全息p波超导相变的磁效应和高阶修正效应

Holographic p-Wave Superconductor in Lifshitz Gravity

在探子极限下,通过解析方法研究了超导体相变的磁效应和高阶修正效应。具体来说,我们把带质量的麦克斯韦复矢量场耦合到4维AdS黑洞中,构造了全息p波导体/超导体相变。首先,通过扰动方法得到了表征磁效应的多普勒解,进而对多普勒解叠加得到不同形状的涡流格点。其次,在最低朗道能级下,磁场促进相变,高阶修正抑制相变。在激发态能级下,磁场和高阶修正对超导相变的影响与最低能态下情况相反。并且,解析结果与已有的数值结果定性一致。

This paper numerically studies the effects of the magnetic field as well as the high order derivative correction on the superconductor in the probe limit.Concretely,we construct a holographic p-wave superconductor in the four-dimensional Schwarzschild AdS black hole coupled to a Maxwell complex vector field and the high order derivative correction consisting of the Weyl tensor and Maxwell field strenth.First of all,by using the perturbative method,we solve the droplet solution and thus obtain two kinds of vortex lattices by linear superposition of the droplet solution.Secondly,in the lowest Landau energy state,the stronger magnetic field triggers the phase transition while the larger high order derivative correction makes the phase transition harder.However,the magnetic field and the high order derivative correction behave the opposite influences on the phase transition compared with the case in the lowest energy state.In addition,our analytical results agree well with the ones from the numerical method.