Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2012 Dec 14;109(24):246605. doi: 10.1103/PhysRevLett.109.246605.
A field theory of the Anderson transition in two-dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortexlike topological defects is essential for localization. The sign of vortex fugacity determines the Z(2) topological class of the localized phase. There are two distinct fixed points with the same critical exponents, corresponding to transitions from a metal to an insulator and a topological insulator, respectively. The critical conductivity and correlation length exponent of these transitions are computed in an N=1-[symbol: see text] expansion in the number of replicas, where for small [symbol: see text] the critical points are perturbatively connected to the Kosterlitz-Thouless critical point. Delocalized states, which arise at the surface of weak topological insulators and topological crystalline insulators, occur because vortex proliferation is forbidden due to the presence of symmetries that are violated by disorder, but are restored by disorder averaging.
发展了二维无序系统中具有轨道-自旋相互作用和时间反演对称性的安德森相变的场论，其中涡旋拓扑缺陷的增殖对于局域化是必不可少的。涡旋费米子的符号决定了局域相的 Z(2)拓扑类。存在两个具有相同临界指数的不同固定点，分别对应于金属到绝缘体和拓扑绝缘体的转变。在复数量 N=1-[符号：见正文]展开中计算了这些转变的临界电导率和相关长度指数，其中对于小的[符号：见正文]，临界点可以通过与科斯特利茨-图尔勒斯临界点的微扰连接来处理。由于无序破坏了对称性，但通过无序平均又恢复了对称性，因此在弱拓扑绝缘体和拓扑晶体绝缘体的表面上出现了非局域态。
