Interlayer interaction and related properties of bilayer hexagonal boron nitride: ab initio study

Abstract

Principal characteristics of interlayer interaction and relative motion of hexagonal boron nitride (h-BN) layers are investigated by the first-principles method taking into account van der Waals interactions. Dependences of the interlayer interaction energy on relative translational displacement of h-BN layers (potential energy surfaces) are calculated for two relative orientations of the layers, namely, for the layers aligned in the same direction and in the opposite directions upon relative rotation of the layers by 180 degrees. It is shown that the potential energy surfaces of bilayer h-BN can be approximated by the first Fourier components determined by symmetry. As a result, a wide set of physical qualintities describing relative motion of h-BN layers aligned in the same direction including barriers to their relative sliding and rotation, shear mode frequency and shear modulus are determined by a single parameter corresponding to the roughness of the potential energy surface, similar to bilayer graphene. The properties of h-BN layers aligned in the opposite directions are described by two such parameters. The possibility of partial and full dislocations in stacking of the layers is predicted for h-BN layers aligned in the same and opposite directions, respectively. The extended two-chain Frenkel-Kontorova model is used to estimate the width and formation energy of these dislocations on the basis of the calculated potential energy surfaces.

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

“…To describe the energy and structure of domain walls in bilayer graphene analytically, we use the two-chain Frenkel-Kontorova model. 1,28,29,34,35,48 In this model, it is taken into account that both of the layers change their structure to accomodate domain walls. We, nevertheless, assume that the bilayer is supported 2,3,5 and neglect the out-of-plane buckling.…”

“…According to the two-chain Frenkel-Kontorova model, the energy related to formation of a single domain wall characterized by the angle β between the Burgers vector and normal to the wall per unit length is given by 28,29…”

“…where coordinate x corresponds to the direction perpendicular to the domain wall, V (u) is the interlayer interaction energy per unit area of the bilayer along the minimum energy path between adjacent AB and BA minima given by eq 2 and K(β) = E cos 2 β + G sin 2 β describes the dependence of the elastic constant on the shear and tensile character of the domain wall. 28,29 Here E = k/(1 − ν 2 ) and G = k/2(1 + ν), where ν is the Poisson's ratio and k is the elastic constant under uniaxial stress (determined by the Young's modulus Y and thickness of graphene layers h as k = Y h). The condition δ∆W/δu = 0 corresponds to the optimal relative displacement u(x) that minimizes the formation energy of the domain wall in eq 3.…”

“…The majority of the previous theoretical works on the structure and energetics of domain walls were devoted to isolated domain walls which do not cross. 1,3,4,[28][29][30][31] The approach developed in these papers allowed to predict the commensurate-incommensurate phase transition 32 related to the formation of the first domain wall in two-dimensional bilayer systems with one layer stretched uniaxially and another layer free, such as bilayer graphene, 1,29 bilayer boron nitride 28,29 and graphene-boron nitride heterostructure. 30 Although it is in principle possible to study the structure of triangular domain wall networks by atomistic 22,25 and multiscale 33 simulations, the number of atoms in the supercell grows rapidly with decreasing the angle of relative rotation of the layers.…”

A many-electron perturbation theory study of the hexagonal boron nitride bilayer system*

“…A number of studies of the multilayer h-BN system have already been carried out using (van der Waals corrected) DFT, RPA, LMP2 theory and even quantum Monte Carlo methods [10][11][12][13][14][15][16][17][18][19][20]. These studies have mostly focused on the relative stabilities of different stacking faults, the interlayer binding energies, sliding paths and at the functional form of the binding energy for large interlayer distances.…”