Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride
Abstract
The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the (θGG, θGBN) twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and we show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when (i) the (θGG, θGBN) twist-angle-pair is close enough to a commensurate point that the two moiré patterns yield a supermoiré pattern with a sufficiently long length scale, and (ii) the supermoiré has a percolating topologically nontrivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Finally, further experimental studies that can test this proposal more directly are suggested.
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); Welch Foundation
- OSTI Identifier:
- 1849401
- Grant/Contract Number:
- FG02-02ER45958; F1473
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; materials science; physics; anomalous Hall effect; quantum anomalous Hall effect; graphene; superlattices; mean field theory
Citation Formats
Shi, Jingtian, Zhu, Jihang, and MacDonald, A. H. Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride. United States: N. p., 2021.
Web. doi:10.1103/physrevb.103.075122.
Shi, Jingtian, Zhu, Jihang, & MacDonald, A. H. Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride. United States. https://doi.org/10.1103/physrevb.103.075122
Shi, Jingtian, Zhu, Jihang, and MacDonald, A. H. Thu .
"Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride". United States. https://doi.org/10.1103/physrevb.103.075122. https://www.osti.gov/servlets/purl/1849401.
@article{osti_1849401,
title = {Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride},
author = {Shi, Jingtian and Zhu, Jihang and MacDonald, A. H.},
abstractNote = {The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the (θGG, θGBN) twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and we show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when (i) the (θGG, θGBN) twist-angle-pair is close enough to a commensurate point that the two moiré patterns yield a supermoiré pattern with a sufficiently long length scale, and (ii) the supermoiré has a percolating topologically nontrivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Finally, further experimental studies that can test this proposal more directly are suggested.},
doi = {10.1103/physrevb.103.075122},
journal = {Physical Review. B},
number = 7,
volume = 103,
place = {United States},
year = {Thu Feb 11 00:00:00 EST 2021},
month = {Thu Feb 11 00:00:00 EST 2021}
}
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