When all models are compared from N = 80 down, it is easily seen that bands come in pairs in the bilayer models, and therefore, at N = 80, the equivalent of single-layer

valley splitting is the gap between bands one and three (type 2 in Table 1). Due to their large spatial separation, electrons inhabiting bands one and two will overlap only to a negligible extent and, hence, share the same energy here. (This type 1 separation corresponds to interlayer effects – see ‘Consideration of disorder’ section for further discussion.) As N →4, however, the layers approach and interact; for the C-type model, bands two and three quite clearly cross each other, and it is possible that some mixing of states occurs Dinaciclib solubility dmso – which might well be utilised for information transfer between Ilomastat cell line circuit components in a three-dimensional device design; consider two wires crossing at close distance (N < 16) in order to share a state between them. In fact, the differences columns of Table 1 show that the valley splitting is not particularly

perturbed until the layers are quite close to each other (A 4, B 8, and C 4), whilst bands which are effectively degenerate at N = 80 are not for N ≤ 16. The layers are interacting, affecting the multi-electronic wavefunction under these close-approach conditions. At N = 4, it is currently impossible to say which contributes more to the band structure. Within the approximate treatment in [23] it was concluded that the valley splitting in the interacting delta-layers is the same as that for the individual delta-layer. Here we find that in the DZP approach the valley splitting of 119 meV for the interacting delta-layers is about 30% larger than for the individual delta-layer [19]. Of course, Carter et al. themselves acknowledge that their reduced basis functions are not complete enough to represent the ideal system; the SZP results on disordered systems could not have predicted such a difference. We therefore suggest that their estimate of splitting

of 63 meV be revised upwards somewhat; the 30% buy Talazoparib difference seen between ideal single and double layers may be thought of as an upper bound, since the influence of disorder may well counter O-methylated flavonoid that of introducing the second layer. Density of states and conduction Figure 4 shows the electronic densities of states (DOS) of the A N models. As evidenced by the changes in the band minima, lower N leads to occupation further into the band gap. In all cases, the occupation is maintained across E F , indicating that the structures are conductive. The DOS of high-N models are in good agreement with each other, confirming that these layers are well separated, whilst those of smaller N show shifts of density peaks relative to each other and to A 80. Figure 4 Densities of states of A N models.