Reflection symmetric second-order topological insulators and superconductors

TL;DR

This paper demonstrates how reflection symmetry can be used to systematically generate second-order topological insulators and superconductors, revealing new protected states and quantized Hall conductance in three dimensions.

Contribution

It introduces a method to generate second-order topological phases using reflection symmetry, expanding the classification of topological insulators and superconductors.

Findings

Reflection symmetry enables systematic construction of second-order topological phases.

Protected corner and edge states persist even if reflection symmetry is broken.

A 3D second-order topological insulator exhibits quantized Hall conductance.

Abstract

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of $e^2/h$.