Department of Physics, PUC-Rio, Rio de Janeiro 22451-900, Brazil.
J Phys Condens Matter. 2023 Feb 17;35(15). doi: 10.1088/1361-648X/acba72.
In two-dimensional time-reversal symmetric topological insulators described by Dirac models, theZ2topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry curvature that integrates to the spin Chern number, and introduce its spectral function that can be measured at finite temperature by momentum- and spin-resolved circular dichroism, which may be achieved by pump-probe type of experiments using spin- and time-resolved ARPES. As a result, the sign of the Pfaffian of theZ2invariant can be directly measured. A spin Chern number spectral function is further introduced from the optical spin current response, and is shown to be measurable from the spin-resolved opacity of two-dimensional materials under circularly polarized light, pointing to an optical measurement of theZ2invariant and a frequency sum rule. The spin Chern number expressed in real space is known to yield a spin Chern marker, and we propose that it may be measurable from spin-resolved local heating rate caused by circularly polarized light. A nonlocal spin Chern marker is further proposed to characterize the quantum criticality near topological phase transitions, and is shown to be equivalent to an overlap between spin-selected Wannier states.
在由狄拉克模型描述的二维时间反转对称拓扑绝缘体中，Z2拓扑不变量可以用自旋陈数来描述。我们提出了一种线性响应理论来描述自旋Berry 曲率，它可以积分到自旋陈数，并且引入了它的谱函数，通过动量和自旋分辨圆二色性可以在有限温度下测量，这可以通过使用自旋和时间分辨 ARPES 的泵浦探测类型的实验来实现。结果，Z2不变量的 Pfaffian 的符号可以直接测量。进一步从光学自旋电流响应中引入了自旋陈数谱函数，并表明可以从二维材料在圆偏振光下的自旋分辨不透明度中测量，这指向了 Z2不变量的光学测量和频率和规则。在实空间中表示的自旋陈数已知可以产生自旋陈数标记，我们提出它可能可以通过圆偏振光引起的自旋分辨局部加热率来测量。进一步提出了非局域自旋陈数标记来表征拓扑相变附近的量子临界点，并且被证明等同于自旋选择的 Wannier 态之间的重叠。
