Pseudogap regime of a two-dimensional uniform Fermi gas

TL;DR

This paper analyzes the pseudogap phenomena in a two-dimensional Fermi gas, determining the pseudogap temperature and its relation to the BKT transition, highlighting the importance of amplitude fluctuations and providing insights for improving BKT theories.

Contribution

The study introduces a self-consistent $T$-matrix approach to identify the pseudogap temperature and explores its implications for understanding the BKT transition in 2D Fermi gases.

Findings

Pseudogap temperature $T^*$ is identified where a dip appears in the density of states.

The BKT transition temperature lies within the pseudogap regime.

The pseudogap structure at $T^{ m exp}_{ m BKT}$ differs from a fully-gapped state, emphasizing amplitude fluctuations.

Abstract

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.