Anomalies in isothermal compressibility and exponent of pressure in spin-orbit-coupled degenerate Fermi gases

Abstract

The spin-orbit coupling (SOC) in degenerate Fermi gases can fundamentally change the fate of $s$-wave superfluids. Here we report the anomalous isothermal compressibility ${\ensuremath{\kappa}}_{T}$ in the degenerate Fermi gases with both SOC and Zeeman field. Starting from the Gibbs-Duhem equation, we show that ${\ensuremath{\kappa}}_{T}$ comes from both the explicit contribution of chemical potential and the implicit contribution of the order parameter. In the Bardeen-Cooper-Schrieffer (BCS) limit, ${\ensuremath{\kappa}}_{T}$ is determined by the explicit compressibility, which is proportional to the density of states at the Fermi surface; while in the Bose-Einstein condensate (BEC) regime it is determined by the implicit compressibility, which is uniquely given by the scattering length. Between these two limits, we find a pronouncedly enhanced compressibility in the gapless Weyl phase regime, which is attributed to a remanent effect of the instability of degenerate Fermi gases towards phase separation. This enhanced compressibility also leads to an anomaly in the exponent of pressure. A connection between this exponent and the polytropic index is established. These predictions can be measured from the anomaly in sound velocity, density fluctuation, and collective vibration frequencies.