Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions

Abstract

Static disorder in a noninteracting gas of electrons confined to two dimensions can drive a continuous quantum (Anderson) transition between a metallic and an insulating state when time-reversal symmetry is preserved but spin-rotation symmetry is broken. The critical exponent $\ensuremath{\nu}$ that characterizes the diverging localization length and the bulk multifractal scaling exponents that characterize the amplitudes of the critical wave functions at the metal-insulator transition do not depend on the topological nature of the insulating state, i.e., whether it is topologically trivial (ordinary insulator) or nontrivial (a ${\mathbb{Z}}_{2}$ insulator supporting a quantum spin Hall effect). This is not true of the boundary multifractal scaling exponents, which we show (numerically) to depend on whether the insulating state is topologically trivial or not.