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Related papers: Bulk-Edge Correspondence for Finite Two-dimensiona…

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Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…

Mesoscale and Nanoscale Physics · Physics 2020-11-30 Ananya Ghatak , Martin Brandenbourger , Jasper van Wezel , Corentin Coulais

The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…

Optics · Physics 2022-02-09 Samaneh Pakniyat , S. Ali Hassani Gangaraj , George W Hanson

The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. For topological superconductors in two…

Mesoscale and Nanoscale Physics · Physics 2017-11-22 Nicholas Sedlmayr , Vardan Kaladzhyan , Clément Dutreix , Cristina Bena

Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…

Mathematical Physics · Physics 2025-05-12 Gian Michele Graf , Alessandro Tarantola

We substantiate a complete picture of the "bulk-edge correspondence" conjecture for topological phases. By studying the eigenstates in the entanglement spectrum for both the ideal and realistic Coulomb ground state of the fractional quantum…

Strongly Correlated Electrons · Physics 2019-01-29 Bin Yan , Rudro R. Biswas , Chris H. Greene

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary…

Mesoscale and Nanoscale Physics · Physics 2020-04-29 Elis Roberts , Jan Behrends , Benjamin Béri

We perform both analytical and numerical studies of the one-dimensional tight-binding Hamiltonian with stochastic uncorrelated on-site energies and non-fluctuating long-range hopping integrals . It was argued recently [A. Rodriguez at al.,…

Disordered Systems and Neural Networks · Physics 2009-11-10 F. A. B. F. de Moura , A. V. Malyshev , M. L. Lyra , V. A. Malyshev , F. Dominguez-Adame

We report on the transition from magnetic edge to electric edge transport in a split magnetic gate device which applies a notch magnetic field to a two-dimensional electron gas. The gate bias allows tuning the overlap of magnetic and…

Mesoscale and Nanoscale Physics · Physics 2017-08-09 Alain Nogaret , Puja Mondal , Ankip Kumar , Sankalpa Ghosh , Harvey Beere , David Ritchi

We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal…

Disordered Systems and Neural Networks · Physics 2018-09-12 Tong Liu , Hao Guo

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…

Mathematical Physics · Physics 2016-10-28 Julio Cesar Avila , Hermann Schulz-Baldes , Carlos Villegas-Blas

We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…

K-Theory and Homology · Mathematics 2025-09-12 Shin Hayashi

Topological insulators in three spatial dimensions are known to possess a precise bulk/boundary correspondence, in that there is a one-to-one correspondence between the 5 classes characterized by bulk topological invariants and Dirac…

Strongly Correlated Electrons · Physics 2015-06-04 Denis Bernard , Eun-Ah Kim , André LeClair

Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge…

Strongly Correlated Electrons · Physics 2023-09-08 Dean Johnstone , Matthew J. Colbrook , Anne E. B. Nielsen , Patrik Öhberg , Callum W. Duncan

Nonlinear transport has emerged as a powerful approach to probe the quantum geometry of electronic wavefunctions, such as Berry curvature and quantum metric, in topological materials. While nonlinear responses governed by bulk quantum…

Mesoscale and Nanoscale Physics · Physics 2025-12-09 Deyi Zhuo , Xiaoda Liu , Huu-Thong Le , Annie G. Wang , Han Tay , Bomin Zhang , Ling-Jie Zhou , Binghai Yan , Chao-Xing Liu , Cui-Zu Chang

We consider Haldane-like $2d$ topological insulators on the cylinder, in the presence of weak quasi-periodic disorder. We prove that, at large distances, the boundary correlations agree with the correlations of a renormalized,…

Mathematical Physics · Physics 2024-10-08 Fabrizio Caragiulo , Vieri Mastropietro , Marcello Porta

We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…

Disordered Systems and Neural Networks · Physics 2016-03-11 Yevgeny Bar Lev , David R. Reichman

We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk…

Mesoscale and Nanoscale Physics · Physics 2009-01-05 Ningning Hao , Ping Zhang , Zhigang Wang , Wei Zhang , Yupeng Wang

The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…

Mathematical Physics · Physics 2026-01-21 Huajie Song , Haitao Xu

We study the edge transport properties of $2d$ interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the…

Mathematical Physics · Physics 2018-08-15 Giovanni Antinucci , Vieri Mastropietro , Marcello Porta

Continuum grid-like frames composed of rigidly jointed beams are classic subjects in the field of structural mechanics, whose topological dynamical properties have only recently been revealed. For two-dimensional frames, higher-order…

Materials Science · Physics 2026-05-05 Yimeng Sun , Jiacheng Xing , Li-Hua Shao , Jianxiang Wang