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The intrinsic orbital magnetization of a TMD monolayer is usually calculated for periodic crystals without mentioning the geometrical shape of samples and boundary conditions (BCs) for the electron wave functions. Such approaches, based on Bloch's theorem, involves a contribution from the Berry curvature, also in the case when the system is described by the two-band minimal model (Xiao et al 2012 Phys. Rev. Lett.  108 196802). In the present paper, we show that the geometrical and topological properties of the specimen, as well as the BCs, play an important role in the problem of valley orbital magnetization even for a macroscopic sample.

Size and shape effects in the orbital magnetization of TMDs monolayers