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

Abstract

Robustness of helical hinge states of three-dimensional weak second-order topological i sulators (WSOTIs) against disorders is studied. The pure WSOTI is obtained from a weak ${\mathbb{Z}}_2$ 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 inter-valley 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.

6 pages, 4 figures

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• Quantized charge-pumping in higher-order topological insulators
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Hinge modes of three-dimensional Euler insulators