Reflection symmetric second-order topological insulators and superconductors

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 $e^2/h$.

13 pages with supplemental material

References in corpus (8)

• Topological Crystalline Insulators
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• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
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Cited by in corpus (22)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Realization of an acoustic third-order topological insulator
• Higher-Order Weyl Semimetals
• Observation of a Majorana zero mode in a topologically protected edge channel
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Plasmon-polaritonic quadrupole topological insulators
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Hinged Quantum Spin-Hall Effect in Antiferromagnetic Topological Insulators
• Observation of backscattering induced by magnetism in a topological edge state
• Boundary edge networks induced by bulk topology
• Hinge states in a system of coupled Rashba layers
• Interaction-Driven Topological Switch in a $P$-Band Honeycomb Lattice
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• Higher-order Quantum Spin Hall Effect of Light