Disorder dependence of helical edge states in HgTe/CdTe quantum wells

In recent years, extensive attention has been focused on a new topological phase induced by nonmagnetic disorder, known as the topological Anderson insulator (TAI). In this work, we study the disorder strength dependence of the edge states in TAI phase in disordered HgTe/CdTe quantum wells. It is shown clearly that the disorder-induced edge states appear above a critical disorder strength after a gap-closing phase transition. These edge states are then found to decline with an increase of disorder strength in a stepwise pattern due to the finite-width effect, where the opposite edges couple to each other through the localized bulk states. This is in sharp contrast with the localization of the edge states themselves by time-reversal symmetry breaking. The size-independent phase boundaries are further obtained through scaling analysis, where a metallic phase is found separating two topologically distinct phases, which is due to the Fermi energy and mass renormalization.