The density functional theory (DFT) has been one of the best tools to study material properties like electronic properties, structural properties, phonon properties, optical properties, etc.
In the crystals, since the lattice structure is periodic, it is well known that a single unit-cell is enough to calculate required properties. My question is, under what condition, the single unit-cell is not enough to correctly predict the material properties (specifically electronic and phononic properties), but a supercell is required.
For phonon calculations, if you used frozen phonon (aka finite difference) method, you certainly need a sufficiently large supercell.
For electronic structure calculations, it depends on the property you want to calculate. For example, for pristine non-magnetic or collinearly ferromagnetic systems, the primitive cell should be sufficient. On the other hand, for antiferromagnetic or non-collinear spin textures, a supercell is needed. Treating any structural impurities also need a supercell.
@Mohammad Saeed Bahramy, can band structure also be different in the two cases (other than band folding) if intrinsic impurity is there in the system, like monolayer WSe2. Thank you for your response.
As long as the supercell is symmetrically foldable to its primitive cell, then the answer is No, both band structure would be essentially the same (other than band folding). Both intrinsic and extrinsic impurities cause symmetry reduction, at least locally. So you should be more specific about the type and properties of the impurity you're interested in.
As it was suggested, as long as you are computing bandstructure for intrinsic WSe2, the single unit cell or a supercell will give you same result (other than band-folding). However, the presence of localized impurities or vacancies will break the symmetry and you need to adapt a supercell approach in such a case. People also use supercell approach to compute the bandstructure of an alloy (the size of which will, of course, depend on the different compositions one is interested in).
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