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 $\nu$ 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 $Z_2$ 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.

12 pages, 13 figures, selected for an Editors' Suggestion in PRB

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Exact relations between multifractal exponents at the Anderson transition
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Boundary multifractality in critical 1D systems with long-range hopping

Cited by in corpus (6)

• Anderson Transitions
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Thermal metal-insulator transition in a helical topological superconductor
• Conductance distributions in disordered quantum spin-Hall systems
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• Conductance Distribution in Disordered Quantum Wires with a Perfectly Conducting Channel