Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice [PDF]
, 2016 The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of topological band theory,
Andersson, Erika +6 more
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Quantitative mappings between symmetry and topology in solids
Nature Communications, 2018 The defining quantities of topological materials—the topological invariants—are often difficult to calculate. Here, Song et al. report a simplified method to calculate both the symmetry data and the topological invariants for arbitrary gapped band ...
Zhida Song +3 more
doaj +1 more source
Topological gravity and Chern–Simons forms in d=4
Physics Letters B, 2015 Following the construction introduced by Antoniadis and Savvidy in Refs. [1–3], we study metric-independent topological invariants on a (2n+1)-dimensional space–time.
P. Catalán +3 more
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Symmetry representation approach to topological invariants in C2zT -symmetric systems [PDF]
Physical review B, 2018 We study the homotopy classification of symmetry representations to describe the bulk topological invariants protected by the combined operation of a two-fold rotation $C_{2z}$ and time-reversal $T$ symmetries.
J. Ahn, Bohm-Jung Yang
semanticscholar +1 more source
Lattice-Invariant Topological Properties [PDF]
Proceedings of the American Mathematical Society, 1972 The purpose of this paper is to show that an isomorphism between the lattices of all closed sets of two topological spaces induces an isomorphism on the lattices of their zero-sets. This is achieved by showing that any continuous real-valued function on a space X can be transferred to any space lattice-equivalent to X.
openaire +1 more source
Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators [PDF]
, 1996 The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians.
Mostafazadeh, Ali
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Measurement of Corner-Mode Coupling in Acoustic Higher-Order Topological Insulators
Frontiers in Physics, 2021 Recent developments of band topology have revealed a variety of higher-order topological insulators (HOTIs). These HOTIs are characterized by a variety of different topological invariants, making them different at a fundamental level.
Xiao Li +7 more
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Topological invariants for interface modes [PDF]
Communications in Partial Differential Equations, 2019 This article concerns topologically non-trivial interface Hamiltonians that find many applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected, asymmetric edge ...
G. Bal
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Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects [PDF]
, 2017 Periodically driven (Floquet) systems have been under active theoretical and experimental investigations. This paper aims at a systematic study in the following aspects of Floquet systems: (i) a systematic formulation of topological invariants of Floquet
Shunyu Yao, Zhongbo Yan, Zhong Wang
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Floquet engineering with particle swarm optimization: Maximizing topological invariants [PDF]
Physical review B, 2019 It is of theoretical and experimental interest to engineer topological phases with very large topological invariants via periodic driving. As advocated by this paper, such Floquet engineering can be elegantly achieved by the particle swarm optimization ...
Shikun Zhang, J. Gong
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