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I would like to simulate a layer of graphene on a solid substrate, say Cu or quartz. I'm interested in their binding energy and other physical or chemical properties. However, their periods do not match each other, so if I want to use some standard DFT package like VASP or Quantum Expresso, I cannot use a single period for the whole supercell. I had some experience with molecules absorbed on some specific surface, which is an easier case because the period of the supercell is just that of the substrate.

Does anyone have experience with this situation? Thanks.

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I have found a useful reference here

Basically the idea is to avoid the mismatch by best fitting their primitive cell unit vectors.

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    $\begingroup$ Another useful reference may be found here. The authors model MoS2 monolayers on a range of periodic support materials and therefore have to address this issue as well. $\endgroup$
    – Argon
    Commented Apr 27, 2018 at 5:27

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