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So, I know that to calculate surface band structure of a material, you have to take its 2D system eg. single or few-layered. But, how to find the surface band structure in the case of heterostructures. This paper does it "Proximity-induced topological state in graphene " but uses VASP instead. Is it possible to do the same using Quantum espresso?

Thank you

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I believe what you are referring to is a "projected" or "fat" band structure diagram. By assigning colors (or line thickness) to a basis on which you project the Kohn-Sham states (pseudoatomic orbitals, Wannier functions, etc.) you can plot the band structure in a way that shows the composition of all the states in the bands in terms of this basis. There are a few ways to do this in Quantum ESPRESSO.

  1. This capability has been included for the last few versions in Quantum ESPRESSO itself. Look in the folder q-e/PP/examples/projected_bands_example/ for an example that shows how to do this. The projected states you're interested in will be those that correspond to the atoms on your surface. The projwfc.x output labels these states according to the atom order you specify in your ATOMIC_POSITIONS part of your input file.

  2. Other codes that interface with QE can generate projected band structures. One example is LOBSTER. See section 3 of the user's guide. Wannier90 can also create projected band diagrams in terms of the maximally-localized Wannier functions it generates.

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