The local thermodynamic instability from negative susceptibility in a holographic superfluid with nonlinear terms

The local thermodynamic stability from the charge susceptibility of a holographic superfluid model at finite superfluid velocity is studied in the probe limit. Previous studies show that beyond a finite value of the superfluid velocity, the superfluid phase transition in the grand canonical ensemble becomes first order. We further reveal that in the canonical ensemble, the superfluid phase transition is still second order, and the difference indicates a section with negative susceptibility which means local thermodynamic instability beyond this superfluid velocity. However, we also meet the ``cave of wind'' behavior at larger superfluid velocity which complicate the phase diagram. We further study the influence of the two nonlinear terms $\lambda|\psi|^4$ and $\tau|\psi|^6$ with parameters $\lambda$ and $\tau$ on the condensate curves, and set appropriate values of $\lambda$ and $\tau$ to remove the "cave of wind" region in the canonical ensemble to get a more elegant phase diagram and better represent the region with such instability, which is possible to be used to realize spontaneous formation of vortexes and quantum turbulence.