Adiabatic transition from a BCS superconductor to a Fermi liquid and phase dynamics

TL;DR

This paper explores the adiabatic transition from a BCS superconductor to a Fermi liquid, revealing memory effects, phase dynamics, and gauge invariance restoration during the process.

Contribution

It introduces a detailed analysis of the phase evolution and memory effects during the adiabatic transition, including methods to reverse the dynamics and control the chemical potential.

Findings

The metal retains memory of the BCS state during slow transition.

The phase dynamics enable reversing the transition to the original state.

Gauge invariance is restored through phase and vector field analysis.

Abstract

We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. In particular, we show that the metal keeps memory of the parent BCS state so it is possible to reverse the dynamics and go back to the original state similarly to a spin/photon echo experiment. Moreover, we study the evolution of the order parameter phase phi in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density we explicitly show how to use the dynamics of phi together with gauge invariance to build up the non-interacting chemical potential away from particle-hole symmetry. We further analyze the role of phi in restoring the gauge invariant current response when the non-interacting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field.