Transformation of the Eilenberger Equations of Superconductivity to a Scalar Riccati Equation
arXiv:cond-mat/9804064
Abstract
A new parametrisation of the Eilenberger equations of superconductivity in terms of the solutions to a scalar differential equation of the Riccati type is introduced. It is shown that the quasiclassical propagator, and in particular the local density of states, may be reconstructed, without explicit knowledge of any eigenfunctions and eigenvalues, by solving a simple initial value problem for the linearised Bogoliubov-de Gennes equations. The Riccati parametrisation of the quasiclassical propagator leads to a stable and fast numerical method to solve the Eilenberger equations. For some spatially varying model pair potentials exact solutions to the Eilenberger Equations are found.
arXiv comment17 pages
Cited by in corpus (10)
- Quasiclassical theory of superconductivity: a multiple interface geometry(II)
- Triplet Cooper pairs induced in diffusive s-wave superconductors interfaced with strongly spin-polarized magnetic insulators or half-metallic ferromagnets
- Spontaneously broken translational symmetry at edges of high-temperature superconductors: thermodynamics in magnetic field
- Quasiclassical expressions for the free energy of superconducting systems
- SuperConga: an open-source framework for mesoscopic superconductivity
- Spectral properties of superconductors with ferromagnetically ordered magnetic impurities
- Large spectral gap and impurity-induced states in a two-dimensional Abrikosov vortex
- Charging in the vortex lattice of type-II superconductors
- What is wrong with paramagnons?
- Microwave control of the superconducting proximity effect and minigap in magnetic and normal metals