Robustness Of Helical Hinge States Of Weak Second-Order Topological Insulators

Robustness of helical hinge states of three-dimensional weak second-order topological insulators (WSOTIs) against disorders is studied. The pure WSOTI is obtained from a weak Z(2) first-order topological insulator through a surface band inversion. Both bulk states and surface states in the WSOTI are gapped, and in-gap valley-momentum locked helical hinge states are topologically protected by the surface valley-Chern number. In the presence of weak disorders, helical hinge states are robust against disorders while the quantized conductance of the states is fragile due to the intervalley scattering. As disorder increases, the system undergoes a series of quantum phase transitions: from the WSOTI to the weak first-order topological insulator, then to a diffusive metal and finally to an Anderson insulator. Our results thus fully establish the WSOTI phase as a genuine state of matters and open a door for the second-order valleytronics that allows one to control the valley degree of freedom through helical hinge states.