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Related papers: The Bulk-Edge Correspondence in Three Simple Cases

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We investigate higher-order topological insulators protected by chiral and anticommuting mirror symmetries. Using models in the BDI class, which include the prototypical topological quadrupole insulator, we show that breaking mirror…

Mesoscale and Nanoscale Physics · Physics 2025-12-16 Suman Aich , Babak Seradjeh

The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of…

Optics · Physics 2019-03-06 Mario G. Silveirinha

Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…

Other Condensed Matter · Physics 2024-06-17 Yohei Onuki , Antoine Venaille , Pierre Delplace

The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose…

Strongly Correlated Electrons · Physics 2023-12-21 Nick G. Jones , Ryan Thorngren , Ruben Verresen

Excitonic insulator remains elusive and there has been a lack of reliable identification methods. In this work, we demonstrate the promise of topological excitonic insulators for identification due to their unique bulk-edge correspondence,…

Strongly Correlated Electrons · Physics 2025-10-28 Hongwei Qu , Zeying Zhang , Yuanchang Li

Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…

Mathematical Physics · Physics 2015-12-04 Krzysztof Gawedzki

In this paper, we rigorously prove the bulk-edge correspondence for finite two-dimensional ergodic disordered systems. Specifically, we focus on the short-range Hamiltonians with ergodic disordered on-site potentials. We first introduce the…

Mathematical Physics · Physics 2025-12-15 Habib Ammari , Jiayu Qiu

Electronic topological insulators are one of the breakthroughs of the 21st century condensed matter physics. So far, the search for a light counterpart of an electronic topological insulator has remained elusive. This is due to the…

Mesoscale and Nanoscale Physics · Physics 2016-02-05 Mario G. Silveirinha

Bulk-boundary correspondence is a fundamental principle in topological physics. In recent years, there have been considerable efforts in extending the idea of geometry and topology to classical stochastic systems far from equilibrium.…

Mesoscale and Nanoscale Physics · Physics 2024-05-02 Taro Sawada , Kazuki Sone , Kazuki Yokomizo , Yuto Ashida , Takahiro Sagawa

We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological…

Mathematical Physics · Physics 2025-07-18 David Gontier , Clément Tauber

We establish a quantitative bulk-boundary correspondence in interacting topological insulators by relating many-body topological invariants to characteristic degeneracy structures in the entanglement spectrum. Focusing on generalized…

Mesoscale and Nanoscale Physics · Physics 2026-04-15 Kiran Babasaheb Estake , Dibyendu Roy

We study the bulk-edge correspondence in topological insulators by taking Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant in this model is Z2 invariant modulo the spectral flow of a single-parameter family of…

Mesoscale and Nanoscale Physics · Physics 2017-02-22 Yue Yu , Yong-Shi Wu , Xincheng Xie

We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends.…

Mesoscale and Nanoscale Physics · Physics 2016-09-15 Arbel Haim , Konrad Wölms , Erez Berg , Yuval Oreg , Karsten Flensberg

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase…

Strongly Correlated Electrons · Physics 2019-08-14 Antonio Zegarra , Denis R. Candido , J. Carlos Egues , Wei Chen

The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions…

Mesoscale and Nanoscale Physics · Physics 2013-02-20 Ken Shiozaki , Satoshi Fujimoto

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that…

Strongly Correlated Electrons · Physics 2019-10-09 Jun Ho Son , Jason Alicea

The one-to-one relation between the winding number and the number of robust zero-energy edge states, known as bulk-boundary correspondence, is a celebrated feature of 1d systems with chiral symmetry. Although this property can be explained…

Mesoscale and Nanoscale Physics · Physics 2024-02-01 Chen-Shen Lee

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional…

The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional…

Strongly Correlated Electrons · Physics 2021-06-02 Tohru Kawarabayashi , Yasuhiro Hatsugai

Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological…

Analysis of PDEs · Mathematics 2024-04-23 Guillaume Bal , Jiming Yu