Hofstadter Topology: Noncrystalline Topological Materials at High Flux
Abstract
he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~104 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally.more »
- Authors:
-
[1];
- Princeton Univ., NJ (United States)
- Princeton Univ., NJ (United States); Sorbonne Univ., Paris (France)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); Schmidt Fund for Innovation Research; Packard Foundation; National Science Foundation (NSF); BSF Israel US Foundation
- OSTI Identifier:
- 1852152
- Grant/Contract Number:
- SC0016239; 404513; DMR-1643312; DMR-142041; 2018226; N00014-20-1-2303
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 125; Journal Issue: 23; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; physics; quantum Hall effect; quantum spin Hall effect; symmetry protected topological states; topological Hall effect; topological insulators; topological materials; topological phase transition; topological phases of matter; graphene
Citation Formats
Herzog-Arbeitman, Jonah, Song, Zhi-Da, Regnault, Nicolas, and Bernevig, B. Andrei. Hofstadter Topology: Noncrystalline Topological Materials at High Flux. United States: N. p., 2020.
Web. doi:10.1103/physrevlett.125.236804.
Herzog-Arbeitman, Jonah, Song, Zhi-Da, Regnault, Nicolas, & Bernevig, B. Andrei. Hofstadter Topology: Noncrystalline Topological Materials at High Flux. United States. https://doi.org/10.1103/physrevlett.125.236804
Herzog-Arbeitman, Jonah, Song, Zhi-Da, Regnault, Nicolas, and Bernevig, B. Andrei. Wed .
"Hofstadter Topology: Noncrystalline Topological Materials at High Flux". United States. https://doi.org/10.1103/physrevlett.125.236804. https://www.osti.gov/servlets/purl/1852152.
@article{osti_1852152,
title = {Hofstadter Topology: Noncrystalline Topological Materials at High Flux},
author = {Herzog-Arbeitman, Jonah and Song, Zhi-Da and Regnault, Nicolas and Bernevig, B. Andrei},
abstractNote = {he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~104 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.},
doi = {10.1103/physrevlett.125.236804},
journal = {Physical Review Letters},
number = 23,
volume = 125,
place = {United States},
year = {Wed Dec 02 00:00:00 EST 2020},
month = {Wed Dec 02 00:00:00 EST 2020}
}
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Works referencing / citing this record:
Bulk and Edge Properties of Twisted Double-Bilayer Graphene
text, January 2021
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