Quasiclassical expressions for the free energy of superconducting systems

Abstract

In the seminal work by G. Eilenberger [Z. Phys. 214, 195 (1968)], the quasiclassical expression for the free energy of spin-singlet superconductor has been suggested. Starting from the Luttinger-Ward formulation we derive the Eilenberger free energy and find its generalization for superconductor or superfluid with spin-triplet correlations. Besides ordinary superconductors with various scattering mechanisms, the obtained free energy functional can be used for systems with spin-triplet pairing such as superfluid ${}^3$He and superconducting systems with spatially-inhomogeneous exchange field or spin-orbit coupling. Using this general result we derive the simplified expression for the free energy in the diffusive limit in terms of the momentum-averaged propagators.

7 pages

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• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory
• Quasiparticle density of states and triplet correlations in superconductor/ferromagnetic-insulator structures across a sharp domain wall
• Applications of Lattice Gauge Equivariant Neural Networks
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Interplay between Superconductivity and Altermagnetism in Disordered Materials and Heterostructures
• Proximity Induced Non-collinear Magnetic States in Planar Superconductor/Ferromagnet Hybrids
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors
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