Search results for "Pauli paramagneism"

Quasiclassical free energy of superconductors : Disorder-driven first-order phase transition in superconductor/ferromagnetic-insulator bilayers

2020

In the seminal work by G. Eilenberger, Z. Phys. 214, 195 (1968), a closed-form expression for the free energy of inhomogeneous spin-singlet superconductor in terms of quasiclassical propagators has been suggested. However, deriving this expression and generalizing it for superconductors or superfluids with general matrix structure, e.g., spin-triplet correlations, has remained problematic. Starting from the Luttinger-Ward formulation, we discuss here the general solution. Besides ordinary superconductors with various scattering mechanisms, the obtained free-energy functional can be used for systems, such as superfluid $^{3}\mathrm{He}$ and superconducting systems with spatially inhomogeneou…