Axion effects on new p-wave superconductors induced by electromagnetic fields

Abstract

Based on the holographic duality, we construct the new p-wave metal/superconductor phase transitions triggered by the electric and magnetic fields. Especially, using the axion field, we introduce simultaneously the spontaneous (SBT) and explicit (EBT) breaking of translation and then investigate how the SBT and EBT corrections influence on the critical temperature, vector condensate and the optical conductivity. Concretely, for the case with pure electric field, both the EBT correction with weak SBT correction and the SBT correction lower the critical temperature $T_c$ and soften the energy gap. Interestingly, for the strong enough SBT correction, the increasing EBT correction enhances firstly and then inhibits the phase transition. Meanwhile, the increasing EBT correction suppresses the SBT effect on $T_c$. At the lowest Landau energy level, the stronger SBT correction suppresses the phase transition for the weak magnetic field, whose inhibiting effect is finally eliminated by the strong enough magnetic field. The monotonic dependence of $T_c$ on the EBT correction only exists for the weak SBT correction. For the Landau energy level in the excited state, the monotonic dependence of $T_c$ on the EBT correction vanishes for the intermediate SBT correction with large magnetic field.