Pfaffian formalism for higher-order topological insulators

Abstract

We generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of four-fold rotational symmetry $C_4$ and the time-reversal symmetry $T$. This Pfaffian description reveals a deep and fundamental link between TIs and HOTIs, and allows important conclusions about TIs to be generalized to HOTIs. As examples, we demonstrate in the Letter how to generalize Fu-Kane's parity criterion for TIs to HOTIs, and also present a general method to efficiently compute the $Z_2$ index of 3D chiral HOTIs without a global gauge.

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• Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology
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• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Hinge solitons in three-dimensional second-order topological insulators
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Dynamical Piezomagnetic Effect in Time-Reversal Invariant Weyl Semimetals with Axionic Charge-Density Waves
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Floquet higher-order topological phases in momentum space
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Gapless Fermionic Systems as Phase-space Topological Insulators: Non-perturbative Results from Anomalies
• Pfaffian invariant identifies magnetic obstructed atomic insulators
• Gapless Criterion for Crystals from Effective Axion Field
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Scattering theory of higher order topological phases
• Intrinsic (Axion) Statistical Topological Insulator
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges