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Lattice models with exactly solvable topological hinge and corner states

Flore K. Kunst, Guido van Miert, and Emil J. Bergholtz
Phys. Rev. B 97, 241405(R) – Published 11 June 2018

Abstract

We devise a generic recipe for constructing D-dimensional lattice models whose d-dimensional boundary states, located on surfaces, hinges, corners, and so forth, can be obtained exactly. The solvability is rooted in the underlying lattice structure and as such does not depend on fine tuning, allowing us to track their evolution throughout various phases and across phase transitions. Most saliently, our models provide “boundary solvable” examples of the recently introduced higher-order topological phases. We apply our general approach to breathing and anisotropic kagome and pyrochlore lattices for which we obtain exact corner eigenstates, and to periodically driven two-dimensional models as well as to three-dimensional lattices where we present exact solutions corresponding to one-dimensional chiral states at the hinges of the lattice. We relate the higher-order topological nature of these models to reflection symmetries in combination with their provenance from lower-dimensional conventional topological phases.

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  • Received 29 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.241405

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Flore K. Kunst1, Guido van Miert2, and Emil J. Bergholtz1

  • 1Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
  • 2Institute for Theoretical Physics, Centre for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands

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Issue

Vol. 97, Iss. 24 — 15 June 2018

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