Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

Shi, Jingtian; Zhu, Jihang; MacDonald, A. H.

doi:10.1103/physrevb.103.075122

Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

Journal Article · Wed Feb 10 23:00:00 EST 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.075122· OSTI ID:1849401

^[1]; Zhu, Jihang ^[2]; MacDonald, A. H. ^[2]

Univ. of Texas, Austin, TX (United States); OSTI
Univ. of Texas, Austin, TX (United States)

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 (θ_GG, θ_GBN) 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 (θ_GG, θ_GBN) 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Welch Foundation

Grant/Contract Number:: FG02-02ER45958

OSTI ID:: 1849401

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 7 Vol. 103; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

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