Second-order topological insulators and superconductors with an order-two crystalline symmetry

By M. Geier, Luka Trifunovic, Max S M Hoskam, P. Brouwer. 2018

317 citations recorded by the source corpus.

Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys. Rev. B 90, 165114 (2014)PRBMDO1098-012110.1103/PhysRevB.90.165114], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all corresponding second-order topological insulators and superconductors. The classification also includes antiunitary symmetries and antisymmetries.

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

View Paper: https://www.semanticscholar.org/paper/74599b0a6177cd0781e05125b7be3654280f1ae1

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle (2018, background): “The surface degrees of freedom are given by projecting the matrices under P (θ) = 12 (1 + iΓ1(θ)Γ3), and H 0 ≡ −(PΓ2P )Ri∂θ|r=R describes the two oppositely-propagating chiral edge states [67, 68, 78].”
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].”
Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, background): “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”