title: Band of critical States in anderson localization in a strong magnetic field with random spin-orbit scattering.
abstract: 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.
authors: Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.|HKUST Shenzhen Research Institute, Shenzhen 518057, China.
authors: C
authors: C
authors: Wang
authors: Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.|HKUST Shenzhen Research Institute, Shenzhen 518057, China.
authors: Ying
authors: Y
authors: Su
authors: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
authors: Y
authors: Y
authors: Avishai
authors: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
authors: Yigal
authors: Y
authors: Meir
authors: Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong.|HKUST Shenzhen Research Institute, Shenzhen 518057, China.
authors: X R
authors: XR
authors: Wang