Takagi Topological Insulator on the Honeycomb Lattice

Abstract

Recently, real topological phases protected by $PT$ symmetry have been actively investigated. In two dimensions, the corresponding topological invariant is the Stiefel-Whitney number. A recent theoretical advance is that in the presence of the sublattice symmetry, the Stiefel-Whitney number can be equivalently formulated in terms of Takagi's factorization. The topological invariant gives rise to a novel second-order topological insulator with odd $PT$-related pairs of corner zero modes. In this article, we review the elements of this novel second-order topological insulator, and demonstrate the essential physics by a simple model on the honeycomb lattice.

References in corpus (12)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• Topology of crystalline insulators and superconductors
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Quasiparticle tunneling and 1/f charge noise in ultrastrongly coupled superconducting qubit and resonator

Cited by in corpus (2)

• Second-order topological insulator in Bilayer borophene
• Topological analysis of the complex SSH model using the quantum geometric tensor