Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators

By E. Khalaf, H. Po, Ashvin Vishwanath, Haruki Watanabe. Physical Review X, 2017

258 citations recorded by the source corpus.

The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the symmetries at hand. While isolated examples of TCI have been identified and studied, the same variety demands a unified theoretical framework. In this work, we show how the surfaces of TCIs can be analyzed within a general surface theory with multiple flavors of Dirac fermions, whose mass terms transform in specific ways under crystalline symmetries. We identify global obstructions to achieving a fully gapped surface, which typically lead to gapless domain walls on suitably chosen surface geometries. We perform this analysis for all 32 point groups, and subsequently for all 230 space groups, for spin-orbit-coupled electrons. We recover all previously discussed TCIs in this symmetry class, including those with "hinge" surface states. Finally, we make connections to the bulk band topology as diagnosed through symmetry-based indicators. We show that spin-orbit-coupled band insulators with nontrivial symmetry indicators are always accompanied by surface states that must be gapless somewhere on suitably chosen surfaces. We provide an explicit mapping between symmetry indicators, which can be readily calculated, and the characteristic surface states of the resulting TCIs.

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

View Paper: https://www.semanticscholar.org/paper/2140f491db361900d78ee9b073ed1823d141a31f

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, background): “[33] Eslam Khalaf, Hoi Chun Po, Ashvin Vishwanath, and Haruki Watanabe, “Symmetry indicators and anomalous surface states of topological crystalline insulators,” Phys.”
Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, methodology): “Two approaches have been taken for the classification of anomalous, termination-independent HOTPs: A bulk-based approach, which starts from the classification of the bulk band structure and then shows under which circumstances a nontrivial bulk topology implies a higher-order topological phase [30,4”
Higher-order non-Hermitian skin effect (2020, background): “Recently, higher-order counterparts of topological phases were revealed and investigated extensively [7–19].”