Open AccessJournal Article
Reflection symmetric second-order topological insulators and superconductors
TLDR
It is shown that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners or at crystal edges continue to exist if reflection symmetry is broken.Abstract:
Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but with topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of e^{2}/h.read more
Citations
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References
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Book
Topological Insulators and Topological Superconductors
TL;DR: Topological insulators and superconductors as discussed by the authors are one of the most exciting areas of research in condensed matter physics and have been studied extensively in the last few decades and decades.
Journal ArticleDOI
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems.
TL;DR: This work provides a comprehensive framework for generalized bulk-boundary correspondence and a quantized biorthogonal polarization that is formulated directly in systems with open boundaries, including exactly solvable non-Hermitian extensions of the Su-Schrieffer-Heeger model and Chern insulators.
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Higher-Order Topological Insulators
Frank Schindler,A. M. Cook,Maia G. Vergniory,Maia G. Vergniory,Zhijun Wang,Stuart S. P. Parkin,B. Andrei Bernevig,B. Andrei Bernevig,B. Andrei Bernevig,Titus Neupert +9 more
TL;DR: The notion of three-dimensional topological insulators is extended to systems that host no gapless surface states but exhibit topologically protected gapless hinge states and it is shown that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topology insulators.
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A complete catalogue of high-quality topological materials
Maia G. Vergniory,Maia G. Vergniory,Maia G. Vergniory,Luis Elcoro,Claudia Felser,Nicolas Regnault,B. Andrei Bernevig,B. Andrei Bernevig,B. Andrei Bernevig,Zhijun Wang,Zhijun Wang +10 more
TL;DR: Using a recently developed formalism called topological quantum chemistry, a high-throughput search of ‘high-quality’ materials in the Inorganic Crystal Structure Database is performed and it is found that more than 27 per cent of all materials in nature are topological.
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Higher-Order Topological Insulators and Semimetals on the Breathing Kagome and Pyrochlore Lattices.
TL;DR: A second-order topological insulator in d dimensions is an insulator which has no d-1 dimensional topological boundary states but has d-2 dimensional topology boundary states, which constitutes the bulk topological index.