Modified Fermi-sphere, pairing gap and critical temperature for the BCS-BEC crossover

TL;DR

This paper uses functional renormalization group equations to analyze the phase diagram of two-component fermions across the BCS-BEC crossover, focusing on quantum fluctuations, Fermi surface modifications, and critical temperature predictions.

Contribution

It introduces a method to incorporate quantum fluctuations into the analysis of the BCS-BEC crossover, providing detailed insights into the Fermi surface and excitation dispersion throughout the transition.

Findings

Results agree with BCS theory and Gorkov's correction for small negative scattering length.

At unitarity, the zero-temperature gap matches Quantum Monte Carlo results.

Critical temperature predictions differ from Quantum Monte Carlo at unitarity.

Abstract

We investigate the phase diagram of two-component fermions in the BCS-BEC crossover. Using functional renormalization group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wavefunction renormalization, an effective Fermi radius and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkov's correction for small negative scattering length a and with an interacting Bose gas for small positive a. At the unitarity point the result for the gap at zero temperature agrees well with Quantum-Monte-Carlo simulations while the critical temperature differs.