论文标题
量子自旋效应中运输系数的新方法
A new approach to transport coefficients in the quantum spin Hall effect
论文作者
论文摘要
我们研究了旋转传输量子理论中的一些基本问题，在普遍的情况下，鉴于Rashba互动，不受干扰的汉密尔顿操作员$ H_0 $不与旋转操作员上下班，就像量子旋转厅效应的典型模型中一样。 通过在$ j $ -th的方向上添加一个恒定的强度电场$ \ varepsilon \ ll 1 $ 1 $的恒定电场，并在$ i $ $ i $中计算出$ s $ crurnent的线性响应，从而计算出$ s $ n的线性响应，$ j $ theques $ j $ theper of $ j $ - s $是计算$ s $ s $，$ j $ h_0 $ h_0 $ h_0 $通过$ j $ thioreed in $ j $ thireect中的恒定电场来受到干扰。我们为自旋电导率提供了一个通用公式，该公式涵盖了常规旋转电流操作员的选择。我们研究了自旋电导率从基本细胞的选择（单位细胞一致性）的独立性，并分离了一个离散周期模型的子类，在这些模型中，常规和适当的$ s $传导性同意，因此表明，关于旋转当前操作员的选择至关重要。由于一般理论，我们得到的是，每当旋转（几乎）保守时，自旋电导率都会（大约）等于自旋切尔克数。该方法依赖于非平衡几乎平稳状态（NEASS）的表征，该状态符合系统的物理状态（从空间 - 绝热扰动理论的意义上），并且允许计算绝热$ s $ current的响应，因为$ s $ s $ s $ s $ s $ current Murrent timer the neass the neass the neass the neass the neass the neass the neass the neass the Neass。该技术可以应用于一般框架，其中包括离散模型和连续模型。
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator $H_0$ does not commute with the spin operator in view of Rashba interactions, as in the typical models for the Quantum Spin Hall effect. A gapped periodic one-particle Hamiltonian $H_0$ is perturbed by adding a constant electric field of intensity $\varepsilon \ll 1$ in the $j$-th direction, and the linear response in terms of a $S$-current in the $i$-th direction is computed, where $S$ is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (Unit Cell Consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper $S$-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic $S$-current as the trace per unit volume of the $S$-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models.
