Symmetry-based indicators of band topology in the 230 space groups

By H. Po, Ashvin Vishwanath, Haruki Watanabe. Nature Communications, 2017

826 citations recorded by the source corpus.

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials. Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/6538143739703a6fd93b142a476a31442ff12589

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Topological Semimetals from First Principles (2018, background): “These attempts have led to a set of recent ideas centered around the notion of symmetry indicators (162, 163, 164, 165, 140).”
Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, neutral): “) The two topological invariants are the Chern number C and the number N1⁄4noð0;0Þ−noðπ;0Þ−noð0;πÞþnoðπ;πÞ, where nðkx; kyÞ is the number of occupied odd-parity bands at the high-symmetry momentum ðkx; kyÞ [16,18,21].”