(d-2)-Dimensional Edge States of Rotation Symmetry Protected Topological States.

By Zhida Song, Z. Fang, Chen Fang. Physical Review Letters, 2017

739 citations recorded by the source corpus.

We study fourfold rotation-invariant gapped topological systems with time-reversal symmetry in two and three dimensions (d=2, 3). We show that in both cases nontrivial topology is manifested by the presence of the (d-2)-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through the explicit construction of microscopic models having robust (d-2)-dimensional edge states.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/58bba820eb1cc5db921e8cf19caaffa7792816e9

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Corner states of light in photonic waveguides (2018, background): “states localised to corners of two- or three-dimensional lattices or the hinges of three-dimensional lattices [11, 12, 13, 14, 15, 16, 17].”
Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, background): “Depending on the geometry, this phase may feature “hinge” type 1D edge states [19, 23] which we will discuss in Sec.”
Observation of second-order topological insulators in sonic crystals (2018, background): “Recently, by gapping out the edge states of topological insulators, HOTIs are created, where robust corner or hinge states emerge in the edge gap due to topological mechanisms [24-35].”