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Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…

Strongly Correlated Electrons · Physics 2025-06-17 Chao Xu , Yunlong Zang , Yixin Ma , Yingfei Gu , Shenghan Jiang

An optical flux lattice is a set of light beams that couple different internal states of an atom, thereby producing topological energy bands. Here we present a configuration in which the atoms exhibit a dark state, i.e. an internal state…

Quantum Gases · Physics 2025-09-04 Sylvain Nascimbene , Jean Dalibard

We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…

Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…

Mesoscale and Nanoscale Physics · Physics 2019-05-29 Haiyan Fan , Baizhan Xia , Liang Tong , Shengjie Zheng , Dejie Yu

Edge states in 2D materials are vital for advancements in spintronics, quantum computing, and logic transistors. For graphene nanoribbons, it is well known that the zigzag edges can host edge states, but realization of armchair edge states…

Optics · Physics 2025-03-12 Qi Zhong , Yongsheng Liang , Shiqi Xia , Daohong Song , Zhigang Chen

The hallmark of topological insulators is the scatter-free propagation of waves in topologically protected edge channels. This transport is strictly chiral on the outer edge of the medium, and therefore capable of bypassing sharp corners…

We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and…

Strongly Correlated Electrons · Physics 2018-08-24 Yang-Zhi Chou , Rahul M. Nandkishore , Leo Radzihovsky

Topological optical states exhibit unique immunity to defects and the ability to propagate without losses rendering them ideal for photonic applications.A powerful class of such states is based on time-reversal symmetry breaking of the…

Optics · Physics 2018-02-07 Deng Pan , Rui Yu , Hongxing Xu , F. Javier García de Abajo

The edge states that emerge at hydrogen-terminated zigzag edges embedded in dominant armchair edges of graphite are carefully investigated by ultrahigh-vacuum scanning tunneling microscopy (STM) measurements. The edge states at the zigzag…

Materials Science · Physics 2009-11-11 Yousuke Kobayashi , Ken-ichi Fukui , Toshiaki Enoki , Koichi Kusakabe

A second-order topological insulator on a two-dimensional square lattice hosts zero-dimensional states inside a band gap. They are localized near $90^{\circ}$ and $270^{\circ}$ corners constituting an edge of the system. When the edge is in…

Mesoscale and Nanoscale Physics · Physics 2021-09-22 Yuki Nagasato , Yositake Takane , Yukinori Yoshimura , Shin Hayashi , Takeshi Nakanishi

We use a coherent Bragg diffraction method to impart an external momentum to ultracold bosonic atoms trapped in a one-dimensional optical lattice. This method is based on the application of a single light pulse, with conditions where…

Quantum Gases · Physics 2015-05-27 Xinxing Liu , Xiaoji Zhou , Wei Zhang , Thibault Vogt , Bo Lu , Xuguang Yue , Xuzong Chen

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of…

Mesoscale and Nanoscale Physics · Physics 2016-04-19 János K. Asbóth , László Oroszlány , András Pályi

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due…

We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The…

Strongly Correlated Electrons · Physics 2015-03-18 Linhu Li , Shu Chen

Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge…

We have studied topological edge states in bowtie ladders with various edge truncations. The symmetric bowtie ladder, which comprises two trivial Su-Schrieffer-Heeger (SSH) lattices, exhibits an insulator-metal transition with trivial…

Mesoscale and Nanoscale Physics · Physics 2020-12-02 Jung-Wan Ryu , Sungjong Woo , Nojoon Myoung , Hee Chul Park

An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge…

Mathematical Physics · Physics 2016-09-07 Charles L. Fefferman , James P. Lee-Thorp , Michael I. Weinstein

We study the topological optical states in one-dimensional (1D) dimerized ultracold atomic chains, as an extension of the Su-Schrieffer-Heeger (SSH) model. By taking the fully retarded near-field and far-field dipole-dipole interactions…

Optics · Physics 2018-08-15 B. X. Wang , C. Y. Zhao

Scattering theory has been suggested as a convenient method to identify topological phases of matter, in particular of disordered systems for which the Bloch band-theory approach is inapplicable. Here we examine this idea, employing as a…

Mesoscale and Nanoscale Physics · Physics 2024-03-14 Zhi-Hai Liu , O. Entin-Wohlman , A. Aharony , J. Q. You , H. Q. Xu

Topological photonics has recently emerged as a route to realize robust optical circuitry, and nonlinear effects are expected to enable tunability of topological states with the light intensity. Here we realize experimentally nonlinear…