Critical region of the superfluid transition in the BCS-BEC crossover

TL;DR

This paper uses a renormalization-group approach to analyze the size and asymmetry of the critical region around the superfluid transition temperature in a three-dimensional fermion gas across the BCS-BEC crossover, highlighting differences between the BCS and BEC sides.

Contribution

It provides a detailed determination of the critical region in the BCS-BEC crossover using a renormalization-group approach, revealing asymmetry and suppression effects.

Findings

Critical region size is of order T_c around the transition.

Asymmetry in the critical region with a ratio of about 8.

Critical region is suppressed on the BCS side but significant on the BEC side.

Abstract

We determine the size of the critical region of the superfluid transition in the BCS-BEC crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[T_G^-,T_G^+]$, of order $T_c$, around the transition temperature $T_c$ with a pronounced asymmetry: $|T_G^+-T_c|/|T_G^--T_c|\sim8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.