Topologically Protected Edge States in Triangular Lattices

Abstract

We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the perspective of Berry curvature, but result instead from an interplay between crystalline symmetries and finite boundary effects. Regardless, we show such states are in a distinct topological phase, provided the gauge-dependent symmetries are maintained. Such a model describes a number of recent bosonic experimental demonstrations on triangular lattices, the physics for which has thus far eluded explanation.

12 pages, 10 figures. Accepted to Physical Review B

References in corpus (9)

• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Novel Topological Phase with Zero Berry Curvature
• Marginality of bulk-edge correspondence for single-valley Hamiltonians
• Generalized Bloch theorem and topological characterization
• Discovery of Ĉ${}_2$ rotation anomaly in topological crystalline insulator SrPb

Cited by in corpus (2)

• On-chip unidirectional waveguiding for surface acoustic waves along a defect line in a triangular lattice
• Design of a room-temperature topological exciton-polariton laser in a ZnO/TiO${}_2$-photonic crystal slab