Deep learning topological invariants of band insulators [PDF]
Physical review B, 2018 In this work we design and train deep neural networks to predict topological invariants for one-dimensional four-band insulators in AIII class whose topological invariant is the winding number, and two-dimensional two-band insulators in A class whose ...
Ning Sun +4 more
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Atiyah-Hirzebruch spectral sequence in band topology: General formalism and topological invariants for 230 space groups [PDF]
Physical review B, 2018 We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant K-theory in the context of band theory. Various notions in the band theory such as irreducible representations at high-symmetric points, the compatibility relation, topological ...
Ken Shiozaki, M. Sato, Kiyonori Gomi
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Topological invariants of time-reversal-invariant band structures [PDF]
, 2006 The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the $\mathbb{Z}_2$ invariant found by Kane and Mele.
Joel E. Moore, Joel E. Moore, L. Balents
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Local Noether theorem for quantum lattice systems and topological invariants of gapped states [PDF]
Journal of Mathematics and Physics, 2022 We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the ...
A. Kapustin, Nikita Sopenko
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Detecting Non-Bloch Topological Invariants in Quantum Dynamics. [PDF]
Physical Review Letters, 2021 Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology.
Kunkun Wang +5 more
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Unification of topological invariants in Dirac models [PDF]
Physical review B, 2021 Topological phases of materials are characterized by topological invariants that are conventionally calculated by different means according to the dimension and symmetry class of the system.
G. von Gersdorff, S. Panahiyan, Wei Chen
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Edge States and Topological Invariants of Non-Hermitian Systems. [PDF]
Physical Review Letters, 2018 The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates redefinition of topological invariants in a generalized Brillouin zone.
Shunyu Yao, Zhong Wang
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Measuring Topological Invariants in a Polaritonic Analog of Graphene.
Physical Review Letters, 2021 Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an
P. St-Jean +12 more
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Non-Hermiticity and topological invariants of magnon Bogoliubov–de Gennes systems [PDF]
Progress of Theoretical and Experimental Physics, 2020 Since the theoretical prediction and experimental observation of the magnon thermal Hall effect, a variety of novel phenomena that may occur in magnonic systems have been proposed.
H. Kondo, Y. Akagi, H. Katsura
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Non-Hermitian Topological Invariants in Real Space. [PDF]
Physical Review Letters, 2019 The topology of non-Hermitian systems is drastically shaped by the non-Hermitian skin effect, which leads to the generalized bulk-boundary correspondence and non-Bloch band theory.
F. Song, Shunyu Yao, Zhong Wang
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