositions, consi…

Exploring the graphene edges with coherent electron focusing

We study theoretically the coherent electron focusing in graphene nanoribbons. Using semiclassical and numerical tight binding calculations we show that perfect armchair edges give rise to equidistant peaks in the focusing spectrum. In the case of zigzag edges at low magnetic fields one can also observe focusing peaks but with increasing magnetic field a more complex interference structure emerges in the spectrum. This difference in the spectra can be observed even if the zigzag edge undergoes structural reconstruction. Therefore transverse electron focusing can help in the identification and characterisation of the edge structure of graphene samples.

Graphene nanoribbons subject to gentle bends

Since graphene nanoribbons are thin and flimsy, they need support. Support gives firm ground for applications, and adhesion holds ribbons flat, although not necessarily straight: ribbons with high aspect ratio are prone to bend. The effects of bending on ribbons' electronic properties, however, are unknown. Therefore, this article examines the electromechanics of planar and gently bent graphene nanoribbons. Simulations with density-functional tight-binding and revised periodic boundary conditions show that gentle bends in armchair ribbons can cause significant widening or narrowing of energy gaps. Moreover, in zigzag ribbons sizeable energy gaps can be opened due to axial symmetry breaking,…

Single scatterings in single artificial atoms: Quantum coherence and entanglement

We employ the quantum-jump approach to study single scatterings in single semiconductor quantum dots. Two prototypical situations are investigated. First, we analyze two-photon emissions from the cascade biexciton decay of a dot where the single-exciton states exhibit a fine-structure splitting. We show that this splitting results for appropriately chosen polarization filters in an oscillatory behavior of two-photon correlations, and carefully examine the proper theoretical description of the underlying scattering processes. Secondly, we analyze the decay of a single-electron charged exciton in a quantum dot embedded in a field effect structure. We show how the quantum properties of the cha…

Twisting graphene nanoribbons into carbon nanotubes

Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.

Visualising the temporal aspects of collaborative inquiry-based learning processes in technology-enhanced physics learning

This study presents new ways of visualising technology-enhanced collaborative inquiry-based learning (CIBL) processes in an undergraduate physics course. The data included screen-capture videos from a technology-enhanced learning environment and audio recordings of discussions between students. We performed a thematic analysis based on the phases of inquiry-based learning (IBL). The thematic analysis was complemented by a content analysis, in which we analysed whether the utilisation of technological tools was on a deep-level, surface-level, or nonexistent basis. Student participation was measured in terms of frequency of contributions as well as in terms of impact. We visualised the sequen…

Electronic structure and elasticity of two-dimensional metals of group 10 : A DFT study

The discovery of two-dimensional (2D) iron monolayer in graphene pores stimulated experimental and computational material scientists to investigate low-dimensional elemental metals. There have been many advances in their synthesis, stability, and properties in the last few years. Inspired by these advancements, we investigated the electronic structure and elasticity of free-standing monolayers of group 10 elemental metals, viz. Ni, Pd, and Pt. Using density-functional theory (DFT), we explored the energetic, geometric, electronic, and elastic properties of hexagonal, honeycomb, and square lattice structures of each element, in both planar and buckled forms. Among planar configurations, the …

Bright beaches of nanoscale potassium islands on graphite in STM imaging,

We demonstrate, via scanning tunneling microscopy (STM) measurements performed at 48 K, the existence of “bright beaches” at the edges of K islands (diameter ∼ 5 – 500     nm ) on the graphite surface. The enhanced tunneling current is only observed in monolayer-high islands on graphite, and not in islands of similar geometry on top of a K monolayer film. First-principles density functional calculations and STM simulations suggest that this is an STM field effect, which appears as the positive tip attracts donated electrons back to the metallic K islands. The restored charge accumulates preferentially at the island edges. peerReviewed

Limits of stability in supported graphene nanoribbons subject to bending

Graphene nanoribbons are prone to in-plane bending even when supported on flat substrates. However, the amount of bending that ribbons can stably withstand remains poorly known. Here, by using molecular dynamics simulations, we study the stability limits of 0.5-1.9 nm wide armchair and zigzag graphene nanoribbons subject to bending. We observe that the limits for maximum stable curvatures are below ~10 deg/nm, in case the bending is externally forced and the limit is caused by buckling instability. Furthermore, it turns out that the limits for maximum stable curvatures are also below ~10 deg/nm, in case the bending is not forced and the limit arises only from the corrugated potential energy…

Efficient Approach for Simulating Distorted Materials

The operation principles of nanoscale devices are based upon both electronic and mechanical properties of materials. Because these properties can be coupled, they need to be investigated simultaneously. At this moment, however, the electronic structure calculations with custom-made long-range mechanical distortions are impossible, or expensive at best. Here we present a unified formalism to solve exactly the electronic structures of nanomaterials with versatile distortions. We illustrate the formalism by investigating twisted armchair graphene nanoribbons with the least possible number of atoms. Apart from enabling versatile material distortions, the formalism is capable of reducing computa…

Approximate Modeling of Spherical Membrane

Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical systems, using revised periodic boundary conditions adapted to spherical symmetry. Method reduces computational costs by orders of magnitude, and is applicable for both solid and liquid membranes, provided the curvature is sufficiently small. We demonstrate the method by calculating the bending and Gaussian curvature moduli of single- and multi-layer graphene. Method works with any interaction (ab initio, classical interactions), with any approach (molecular …

From Seeds to Islands: Growth of Oxidized Graphene by Two-Photon Oxidation

The mechanism of two-photon induced oxidation of single-layer graphene on Si/SiO2 substrates is studied by atomic force microscopy (AFM) and Raman microspectroscopy and imaging. AFM imaging of areas oxidized by using a tightly focused femtosecond laser beam shows that oxidation is not homogeneous but oxidized and nonoxidized graphene segregate into separate domains over the whole irradiated area. The oxidation process starts from point-like “seeds” which grow into islands finally coalescing together. The size of islands before coalescence is 30–40 nm, and the density of the islands is on the order of 1011 cm–2. Raman spectroscopy reveals growth of the D/G band ratio along the oxidation. Sha…

Oxidation of magnesia-supported Pd-clusters leads to the ultimate limit of epitaxy with a catalytic function

Oxide-supported transition-metal clusters and nanoparticles have attracted significant attention owing to their important role as components of model catalysts, sensors, solar cells and magnetic recording devices. For small clusters, functionality and structure are closely interrelated. However, knowledge of the structure of the bare cluster is insufficient as the interaction with the chemical environment might cause drastic structural changes. Here we show by ab initio simulations based on the density functional theory that the reaction with molecular oxygen transforms small, non-crystalline, magnesia-supported Pd-clusters to crystalline Pd(x)O(y) nano-oxide clusters that are in epitaxy wi…

Peeling of multilayer graphene creates complex interlayer sliding patterns

Peeling, shearing, and sliding are important mechanical phenomena in van der Waals solids. However, theoretically they have been studied mostly using minimal periodic cells and in the context of accurate quantum simulations. Here, we investigate the peeling of large-scale multilayer graphene stacks with varying thicknesses, stackings, and peeling directions by using classical molecular dynamics simulations with a registry-dependent interlayer potential. Simulations show that, while at large scale the peeling proceeds smoothly, at small scale the registry shifts and sliding patterns of the layers are unexpectedly intricate and depend both on the initial stacking and on the peeling direction.…

Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations

A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on a novel control of periodic symmetry, which eliminates artifacts due to deformation constraints and quantum finite-size effects, and allows transparent electronic structure analysis. Via density-functional tight-binding implementation, the technique demonstrates its utility by predicting novel electromechanical properties in carbon nanotubes and abrupt behavior in the structural yielding of Au7 and MoS nanowires. The technique drives simulations markedly closer to the reali…

Ruotiminen : toimintamalli harjoitustehtävien läpikäyntiin

Self-Passivating Edge Reconstructions of Graphene

Planar reconstruction patterns at the zigzag and armchair edges of graphene were investigated with density functional theory. It was unexpectedly found that the zigzag edge is metastable and a planar reconstruction spontaneously takes place at room temperature. The reconstruction changes electronic structure and self-passivates the edge with respect to adsorption of atomic hydrogen from molecular atmosphere.

Laatuaikaoppiminen : vuorovaikutteista ja yhteistoiminnallista fysiikan opiskelua

Esittelemme artikkelissa Jyväskylän yliopiston fysiikan laitoksella kehitettyä opetuksen toimintamallia, joka perustuu teknologiatuettuun pienryhmäopiskeluun ja kurssin aikaiseen formatiiviseen arviointiin. Toimintamalli kehittää työelämätaitoja, tehostaa opettajien ja opiskelijoiden ajankäyttöä, vahvistaa opiskelijoiden välistä vuorovaikutusta ja hyödyntää suunnitelmallisesti tuloksia fysiikan opetuksen tutkimuksesta. Alustavat kokemukset toimintamallista ovat rohkaisevia. nonPeerReviewed

Ultrastiff graphene

Graphene has exceptionally high in-plane strength, which makes it ideal for various nanomechanical applications. At the same time, its exceptionally low out-of-plane stiffness makes it also flimsy and hard to handle, rendering out-of-plane structures unstable and difficult to fabricate. Therefore, from an application point of view, a method to stiffen graphene would be highly beneficial. Here we demonstrate that graphene can be significantly stiffened by using a laser writing technique called optical forging. We fabricate suspended graphene membranes and use optical forging to create stable corrugations. Nanoindentation experiments show that the corrugations increase graphene bending stiffn…

Revised periodic boundary conditions: Fundamentals, electrostatics, and the tight-binding approximation

Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum-mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper we summarize the underlying theory, present the practical details of RPBC, especially related to a non-orthogonal tight-binding formulation, discuss selected featur…

Pehmoilua kovissa tieteissä

Tight-Binding Model for Spontaneous Magnetism of Quantum Dot Lattices

We use a simple tight-binding model to study the magnetism of two-dimensional quantum dot lattices with 1 to 12 electrons per dot. The results show that in the middle of an electron shell the lattice favours antiferromagnetism while with nearly empty or full shells ferromagnetism is favoured. The size of the antiferromagnetic region increases with the coordination number of the dot. A one-dimensional dot lattice shows a spin-Peierls transition. The results for a square lattice are in good agreement with density functional calculations of Koskinen et al.

Optimizing density-functional simulations for two-dimensional metals

Unlike covalent two-dimensional (2D) materials like graphene, 2D metals have non-layered structures due to their non-directional, metallic bonding. While experiments on 2D metals are still scarce and challenging, density-functional theory (DFT) provides an ideal approach to predict their basic properties and assist in their design. However, DFT methods have been rarely benchmarked against metallic bonding at low dimensions. Therefore, to identify optimal DFT attributes for a desired accuracy, we systematically benchmark exchange-correlation functionals from LDA to hybrids and basis sets from plane waves to local basis with different pseudopotentials. With 1D chain, 2D honeycomb, 2D square, …

Efficient approach for simulating distorted materials

The operation principles of nanoscale devices are based upon both electronic and mechanical properties of materials. Because these properties can be coupled, they need to be investigated simultaneously. At this moment, however, the electronic structure calculations with custom-made long-range mechanical distortions are impossible, or expensive at best. Here we present a unified formalism to solve exactly the electronic structures of nanomaterials with versatile distortions. We illustrate the formalism by investigating twisted armchair graphene nanoribbons with the least possible number of atoms. Apart from enabling versatile material distortions, the formalism is capable of reducing computa…

Effects of Bending on Raman-active Vibration Modes of Carbon Nanotubes

We investigate vibration modes and their Raman activity of single-walled carbon nanotubes that are bent within their intrinsic elastic limits. By implementing novel boundary conditions for density-functional based tight-binding, and using non-resonant bond polarization theory, we discover that Raman activity can be induced by bending. Depending on the degree of bending, high-energy Raman peaks change their positions and intensities significantly. These effects can be explained by migration of nodes and antinodes along tube circumference. We discuss the challenge of associating the predicted spectral changes with experimental observations.

Self-Consistent Charge Density-Functional Tight-Binding Parametrization for Pt–Ru Alloys

We present a self-consistent charge density-functional tight-binding (SCC-DFTB) parametrization for PtRu alloys, which is developed by employing a training set of alloy cluster energies and forces obtained from Kohn-Sham density-functional theory (DFT) calculations. Extensive simulations of a testing set of PtRu alloy nanoclusters show that this SCC-DFTB scheme is capable of capturing cluster formation energies with high accuracy relative to DFT calculations. The new SCC-DFTB parametrization is employed within a genetic algorithm to search for global minima of PtRu clusters in the range of 13-81 atoms and the emergence of Ru-core/Pt-shell structures at intermediate alloy compositions, consi…

Topological Signatures in the Electronic Structure of Graphene Spirals

Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to tim…

Lithium adsorption at prismatic graphite surfaces enhances interlayer cohesion

Abstract We use density functional calculations to determine the binding sites and binding energies of Li + at graphene edges and prismatic graphite surfaces. Binding is favorable at bare and carbonyl terminated surfaces, but not favorable at hydrogen terminated surfaces. These findings have implications for the exfoliation of graphitic anodes in lithium-ion batteries that happens if solute and solvent co-intercalate. First, specific adsorption facilitates desolvation of Li + . Second, chemisorption lowers the surface energy by about 1 J m −2 prismatic surface area, and gives graphite additional stability against exfoliation. The results offer an explanation for experiments that consistentl…

Density-functional tight-binding for beginners

This article is a pedagogical introduction to density-functional tight-binding (DFTB) method. We derive it from the density-functional theory, give the details behind the tight-binding formalism, and give practical recipes for parametrization: how to calculate pseudo-atomic orbitals and matrix elements, and especially how to systematically fit the short-range repulsions. Our scope is neither to provide a historical review nor to make performance comparisons, but to give beginner's guide for this approximate, but in many ways invaluable, electronic structure simulation method--now freely available as an open-source software package, hotbit.

Electronic and optical trends in carbon nanotubes under pure bending

The high aspect ratio of carbon nanotubes makes them prone to bending. To know how bending affects the tubes is therefore crucial for tube identification and for electrical component design. Very few studies, however, have investigated tubes under small bending well below the buckling limit, because of technical problems due to broken translational symmetry. In this Letter a cost-effective and exact modeling of singe-walled nanotubes under such small bending is enabled by revised periodic boundary conditions, combined with density-functional tight-binding. The resulting, bending-induced changes in electronic and optical properties fall in clear chirality-dependent trend families. While the …

Nanomechanical cleavage of molybdenum disulphide atomic layers.

The discovery of two-dimensional materials became possible due to the mechanical cleavage technique. Despite its simplicity, the as-cleaved materials demonstrated surprising macrocontinuity, high crystalline quality and extraordinary mechanical and electrical properties that triggered global research interest. Here such cleavage processes and associated mechanical behaviours are investigated by a direct in situ transmission electron microscopy probing technique, using atomically thin molybdenum disulphide layers as a model material. Our technique demonstrates layer number selective cleavage, from a monolayer to double layer and up to 23 atomic layers. In situ observations combined with mole…

From Seeds to Islands: Growth of Oxidized Graphene by Two-Photon Oxidation

The mechanism of two-photon induced oxidation of single-layer graphene on Si/SiO2 substrates is studied by atomic force microscopy (AFM) and Raman microspectroscopy and imaging. AFM imaging of areas oxidized by using a tightly focused femtosecond laser beam shows that oxidation is not homogeneous but oxidized and nonoxidized graphene segregate into separate domains over the whole irradiated area. The oxidation process starts from point-like “seeds” which grow into islands finally coalescing together. The size of islands before coalescence is 30–40 nm, and the density of the islands is on the order of 1011 cm–2. Raman spectroscopy reveals growth of the D/G band ratio along the oxidation. Sha…

Structural, chemical and dynamical trends in graphene grain boundaries

Grain boundaries are topological defects that often have a disordered character. Disorder implies that understanding general trends is more important than accurate investigations of individual grain boundaries. Here we present trends in the grain boundaries of graphene. We use density-functional tight-binding method to calculate trends in energy, atomic structure (polygon composition), chemical reactivity (dangling bond density), corrugation heights (inflection angles), and dynamical properties (vibrations), as a function of lattice orientation mismatch. The observed trends and their mutual interrelations are plausibly explained by structure, and supported by past experiments.

Density-Functional Tight-Binding Simulations of Curvature-Controlled Layer Decoupling and Band-Gap Tuning in BilayerMoS2

Monolayer transition-metal dichalcogenides (TMDCs) display valley-selective circular dichroism due to the presence of time-reversal symmetry and the absence of inversion symmetry, making them promising candidates for valleytronics. In contrast, in bilayer TMDCs both symmetries are present and these desirable valley-selective properties are lost. Here, by using density-functional tight-binding electronic structure simulations and revised periodic boundary conditions, we show that bending of bilayer MoS2 sheets breaks band degeneracies and localizes states on separate layers due to bending-induced strain gradients across the sheets. We propose a strategy for employing bending deformations in …

Size-Dependent Structural Evolution and Chemical Reactivity of Gold Clusters

Ground-state structures and other experimentally relevant isomers of Au(15) (-) to Au(24) (-) clusters are determined through joint first-principles density functional theory and photoelectron spectroscopy measurements. Subsequent calculations of molecular O(2) adsorption to the optimal cluster structures reveal a size-dependent reactivity pattern that agrees well with earlier experiments. A detailed analysis of the underlying electronic structure shows that the chemical reactivity of the gold cluster anions can be elucidated in terms of a partial-jellium picture, where delocalized electrons occupying electronic shells move over the ionic skeleton, whose geometric structure is strongly infl…

Optical and electronic properties of graphene nanoribbons upon adsorption of ligand-protected aluminum clusters

We have carried out first-principles calculations to investigate how the electronic and optical features of graphene nanoribbons are affected by the presence of atomic clusters. Aluminum clusters of different sizes and stabilized by organic ligands were deposited on graphene nanoribbons from which the energetic features of the adsorption plus electronic structure were treated within density-functional theory. Our results point out that, depending on their size and structure shape, the clusters perturb distinctively the electronic properties of the ribbons. We suggest that such selective response can be measured through optical means revealing that graphene nanoribbons can work as an efficie…

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring.

Limits of lateral expansion in two-dimensional materials with line defects

The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well belo…

Rippling of two-dimensional materials by line defects

Two-dimensional materials and their mechanical properties are known to be profoundly affected by rippling deformations. However, although ripples are fairly well understood, less is known about their origin and controlled modification. Here, motivated by recent reports of laser-controlled creation of line defects in graphene, we investigate how line defects could be used to control rippling in graphene and other two-dimensional materials. By sequential multi-scale coupling of density-functional tight-binding and continuum elasticity simulations, we quantify the amount of rippling when the number and the cumulative length of the line defects increase. Simulations show that elastic sheets wit…

Plenty of motion at the bottom: atomically thin liquid gold membrane

The discovery of graphene some ten years ago was the first proof of a free-standing two-dimensional (2D) solid phase. Here, using quantum molecular dynamics simulations of nanoscale gold patches suspended in graphene pores, we predict the existence of an atomically thin, free-standing 2D liquid phase. The liquid phase, enabled by the exceptional planar stability of gold due to relativistic effects, demonstrates extreme fluxionality of metal nanostructures and opens possibilities for a variety of nanoscale phenomena.

Bending-Induced Delamination of van der Waals Solids

Although sheets of layered van der Waals solids offer great opportunities to custom-design nanomaterial properties, their weak interlayer adhesion challenges structural stability against mechanical deformation. Here, bending-induced delamination of multilayer sheets is investigated by molecular dynamics simulations, using graphene as an archetypal van der Waals solid. Simulations show that delamination of a graphene sheet occurs when its radius of curvature decreases roughly below $R_c=5.3\text{nm}\times (\text{number of layers})^{3/2}$ and that, as a rule, one-third of the layers get delaminated. These clear results are explained by a general and transparent model, a useful future referenc…

Electronic and optical properties of carbon nanotubes under pure bending

The high aspect ratio of carbon nanotubes makes them prone to bending. To know how bending affects the tubes is therefore crucial for tube identification and for electrical component design. Very few studies, however, have investigated tubes under small bending well below the buckling limit, because of technical problems due to broken translational symmetry. In this Brief Report a cost-effective and exact modeling of singe-walled nanotubes under such small bending is enabled by revised periodic boundary conditions, combined with density-functional tight-binding. The resulting, bending-induced changes in electronic and optical properties fall in clear chirality-dependent trend families. Whil…

Optical Forging of Graphene into Three-Dimensional Shapes

Atomically thin materials, such as graphene, are the ultimate building blocks for nanoscale devices. But although their synthesis and handling today are routine, all efforts thus far have been restricted to flat natural geometries, since the means to control their three-dimensional (3D) morphology has remained elusive. Here we show that, just as a blacksmith uses a hammer to forge a metal sheet into 3D shapes, a pulsed laser beam can forge a graphene sheet into controlled 3D shapes in the nanoscale. The forging mechanism is based on laser-induced local expansion of graphene, as confirmed by computer simulations using thin sheet elasticity theory. peerReviewed

Density-functional based tight-binding study of small gold clusters

In this paper, we report the ability of self-consistent-charge density-functional based tight-binding method to describe small gold clusters. We concentrate our investigations mainly on anions, and find that the method describes their geometric and electronic structures fairly well, in comparison with density-functional calculations. In particular, the method correctly reproduces the planarity of ground-state structures up to cluster sizes in agreement with experiment and density-functional theory.

Edge-stress -induced spontaneous twisting of graphene nanoribbons

We present a continuum model for spontaneous twisting of graphene nanoribbons driven by compressive edge stresses. Based on a geometrically nonlinear theory of plates, we identify scaling laws for the dependence of twist angles on ribbon width. Strikingly, we find the existence of a critical width below which a ribbon will not undergo spontaneous twisting, preferring an in-plane stretching mode instead. The model predictions are shown to be in excellent qualitative and quantitative agreement with density-functional tight-binding simulations. More generally, our model provides a unifying picture of twisting in graphene nanoribbons with different edge orientations and chemical functionalizati…

Quantum rings for beginners: Energy spectra and persistent currents

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodic…