A Microscopic Derivation of the Critical Magnetic Field in a Superconductor
Detlef Lehmann (Swiss Federal Institute of Technology, Z\"urich;, present address: Institue for Advanced Study, Princeton)
TL;DR
This paper derives a microscopic BCS equation in a magnetic field, showing it has no solutions beyond a critical field, and discusses perturbation theory around the magnetic propagator.
Contribution
It provides a microscopic derivation of the critical magnetic field in superconductors using propagator calculations and extends previous results with new theoretical insights.
Findings
The BCS equation has no solutions at high magnetic fields.
Derived the magnetic field propagator for a noninteracting electron system.
Discussed perturbation theory around the magnetic propagator.
Abstract
The propagator for a noninteracting many electron system in a constant magnetic field in three space time dimensions is computed. This formula and the results of [FT1,2] are used to give a microscopic derivation of a BCS-equation with magnetic field. It is shown that this equation has no solution if the magnetic field is sufficiently large. Perturbation theory in the interaction around the magnetic field propagator is discussed.
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