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A striking example of frustration in physics is Hofstadter's butterfly, a fractal structure that emerges from the competition between a crystal's lattice periodicity and the magnetic length of an applied field. Current methods for…

Mesoscale and Nanoscale Physics · Physics 2025-03-04 Catalin D. Spataru , Wei Pan , Alexander Cerjan

While resonant modes do not exist within band gaps in infinite periodic materials, they may appear as in-gap localized edge modes once the material is truncated to form a finite periodic structure. Here, we provide an analysis framework…

Materials Science · Physics 2023-12-19 Matheus I. N. Rosa , Bruce L. Davis , Liao Liu , Massimo Ruzzene , Mahmoud I. Hussein

Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…

Mesoscale and Nanoscale Physics · Physics 2018-01-24 Thomas Fösel , Vittorio Peano , Florian Marquardt

Motivated by recent developments in quantum simulation of synthetic dimensions, e.g. in optical lattices of ultracold atoms, we discuss here $d$-dimensional periodic, gapped quantum systems for $d \le 4$, with focus on the topology of the…

Mathematical Physics · Physics 2023-02-06 Domenico Monaco , Thaddeus Roussigné

Quasiperiodic systems show a universal gap structure due to quasiperiodicity which is analogous to gap openings at the Brillouin zone boundary in periodic systems. The integrated density of states (IDoS) below those energy gaps are…

Strongly Correlated Electrons · Physics 2023-02-22 Mao Yoshii , Sota Kitamura , Takahiro Morimoto

We show that the fundamental time reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective field theory is described by the 4+1 dimensional Chern-Simons theory and the topological properties of the electronic…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Xiao-Liang Qi , Taylor Hughes , Shou-Cheng Zhang

Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological…

High Energy Physics - Theory · Physics 2007-05-23 Yishi Duan , Libin Fu , Hong Zhang

Energy or quasienergy (QE) band spectra depending on two parameters may have a nontrivial topological characterization by Chern integers. Band spectra of 1D systems that are spanned by just one parameter, a Bloch phase, are topologically…

Mesoscale and Nanoscale Physics · Physics 2017-10-02 Itzhack Dana

As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…

Mesoscale and Nanoscale Physics · Physics 2023-08-01 Kazuki Sone , Motohiko Ezawa , Yuto Ashida , Nobuyuki Yoshioka , Takahiro Sagawa

We represent a new approach to exploring the thermodynamic topology of black holes, without introducing the nonphysical variable $\Theta\in[0,\pi]$ considered in previous studies, where black holes can exchange both energy and matter with…

General Relativity and Quantum Cosmology · Physics 2025-10-29 Cao H. Nam

We investigate whether there could exist topological invariants of gapped 2D materials related to dissipationless thermoelectric transport at low temperatures. We give both macroscopic and microscopic arguments showing that thermoelectric…

Strongly Correlated Electrons · Physics 2021-07-13 Michael Levin , Anton Kapustin , Lev Spodyneiko

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate…

Superconductivity · Physics 2016-08-31 Y. Hatsugai , S. Ryu , M. Kohmoto

Quantum graphs provide an analytically tractable setting for the study of Chern numbers and band degeneracies in periodic systems. We study the Chern numbers of energy bands in a two-dimensional square lattice quantum graph. We approach the…

Mathematical Physics · Physics 2026-05-26 Or Swartzberg , Omri Gat , Boris Gutkin

In recent years, Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions. In this work, we investigate the effects of high-frequency time-periodic driving in a…

Mesoscale and Nanoscale Physics · Physics 2024-01-09 Zheng-Rong Liu , Rui Chen , Bin Zhou

We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…

Mathematical Physics · Physics 2023-07-04 Jui-Hui Chung , Jacob Shapiro

Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…

Quantum Physics · Physics 2016-06-01 Zhihuang Luo , Chao Lei , Jun Li , Xinfang Nie , Zhaokai Li , Xinhua Peng , Jiangfeng Du

We propose a two-spin quantum-mechanical model with applied magnetic fields acting on the Poincar\'e-Bloch sphere, to reveal a new class of topological energy bands with Chern number one half for each spin-1/2. The mechanism behind this…

Mesoscale and Nanoscale Physics · Physics 2023-02-07 Joel Hutchinson , Karyn Le Hur

The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional…

Mesoscale and Nanoscale Physics · Physics 2021-01-08 Sander H. Kooi , Guido van Miert , Carmine Ortix

Topological invariants are crucial for characterizing topological systems. However, experimentally measuring them presents a significant challenge, especially in non-Hermitian systems where the biorthogonal eigenvectors are often necessary.…

Quantum Physics · Physics 2025-04-23 Shuo Wang , Zhengjie Kang , Hao Li , Jiaojiao Li , Yuanjie Zhang , Zhihuang Luo

Chern insulator is a building block of many topological quantum matters, ranging from quantum spin Hall insulators to fractional Chern insulators. Here, we discuss a new type of insulator, which consists of two half filled ordinary Chern…

Mesoscale and Nanoscale Physics · Physics 2017-05-24 Li-Jun Lang , Shao-Liang Zhang , Qi Zhou