BCS thermal vacuum of fermionic superfluids and its perturbation theory

TL;DR

This paper develops a thermal vacuum framework for fermionic superfluids based on BCS theory, enabling perturbative calculations of thermodynamic quantities and revealing phenomena like the pseudogap.

Contribution

It introduces a BCS thermal vacuum using thermal field theory, allowing quantum perturbation analysis of superfluid properties at finite temperature.

Findings

Leading-order corrections to the order parameter were evaluated.

The pseudogap phenomenon was explained via perturbation theory.

The thermal vacuum is shown to be a generalized coherent and squeezed state.

Abstract

The thermal field theory is applied to fermionic superfluids by doubling the degrees of freedom of the BCS theory. We construct the two-mode states and the corresponding Bogoliubov transformation to obtain the BCS thermal vacuum. The expectation values with respect to the BCS thermal vacuum produce the statistical average of the thermodynamic quantities. The BCS thermal vacuum allows a quantum-mechanical perturbation theory with the BCS theory serving as the unperturbed state. We evaluate the leading-order corrections to the order parameter and other physical quantities from the perturbation theory. A direct evaluation of the pairing correlation as a function of temperature shows the pseudogap phenomenon results from the perturbation theory. The BCS thermal vacuum is shown to be a generalized coherent and squeezed state. The correspondence between the thermal vacuum and purification of the density matrix allows a unitary transformation, and we found the geometric phase in the parameter space associated with the transformation.