Fig. 2: Characterization of the electrostatic superlattice potential.
From: Universal superlattice potential for 2D materials from twisted interface inside h-BN substrate
a Schematic of a n + n multilayer, consisting of two n-layer AA′ h-BN stacked with a parallel interface. The interface is characterized by the in-plane translation r between the two parallel BN layers. b Charge redistribution due to interlayer coupling at the parallel interface with registry \(r = a/\sqrt 3\). \({\Delta}\rho \equiv \rho _{n + n} - \rho _{n,t} - \rho _{n,b}\), where ρn + n is the plane-averaged charge density of the n + n multilayer calculated using DFT, and ρn, t/b is that of the pristine top/bottom n-layer. Dashed vertical lines indicate atomic planes. For various thickness n considered, Δρ is predominantly distributed with nearly the same profile on the two layers forming the interface. c Electrical polarization in the n + n multilayers, evaluated using \({\int} {z{\Delta}\rho (z)dz}\) (stars), and using ε0Δφ (triangles), Δφ being the vacuum level difference on the two sides of multilayer directly extracted from DFT. d P as a function of r in the 2 + 2 configuration. The dots denote the values from the DFT-calculated Δρ, and the curve is the fitting using Eq. (1). e Laterally modulated polarization P(R) when the interface has a rigid twist from parallel by small angle δ, and the resultant electrostatic superlattice potential V(R, z) on constant z plane (from Eq. (2), c.f. text). V(R) is shown at three vertical distance from the interface which, for the example of δ = 1.5° (period b = 9.6 nm), corresponding to thickness of n = 2, 4, and 6 layers, respectively.
