A New Universal Class of Anderson Transition in Two-Dimensional Systems

Anderson localization of non-interacting two-dimensional electron gas (2DEG) with spin-orbit interactions and in a magnetic field is studied. There are strong numerical evidences that symmetry and dimensionality alone are not enough to classify the metal-to-insulator transition (MIT) for conventionally called sympletctic class. By numerically studying the MIT of 2DEG on a square lattice with Rashba, Dresselhaus, or SU(2) spin-orbit interactions (SOI) in a magnetic field, it is found that the models with Rashba or Dresselhaus SOI undergo normal MIs in which the Anderson transition separates localized states from extended states. However, the models with random SU(2) SOI in a magnetic field has a KT-type transition that separates localized states from a band of critical states while the model supports a normal MIT in the absence of a magnetic field. Furthermore, the wavefunctions of all critical states have fractal structure whose universal dimension is about 1.88.