Horava-Lifshitz引力中超导体的临界行为

Critical Behavior of Superconductor in Horava-Lifshitz Gravity

在探子极限下,通过解析方法和边缘稳定模式研究了Horava-Lifshitz中s波绝缘体/超导体相变的临界行为,尤其得到了修正引力参数α对临界化学势的影响。具体来说:对于α>0,标量场满足的SturmLiouville方程总存在一个最小本征值,即超导体相变的临界化学势。同时,对于任意修正引力参数,标量场在径向方向分布总存在一个边缘稳定模,即n=0模。并且,随着修正参数α的增加,临界化学势增加,即相变变得困难。此外,本文结果与通过数值方法所得结果一致。

We study the effects of Horava-Lifshitz parameter αon the critical behavior of s-wave insulator/superconductor phase transition in the probe limit by both Sturm-Liouville method and marginally stable modes. In particular,the influence of correction parameter α on the critical chemical potential is obtained. Concretely,there always exists a minimal eigenvalue for the Sturm-Liouville equation about the scalar field,i. e.,the critical chemical potential,for any value of α 0. Meanwhile,there is a marginally stable mode for the scalar field in the radial direction,the so called n = 0 mode. Furthermore,with the increasing α,the critical value increases,which means that the phase transition becomes more difficult with the increasing Horava-Lifshitz correction. In addition,our results agree with the ones obtained by the numerical method.