Squeezed-field path-integral description of BCS superconductors

TL;DR

This paper introduces a novel squeezed-field path-integral approach for BCS superconductors, capturing collective order-parameter dynamics and revealing a Higgs mode alongside quasiparticle excitations.

Contribution

It develops a new path-integral formulation using squeezed-fermionic coherent states, explicitly including collective modes in BCS theory.

Findings

Identifies a bosonic Higgs amplitude mode in the spectral function.

Reproduces quasiparticle and quasihole branches of BCS theory.

Provides a framework for analyzing collective excitations in superconductors.

Abstract

We develop a squeezed-field path-integral representation for BCS superconductors utilizing a generalized completeness relation of squeezed-fermionic coherent states. We derive a Grassmann path integral of fermionic quasiparticles that explicitly includes the collective degrees of freedom of the order-parameter dynamics governed by the classical Anderson pseudospin model. Based on this method, we analyze the spectral function of the single-particle excitations, and show that the squeezed-field path integral for the BCS Hamiltonian describes a bosonic sideband branch that corresponds to the Higgs amplitude mode of BCS superconductors, in addition to reproducing the quasiparticle and quasihole excitation branches described by the BCS mean-field approximation.