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掺杂量子自旋霍尔态形成超导的平均场计算

侯迪莎 郭文安

侯迪莎, 郭文安. 掺杂量子自旋霍尔态形成超导的平均场计算[J]. 北京师范大学学报(自然科学版). doi: 10.12202/j.0476-0301.2023145
引用本文: 侯迪莎, 郭文安. 掺杂量子自旋霍尔态形成超导的平均场计算[J]. 北京师范大学学报(自然科学版). doi: 10.12202/j.0476-0301.2023145
HOU Disha, GUO Wen’an. Mean-field calculation of doping-induced quantum spin Hall state to superconductor[J]. Journal of Beijing Normal University(Natural Science). doi: 10.12202/j.0476-0301.2023145
Citation: HOU Disha, GUO Wen’an. Mean-field calculation of doping-induced quantum spin Hall state to superconductor[J]. Journal of Beijing Normal University(Natural Science). doi: 10.12202/j.0476-0301.2023145

掺杂量子自旋霍尔态形成超导的平均场计算

doi: 10.12202/j.0476-0301.2023145
基金项目: 国家自然科学基金资助项目(12175015,11734002)
详细信息
    通讯作者:

    郭文安(1968—),男,博士,二级教授. 研究方向:量子相变. E-mail:waguo@bnu.edu.cn

  • 中图分类号: O414.21

Mean-field calculation of doping-induced quantum spin Hall state to superconductor

  • 摘要: $t-\lambda$模型是一个基于二维狄拉克费米子体系实现量子自旋霍尔绝缘体和超导的 晶格模型,特别重要的是它在费米子系统实现了超越朗道范式的解禁闭量子临界性.本文给出对易面$t-\lambda$模型的详细平均场理论和计算结果,特别是平均场相图, 掺杂纯的量子自旋霍尔态有2种结果:(1)相互作用强度较小时,量子自旋霍尔态和超导态之间发生一级相变;(2)深入量子自旋霍尔态掺杂时,随着掺杂的增大,先经过一连续相变进入两相共存区,再发生量子自旋霍尔态消失的一级相变.计算表明平均场理论可以抓住对称破缺相的特征,但是忽略涨落导致得到了量子自旋霍尔态与超导态共存的错误结论,更无法正确描述拓扑激发导致的相变.

     

  • 图  1  蜂巢晶格上$ t-\lambda $模型序参量示意

    注:黑(蓝)色圆点表示元胞内的A(B)子晶格;红色虚线表示自旋流算符$ \hat{ {\boldsymbol{J}} }_{{\boldsymbol{r}} + {\boldsymbol{\delta}}_n,{\boldsymbol{r}} + {\boldsymbol{\eta}}_n} $,粉色虚线圈表示超导算符$ \hat{\eta}^{\dagger}_{{\boldsymbol{r}},{\boldsymbol{\tilde{\delta}}_a}} $.

    图  2  半满填充时观测量随相互作用强度的变化

    注:$ \Delta=0.3 $;a 序参量,b 单粒子能隙.

    图  3  相互作用强度较小时观测量随化学势的变化

    注:$ \Delta=0.5 $,$ \lambda=0.1 $;a 序参量,b 掺杂因子;在$ \mu=0.6 $处发生从QSH到SSC的一级相变.

    图  4  相互作用较大时观测量随化学势的变化

    注:$ \Delta=0.5 $,$ \lambda=0.2 $;a 序参量,b 掺杂因子;当$ \mu $接近0.8时,系统进入QSH和SSC共存相; 当$ \mu $增大到1时,系统离开QSH,处于单纯的SSC相,此相变为一级相变.

    图  5  固定化学势时序参量随相互作用强度的变化

    注:$ \Delta=0.5 $; a $ \mu=0.5 $,b $ \mu=1 $.

    图  6  相互作用强度和化学势平面内的相图

    注:各向异性强度$ \Delta=0.5 $; QSH+SSC表示QSH和SSC共存态;紫线和红线表示连续相变,绿线表示一级相变.

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出版历程
  • 收稿日期:  2023-07-21
  • 录用日期:  2023-09-06
  • 网络出版日期:  2023-09-17

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