They also considered the approach of using a DZP basis and mixed pseudopotential to describe the disorder; this approach is vastly cheaper computationally and purports to inform us about the splittings due to the presence of the second layer. It is supported by SZP mixed and explicit pseudopotential

results in which these interlayer splittings are preserved. The approach taken in this paper, of calculating the properties of an explicitly ordered bilayer system using a DZP basis, complements that previous work. We can equivalently make comparisons between the ordered single-layer systems of [19] (δ-DZP-ord) and ordered double-layer buy P005091 systems as calculated with DZP bases here (δ δ-DZP-ord), and between the δ-DZP-ord systems of [19] and the (DZP) quasi-disordered single-layer system (δ-DZP-dis) presented in [23], in order to draw inferences about the (intractable, missing) δ δ-DZP-dis model, without at any stage compromising the accuracy of the results by using a less-complete basis set. (We shall now proceed to drop the ‘DZP’ from the labels, since it is ubiquitous here.) One important point in the consideration of disorder from these ideal models is that, at the lowest separation

distances, the crystalline Batimastat cell line order and alignment of the layers is greatly influencing their band structure. In a disordered system, the alignment effects would largely be negated, or averaged out, since one would expect to encounter all possible arrangements.

We therefore limit ourselves to discussing averages of splittings. The δ-ord layers show Ganetespib research buy valley splittings (VS) of 92 meV, as compared to the 120(±10%) meV of the δ δ-ord bilayer systems presented here (apart from separations of less than 8 monolayers). The δ-dis system showed a valley Erastin datasheet splitting of 63 meV, indicating that we might expect a reduction of valley splitting of up to 32% due to the (partial) inclusion of disorder. We can then infer that the valley splitting in the δ δ-dis systems should be around 81 meV, unless their separations are small (see Table 3). Table 3 Model properties and prediction of disordered splittings Separation VS (meV) VS (meV) ILS (Γ, meV) (ML) (ord-δδ, avg.) (dis-δδ, est.) (ord-δδ, avg.) 80 119 81 0 60 119 81 0 40 119 81 0 16 117 80 9 8 142 97 83 4 309a 211a 81a The valley splittings are calculated as the average difference between the lower (or upper) of each pair of bands (type 2 from Table 1), whilst the interlayer splittings (ILS) are calculated as the average difference between the lower (or upper) pair of bands (type 1 from Table 1). aThese values are likely considerably erroneous due to the crossing of bands in some alignments confusing the averaging of VS and ILS, and the vast effect alignment has at this low separation. We can estimate the interlayer splitting by taking the differences between bands 1 and 2 and bands 3 and 4 (except at low separation).