Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition
Universal nonanalytic behavior of the Hall conductance in a Chern insulator at the topologically driven nonequilibrium phase transition
复制标题
拓扑驱动的非平衡相变陈绝缘体中霍尔电导的通用非解析行为
DOI：
10.1103/physrevb.93.085134
复制
发表时间：
2015-11
影响因子：
3.7
通讯作者：
Stefan Kehrein
中科院分区：
文献类型：
--
作者：
Pei Wang;Markus Schmitt;Stefan Kehrein
本文研究了在哈密顿量全局淬灭后，陈氏绝缘子的霍尔电导。将线性响应理论应用于对角系综，得到了长时间内的霍尔电导。它被表示为在布里渊区域上由占领数加权的贝里曲率的积分。我们确定了一个拓扑驱动的非平衡相变，这是由霍尔电导的非解析性作为猝灭后哈密顿量${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$中能量间隙${m}_{f}$的函数来表示的。猝灭态的拓扑不变量是格林函数$W$的圈数，它等于基态${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$的陈恩数。在极限${m}_{f}\ensuremath{\rightarrow}0$中，霍尔电导对${m}_{f}$的导数与$ln|{m}_{f}|$成正比，比例常数为$W$在${m}_{f}=0$处的变化与初始状态的能隙的比值。这种非解析行为在两波段陈氏绝缘体中是普遍存在的，如狄拉克模型、霍尔丹模型或费米子基的基塔耶夫蜂窝模型。
We study the Hall conductance of a Chern insulator after a global quench of the Hamiltonian. The Hall conductance in the long time limit is obtained by applying the linear response theory to the diagonal ensemble. It is expressed as the integral of the Berry curvature weighted by the occupation number over the Brillouin zone. We identify a topologically driven nonequilibrium phase transition, which is indicated by the nonanalyticity of the Hall conductance as a function of the energy gap ${m}_{f}$ in the post-quench Hamiltonian ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$. The topological invariant for the quenched state is the winding number of the Green's function $W$, which equals the Chern number for the ground state of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{f}$. In the limit ${m}_{f}\ensuremath{\rightarrow}0$, the derivative of the Hall conductance with respect to ${m}_{f}$ is proportional to $ln|{m}_{f}|$, with the constant of proportionality being the ratio of the change of $W$ at ${m}_{f}=0$ to the energy gap in the initial state. This nonanalytic behavior is universal in two-band Chern insulators such as the Dirac model, the Haldane model, or the Kitaev honeycomb model in the fermionic basis.
DOI：
10.1007/978-3-642-32858-9
发表时间：
2013-01
期刊：
--
影响因子：
--
作者：
S. Shen
通讯作者：
S. Shen