Weak ferroelectric charge transfer in layer-asymmetric bilayers of 2D semiconductors.

In bilayers of two-dimensional (2D) semiconductors with stacking arrangements which lack inversion symmetry charge transfer between the layers due to layer-asymmetric interband hybridisation can generate a potential difference between the layers. When analyzed using crystalline density functional theory codes, the related difference between vacuum energies above and below the bilayer would contradict the periodicity of supercell boundary conditions. Here, we resolve this constraint by two means: (a) by constructing a larger supercell, including two mirror reflected images of the bilayer separated by a further vacuum, and (b) by using a background dipole correction. We use both methods to compare bilayers of transition metal dichalcogenides (TMDs) - in particular, WSe$_2$ - for which we find a substantial stacking-dependent charge transfer, and InSe, for which the charge transfer is found to be negligibly small. The information obtained about TMDs is then used to map potentials generated by the interlayer charge transfer across the moir\'e superlattice in twistronic bilayers.