Figure 3: Numerical results for BN–BNH₂ interfaces.

(a) Planar average of the local density of states as a function of energy and position along an axis orthogonal to the interfaces, for a q=12 BN–BNH₂ superlattice with p=0 (zigzag interface), shown on top. The dashed line marks the Fermi energy, while the solid line denotes the planar average of the electrostatic potential energy. (b) Schematic representation of an arbitrary interface orientation. The lattice vector along the interface, , forms an angle θ with a zigzag direction; and p=1 here. (c) Free charge density (red circles, left axis) at each zigzag interface as a function of superlattice periodicity, expressed in units of , where is the equilibrium lattice constant along the interface. The dashed line shows the asymptotic value given by equation (1), and up (down) blue triangles denote the residual average electric fields (right axis) inside BN (BNH₂). (d) Same as in c but as a function of the interface orientation angle θ for a q=7 superlattice. The dashed line shows instead the free charge density in the limit q→∞ given by equation (5). In c and d, the scales of the left and right axes map charge densities and electric fields exactly into each other, so that, for example, a density read on the left axis will give the corresponding field on the right axis.