Wang C, Su Ying, Avishai Y, Meir Yigal, Wang X R
Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.
HKUST Shenzhen Research Institute, Shenzhen 518057, China.
Phys Rev Lett. 2015 Mar 6;114(9):096803. doi: 10.1103/PhysRevLett.114.096803. Epub 2015 Mar 5.
The Anderson localization problem for a noninteracting two-dimensional electron gas subject to a strong magnetic field, disordered potential, and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on whether the spin-orbit coupling is uniform or fully random. For uniform spin-orbit coupling (such as Rashba coupling due to a uniform electric field), there is a band of metallic extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy E_{c}, the localization length diverges as ξ(E)∝exp(α/sqrt[|E-E_{c}|]), a behavior which, together with the emergence of a band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.
在正方形晶格上对受强磁场、无序势和自旋轨道耦合作用的非相互作用二维电子气的安德森局域化问题进行了数值研究。相应的局域化 - 退局域化转变的性质以及相关扩展态的性质取决于自旋轨道耦合是均匀的还是完全随机的。对于均匀自旋轨道耦合（例如由均匀电场引起的 Rashba 耦合），如同在“标准”安德森金属 - 绝缘体转变中一样，在朗道带中心存在一个金属扩展态带。然而，对于完全随机自旋轨道耦合，熟悉的朗道带模式消失了。取而代之的是，存在一个具有确定分形结构的临界态中心带，在两个临界能量处与两个局域态边带分开。此外，有限尺寸标度分析表明，对于这种新型转变，在临界能量(E_{c})的局域化一侧，局域化长度按(\xi(E)\propto\exp(\alpha /\sqrt{|E - E_{c}|}))发散，这种行为与临界态带的出现一起让人联想到 Berezinskii - Kosterlitz - Thouless 转变。
