二维中的局域时间反演不变拓扑标记
Local time-reversal-invariant topological markers in two dimensions
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中文总结 AI 辅助
本文提出一种局域陈-西蒙斯后裔标记，用于表征二维时间反演不变拓扑态，并给出选择对合S的实用方法，适用于强自旋轨道耦合和无序系统。
中文摘要 AI 辅助
局域拓扑标记提供了拓扑相在实空间中的表征，适用于非晶体模型。我们从单粒子密度矩阵ρ出发，推导了一种局域拓扑标记——陈-西蒙斯后裔标记，用于表征二维时间反演不变的近高斯态的拓扑性质。我们构造了一个由局域陈-西蒙斯标记表征的辅助三维态，并利用维数约化得到原始二维态的陈-西蒙斯后裔标记。这一推导引入了一个在时间反演下为奇的局域厄米对合S。当[S,ρ]=0时，局域陈-西蒙斯后裔标记约化为S=±1扇区中局域陈标记之差的一半。构造一个与ρ精确对易的S通常需要精细调节，但这并非必需——只要Γ={ρ,S}-S在零附近具有谱隙，局域陈-西蒙斯标记就保持良定义，即使[S,ρ]≠0。这留下了为给定态识别合适S的实际问题，重要的是，即使自旋不是候选者，这一问题也易于解决。我们通过考虑强Rashba和Dresselhaus自旋轨道耦合来展示这一点，对于这些情况，对态物理起源的了解将选择S的一般问题简化为单参数族S(θ)。我们假设平移不变性，解析地评估了使Γ谱隙最大化的最优角度θ，并发现Γ的谱隙在最优角度周围较宽的角度范围内保持开启。相同的θ值在无序系统中仍然有效，为评估态的局域陈-西蒙斯后裔标记提供了一种简便的S选择方法。
英文摘要
Local topological markers provide a real-space characterization of topological phases and are suited to noncrystalline models. We derive a local topological marker, the Chern-Simons descendant marker, for characterizing the topology of two-dimensional time-reversal-invariant near-Gaussian states from the one-particle density matrix \(ρ\). We construct an auxiliary three-dimensional state characterized by the local Chern-Simons marker, and use dimensional reduction to obtain the Chern-Simons descendant marker for the original two-dimensional state. This derivation introduces a local Hermitian involution \(S\) that is odd under time reversal. When \([S,ρ]=0\), the local Chern-Simons descendant marker reduces to half the difference of the local Chern markers in the \(S=\pm1\) sectors. Constructing an \(S\) that commutes exactly with \(ρ\) generally requires fine-tuning, but this is not needed---the local Chern-Simon marker remains well defined whenever \(Γ=\{ρ,S\}-S\) has a spectral gap around zero, even when \([S,ρ]\neq0\). This leaves the practical problem of identifying a suitable \(S\) for a given state, which, importantly, is straightforward even when spin is not a candidate. We show this by considering both strong Rashba and Dresselhaus spin-orbit coupling, for which knowledge of the physical origin of the state reduces the general problem of choosing $S$ to a one-parameter family \(S(θ)\). We evaluate the optimal angle $θ$ maximizing the spectral gap of $Γ$ analytically assuming translation invariance, and find that the gap of $Γ$ remains open for a broad range of angles around the optimum. The same value of \(θ\) remains valid in disordered systems, providing an easy way to obtain choice of \(S\) for evaluating the local Chern-Simons descendant marker of the state.
发表机构
- KTH Royal Institute of Technology（皇家理工学院）
- Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0US, United Kingdom（剑桥大学卡文迪什实验室）
机构由 AI 辅助整理，请以论文原文为准。
