Edge State Dynamics Along Curved Interfaces

Bal, Guillaume; Becker, Simon; Drouot, Alexis; Kammerer, Clotilde Fermanian; Lu, Jianfeng; Watson, Alexander B.

doi:10.1137/22m1489708

Edge State Dynamics Along Curved Interfaces

Journal Article · 12 September 2023 · SIAM Journal of Mathematical Analysis

DOI:https://doi.org/10.1137/22m1489708· OSTI ID:2421324

^[1]; Becker, Simon ^[2]; Drouot, Alexis ^[3]; Kammerer, Clotilde Fermanian ^[4]; ^[5]; ^[6]

University of Chicago, Chicago, IL 60637 USA.; OSTI
ETH Zurich, Zurich, Switzerland.
University of Washington, Seattle, WA 98195 USA.
Univ Paris Est Créteil, Univ Gustave Eiffel, CNRS, Lama UMR8050, F-94010 Creteil, France.
Duke University, Durham, NC 27708 USA.
University of Minnesota, Minneapolis, MN 55455 USA.

Not provided.

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0019449

OSTI ID:: 2421324

Journal Information:: SIAM Journal of Mathematical Analysis, Journal Name: SIAM Journal of Mathematical Analysis Journal Issue: 5 Vol. 55; ISSN 0036-1410

Publisher:: Society for Industrial and Applied Mathematics (SIAM)

Country of Publication:: United States

Language:: English

References (37)

Topology in Shallow-Water Waves: A Violation of Bulk-Edge Correspondence Graf, Gian Michele; Jud, Hansueli; Tauber, Clément Communications in Mathematical Physics, Vol. 383, Issue 2 https://doi.org/10.1007/s00220-021-03982-7	journal	March 2021
Edge States in Honeycomb Structures Fefferman, C. L.; Lee-Thorp, J. P.; Weinstein, M. I. Annals of PDE, Vol. 2, Issue 2 https://doi.org/10.1007/s40818-016-0015-3	journal	December 2016
Edge Current Channels and Chern Numbers in the Integer Quantum hall Effect Kellendonk, J.; Richter, T.; Schulz-Baldes, H. Reviews in Mathematical Physics, Vol. 14, Issue 01 https://doi.org/10.1142/S0129055X02001107	journal	January 2002
Anyons in an exactly solved model and beyond Kitaev, Alexei Annals of Physics, Vol. 321, Issue 1 https://doi.org/10.1016/j.aop.2005.10.005	journal	January 2006
Propagation of Wave Packets for Systems Presenting Codimension One Crossings Fermanian-Kammerer, Clotilde; Lasser, Caroline; Robert, Didier Communications in Mathematical Physics, Vol. 385, Issue 3 https://doi.org/10.1007/s00220-021-04147-2	journal	July 2021
Elliptic Operators with Honeycomb Symmetry: Dirac Points, Edge States and Applications to Photonic Graphene Lee-Thorp, J. P.; Weinstein, M. I.; Zhu, Y. Archive for Rational Mechanics and Analysis, Vol. 232, Issue 1 https://doi.org/10.1007/s00205-018-1315-4	journal	October 2018
Bulk-Edge Correspondence for Two-Dimensional Topological Insulators Graf, Gian Michele; Porta, Marcello Communications in Mathematical Physics, Vol. 324, Issue 3 https://doi.org/10.1007/s00220-013-1819-6	journal	October 2013
The level crossing problem in semi-classical analysis. II. The Hermitian case Colin de Verdière, Yves Annales de l’institut Fourier, Vol. 54, Issue 5 https://doi.org/10.5802/aif.2054	journal	January 2004
The spectral localizer for even index pairings Loring, Terry; Schulz-Baldes, Hermann Journal of Noncommutative Geometry, Vol. 14, Issue 1 https://doi.org/10.4171/JNCG/357	journal	February 2020
The bulk-edge correspondence for continuous honeycomb lattices Drouot, Alexis Communications in Partial Differential Equations, Vol. 44, Issue 12 https://doi.org/10.1080/03605302.2019.1643362	journal	July 2019
Topological photonics Lu, Ling; Joannopoulos, John D.; Soljačić, Marin Nature Photonics, Vol. 8, Issue 11 https://doi.org/10.1038/nphoton.2014.248	journal	October 2014
Continuous bulk and interface description of topological insulators Bal, Guillaume Journal of Mathematical Physics, Vol. 60, Issue 8 https://doi.org/10.1063/1.5086312	journal	August 2019
Mapping topological order in coordinate space Bianco, Raffaello; Resta, Raffaele Physical Review B, Vol. 84, Issue 24 https://doi.org/10.1103/PhysRevB.84.241106	journal	December 2011
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Ubiquity of conical points in topological insulators Drouot, Alexis Journal de l’École polytechnique — Mathématiques, Vol. 8 https://doi.org/10.5802/jep.152	journal	February 2021
The Semi-classical Van-Vleck Formula.: Application to the Aharonov-Bohm Effect Bily, J. M.; Robert, D. Long Time Behaviour of Classical and Quantum Systems https://doi.org/10.1142/9789812794598_0005	conference	April 2001
Traveling edge states in massive Dirac equations along slowly varying edges Hu, Pipi; Xie, Peng; Zhu, Yi IMA Journal of Applied Mathematics, Vol. 88, Issue 3 https://doi.org/10.1093/imamat/hxad015	journal	April 2023
Observation of fractional Chern insulators in a van der Waals heterostructure Spanton, Eric M.; Zibrov, Alexander A.; Zhou, Haoxin Science, Vol. 360, Issue 6384 https://doi.org/10.1126/science.aan8458	journal	March 2018
Topological protection of perturbed edge states Bal, Guillaume Communications in Mathematical Sciences, Vol. 17, Issue 1 https://doi.org/10.4310/CMS.2019.v17.n1.a8	journal	January 2019
Quantum Hall effect and the relative index for projections Avron, Joseph E.; Seiler, Ruedi; Simon, Barry Physical Review Letters, Vol. 65, Issue 17 https://doi.org/10.1103/PhysRevLett.65.2185	journal	October 1990
A Landau-Zener Formula for Non-Degenerated Involutive Codimension 3 Crossings Fermanian Kammerer, Clotilde; Gérard, Patrick Annales Henri Poincaré, Vol. 4, Issue 3 https://doi.org/10.1007/s00023-003-0138-4	journal	June 2003
The noncommutative geometry of the quantum Hall effect Bellissard, J.; van Elst, A.; Schulz‐ Baldes, H. Journal of Mathematical Physics, Vol. 35, Issue 10 https://doi.org/10.1063/1.530758	journal	October 1994
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang, C. -Z.; Zhang, J.; Feng, X. Science, Vol. 340, Issue 6129 https://doi.org/10.1126/science.1234414	journal	March 2013
Erratum: Homogenization limits and Wigner transforms Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J. Communications on Pure and Applied Mathematics, Vol. 53, Issue 2 https://doi.org/10.1002/(SICI)1097-0312(200002)53:2<280::AID-CPA4>3.0.CO;2-6	journal	February 2000
Topological invariants for interface modes Bal, Guillaume Communications in Partial Differential Equations, Vol. 47, Issue 8 https://doi.org/10.1080/03605302.2022.2070852	journal	May 2022
Characterization of edge states in perturbed honeycomb structures Drouot, Alexis Pure and Applied Analysis, Vol. 1, Issue 3 https://doi.org/10.2140/paa.2019.1.385	journal	January 2019
Photonic Floquet topological insulators Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan SPIE NanoScience + Engineering, SPIE Proceedings https://doi.org/10.1117/12.2023842	conference	September 2013
Analogs of quantum-Hall-effect edge states in photonic crystals Raghu, S.; Haldane, F. D. M. Physical Review A, Vol. 78, Issue 3 https://doi.org/10.1103/PhysRevA.78.033834	journal	September 2008
Homogenization limits and Wigner transforms G�rard, Patrick; Markowich, Peter A.; Mauser, Norbert J. Communications on Pure and Applied Mathematics, Vol. 50, Issue 4 https://doi.org/10.1002/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.0.CO;2-C	journal	April 1997
Quantum Anomalous Parity Hall Effect in Magnetically Disordered Topological Insulator Films Haim, Arbel; Ilan, Roni; Alicea, Jason Physical Review Letters, Vol. 123, Issue 4 https://doi.org/10.1103/PhysRevLett.123.046801	journal	July 2019
Persistent currents in topological and trivial confinement in silicene Jurkowski, Piotr; Szafran, Bartłomiej Physical Review B, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevB.101.075408	journal	February 2020
K-theory and pseudospectra for topological insulators Loring, Terry A. Annals of Physics, Vol. 356 https://doi.org/10.1016/j.aop.2015.02.031	journal	May 2015
A non‐commutative Landau‐Zener formula Fermanian Kammerer, Clotilde Mathematische Nachrichten, Vol. 271, Issue 1 https://doi.org/10.1002/mana.200310180	journal	June 2004
Chern number and edge states in the integer quantum Hall effect Hatsugai, Yasuhiro Physical Review Letters, Vol. 71, Issue 22 https://doi.org/10.1103/PhysRevLett.71.3697	journal	November 1993
Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase Simon, Barry Physical Review Letters, Vol. 51, Issue 24 https://doi.org/10.1103/PhysRevLett.51.2167	journal	December 1983
Microlocal Analysis of the Bulk-Edge Correspondence Drouot, Alexis Communications in Mathematical Physics, Vol. 383, Issue 3 https://doi.org/10.1007/s00220-020-03864-4	journal	September 2020
An introduction to topological insulators Fruchart, Michel; Carpentier, David Comptes Rendus Physique, Vol. 14, Issue 9-10 https://doi.org/10.1016/j.crhy.2013.09.013	journal	November 2013

Similar Records

Computing Edge States without Hard Truncation

Journal Article · 2020 · SIAM Journal on Scientific Computing · OSTI ID:1853293

Dynamics of curved interfaces

Journal Article · 2009 · Annals of Physics (New York) · OSTI ID:21308076

Computing Edge States without Hard Truncation

Journal Article · 2021 · SIAM Journal on Scientific Computing · OSTI ID:2280967

Related Subjects

Mathematics

Edge State Dynamics Along Curved Interfaces

Citation Formats

References (37)

Similar Records

Related Subjects