Response of superfluid fermions at finite temperature

TL;DR

This paper develops a microscopic finite-temperature theory for superfluid fermionic systems, incorporating quasiparticle interactions and collective effects, advancing understanding of their response at non-zero temperatures.

Contribution

It introduces a consistent finite-temperature formalism using Bogoliubov quasiparticles and a factorized interaction kernel to include collectivity and quasiparticle-vibration coupling.

Findings

Formulation of a finite-temperature response theory for superfluid fermions.

Inclusion of a minimal truncation capturing collective effects.

Extension of the quasiparticle-vibration coupling vertex to finite temperature.

Abstract

A consistent finite-temperature microscopic theory for the response of strongly coupled superfluid fermionic systems is formulated. We start from the general many-body Hamiltonian with the vacuum (bare) two-fermion interaction and derive the equation of motion (EOM) for the thermally averaged two-time two-fermion correlation function, which determines the spectrum of the system under study. The superfluidity is introduced via the Bogoliubov transformation of the fermionic field operators, and the entire formalism is carried out in the basis of Bogoliubov's quasiparticles, keeping the complete 4x4 block matrix structure of the two-fermion EOM. Fully correlated static and dynamical interaction kernels of the resulting EOM are discussed. A special focus is then placed on the latter kernel, which is advanced to a factorized form, enabling a minimal truncation of the many-body problem while keeping important effects of emergent collectivity and mapping to the quasiparticle-vibration coupling (qPVC). As in the zero-temperature and non-superfluid cases, the qPVC can be associated with a new order parameter, qPVC vertex. In the thermal superfluid theory, the latter vertex, as well as the components of the dynamical kernel, acquire an extended form including thermally unblocked transition amplitudes.