Fragile topology in line-graph lattices with two, three, or four gapped flat bands

Open Access

Fragile topology in line-graph lattices with two, three, or four gapped flat bands

Christie S. Chiu, Da-Shuai Ma, Zhi-Da Song, B. Andrei Bernevig, and Andrew A. Houck

Phys. Rev. Research 2, 043414 – Published 23 December 2020

Abstract

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: Their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.

Received 26 October 2020
Accepted 8 December 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043414

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum simulation Topological insulators

Topological materials

Tight-binding model Wannier function methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christie S. Chiu

Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08540, USA and Princeton Center for Complex Materials, Princeton University, Princeton, New Jersey 08540, USA

Da-Shuai Ma

Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing 100081, China and Department of Physics, Princeton University, Princeton, New Jersey 08540, USA

Zhi-Da Song and B. Andrei Bernevig