Topological States in Generalized Electric Quadrupole Insulators

Abstract

The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlying crystalline symmetries. Henceforth, it is natural to ask what are the consequences of symmetry breaking in these higher multipole insulators. In this work, we investigate topological phases and the consequences of symmetry breaking in generalized electric quadrupole insulators. Explicitly, we generalize the Benalcazar-Bernevig-Hughes model by adding specific terms in order to break the crystalline and non-spatial symmetries. Our results show that chiral symmetry breaking induces an indirect gap phase which hides corner modes in bulk bands, ruining the topological quadrupole phase. We also demonstrate that quadrupole moments can remain quantized even when mirror symmetries are absent in a generalized model. Furthermore, it is shown that topological quadrupole phase is robust against a unique type of disorder presented in the system.

arXiv comment12 pages, 10 figures, and 1 table. Published version

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• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Higher-order Fabry-Pérot Interferometer from Topological Hinge States
• Klein-bottle quadrupole insulators and Dirac semimetals
• Density-driven higher-order topological phase transitions in amorphous solids
• Chiral Majorana Hinge Modes in Superconducting Dirac Materials
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Structural disorder-induced topological phase transitions in quasicrystals
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Corner and Edge States in Topological Sierpinski Carpet Systems
• Random-Flux-Induced Transition Sequence between Weak and Strong Topological Phases with Anisotropic Localization Properties
• Establishing quasi-linear quadrupole functional topology by oxygen-vacancy engineering at a ferroelectric domain wall
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Magnetic doping-induced second-order and first-order topological phase transition inthe photonic alloy