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The quantum anomalous Hall (QAH) effect is sometimes observed in twistedbilayer graphene (tBG) when it is nearly aligned with an encapsulatinghexagonal boron nitride (hBN) layer. We propose that the appearance or absenceof the QAH effect in individual devices could be related to commensurabilitybetween the graphene/graphene and graphene/hBN moir\'e patterns. We identify aseries of points in the $(\theta_{\rm GG},\theta_{\rm GBN})$ twist-angle spaceat which the two moir\'e patterns are commensurate, allowing moir\'e bandtheory to be applied, and show that the band Chern numbers are in this casesensitive to a rigid in-plane hBN displacement. Given this property, we arguethat the QAH effect is likely only when i) the $(\theta_{\rm GG},\theta_{\rmGBN})$ twist-angle-pair is close enough to a commensurate point that the twomoir\'e patterns yield a supermoir\'e pattern with a sufficiently long lengthscale, and ii) the supermoir\'e has a percolating topologically non-trivial QAHphase. For twist angles far from commensurability, the hBN layer acts as asource of disorder that can destroy the QAH effect. Our proposal can explain anumber of current experimental observations. Further experimental studies thatcan test this proposal more directly are suggested.

Moir\'e Commensurability and the Quantum Anomalous Hall Effect in Twisted Bilayer Graphene on Hexagonal Boron Nitride