Holographic superfluid with gauge–axion coupling

We have constructed a holographic superfluid with gauge–axion coupling. Depending on whether the coupling is positive or negative, the system displays metallic or insulating behavior in its normal state. A significant feature of the system is the appearance of a mid-IR peak in the alternating current (AC) conductivity in a certain range of parameters. This peak arises due to competition between explicit symmetry breaking (ESB) and spontaneous symmetry breaking (SSB), which results in the presence of a pseudo-Goldstone mode. Moreover, a dip in low-frequency AC conductivity is observed, stemming from the excitation of the SSB Goldstone mode. In the superfluid phase, the effect of gauge–axion coupling on the condensation or superfluid energy gap is only amplified in the presence of strong momentum dissipation. Notably, for the case with negative gauge–axion coupling, a hard-gap-like behavior at low frequency and a pronounced peak at intermediate frequency are observed, indicating that the evolution of the superfluid component is distinct from that of positive coupling.