Two-dimensional spin-filtered chiral network model for theZ2quantum spin-Hall effect

Abstract

The effects of static disorder on the ${\mathbb{Z}}_{2}$ quantum spin-Hall effect for noninteracting electrons propagating in two-dimensional space are studied numerically. A two-dimensional time-reversal symmetric network model is constructed to account for the effects of static disorder on the propagation of noninteracting electrons subjected to spin-orbit couplings. This network model is different from past network models belonging to the symplectic symmetry class in that the propagating modes along the links of the network can be arranged into an odd number of Kramers doublet. It is found that (1) a two-dimensional metallic phase of finite extent is embedded in a ${\mathbb{Z}}_{2}$ insulating phase in parameter space and (2) the quantum phase transitions between the metallic and ${\mathbb{Z}}_{2}$ insulating phases belong to the conventional symplectic universality class in two space dimensions.