掺杂量子自旋霍尔态后所形成超导的平均场计算

Mean-field calculation of the doping-iduced quantum spin Hall state to superconductor transiton

摘要: 给出了对易面t\text-\lambda模型详细平均场理论和计算的结果，特别是给出了平均场相图．研究表明，掺杂纯的量子自旋霍尔（QSH）态后可获得2种结论： 1）相互作用强度较弱时，QSH态和超导态之间可发生一级相变； 2）相互作用强度较强时，系统经过一个连续相变进入2相共存区，并发生QSH态消失的一级相变．计算结果表明，平均场理论虽然体现了对称破缺相的特征，但是其忽略了涨落，致使其得到QSH态与超导态共存的错误结论，从而使得平均场理论无法准确描述因拓扑激发所引起的相变．

Abstract: The mean-field theory and simulation result of the easy-plane t-λ model and the mean-field phase diagram are given in this paper． Two mean-field scenarios exist for doping the pure QSH state: 1) a first-order QSH-SSC transition occurs in the weak interaction region; 2) a continuous QSH to QSH-SSC co-existence transition followed by a first-order QSH-vanishing transition in the strong interaction region． The mean-field theory is found to capture features for symmetry-broken phases but give the wrong conclusion of QSH-SSC co-existence due to ignoring fluctuation． It is unable to characterize transitions with topological excitation．