论文标题
在三维二阶拓扑绝缘子中，无序诱导的量子相变
Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
论文作者
论文摘要
对三维二阶拓扑绝缘子（3DSOTI）的障碍影响进行数值和分析研究。这项研究基于一个在立方晶格上的非相互作用电子的紧密结合哈密顿，其反射对称性在没有疾病的情况下支持3DSTI。有趣的是，与疾病对拓扑琐碎系统的影响不同，该系统只能是扩散金属（DM）或Anderson绝缘子（AI），疾病可以依次诱导3DSOTIS的四个阶段，三维一维一阶拓扑辅导剂（3DFOTIS），DMS和AIS。当强度$ w $的现场随机潜力低于低临界值$ w_ {c1} $时，地面状态的间隙仍在闭合，而整个批量仍然存在，该系统是一个恒定状态密度和量化整数的特征，该系统是$ e e^2/h $ a $ e^2/h $ a $ h $ a $ h $ a $ h $。批量状态的差距以较高的严重疾病$ W_ {C2} $结束，并且该系统是$ W_ {C1} $和$ W_ {C2} $之间的较低中间疾病中的无序3DFOTI，其中电子传导通过拓扑表面状态。该系统在$ W_ {C2} $和$ W_ {C3} $之间的较高中级疾病中变成了DM，在Fermi级别的状态是本地化的。它在$ w_ {c3} $上经历了普通的三维金属到绝缘子的过渡，并成为$ w> w_ {c3} $的常规AI。自洽的天生近似使人们可以看到散装状态的密度和狄拉克质量如何通过现场疾病来修饰。
Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for non-interacting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topologicalinsulators (3DFOTIs), DMs and AIs. At a weak disorder when the on-site random potential of strength $W$ is below a low critical value $W_{c1}$ at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of $e^2/h$ through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder $W_{c2}$, and the system is a disordered 3DFOTI in a lower intermediate disorder between $W_{c1}$ and $W_{c2}$ in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between $W_{c2}$ and $W_{c3}$ above which the states at the Fermi level are localized. It undergoes a normal three-dimension metal-to-insulator transition at $W_{c3}$ and becomes the conventional AI for $W>W_{c3}$. The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.
