Structural, electronic, and optical properties of periodic graphene/h-BN van der Waals heterostructures

The emerging interest in van der Waals heterostructures as new materials for optoelectronics and photonics poses questions about their stability and structure-property relations. In the framework of density-functional and many-body perturbation theory, we investigate the structural, electronic, and optical properties of periodic heterostructures formed by graphene and hexagonal boron nitride (h-BN). To understand how the constituents affect each other depending on the layer stacking, we examine 12 commensurate arrangements. We find that interaction with graphene improves the stability of bulk h-BN also in those configurations that are predicted to be energetically metastable. In return, the interaction with h-BN can open a band gap of a few hundred meV in graphene. Its actual size can be tuned by the arrangement of the layers. In the semiconducting configurations, the character and spatial distribution of optical excitations are affected by the specific stacking that determines the electronic states involved in the transitions. Remarkably, six out of the 12 explored heterostructures remain semimetallic.

Figure 1

(a) From left to right: Sketch of the vdWh considered in this paper; side and top views of the unit cell; first Brillouin zone with the high-symmetry points marked in red and the path connecting them in blue. (b) The 12 stackings considered in this paper. The graphene sheet $\left(g\right)$ is taken as a reference while A, B, and C label the h-BN layers, depending on their in-plane displacement with respect to graphene; the notation A', B', or C' is used when the positions of all boron and nitrogen atoms are swapped within the h-BN layer.

Figure 2

(a) Electronic charge density in the C$g$B heterostructure; left: side view, right: top view of graphene and h-BN layers. Formation energy computed for b) the two inequivalent h-BN layers, c)-d) graphene and the h-BN layer above and below it. The symbol @ indicates vertically aligned atoms. (Bottom panel) Out-of-plane lattice parameter $c$ and formation energy of the full heterostructures.

Figure 3

(a) PBE band structure of graphene, graphene/h-BN vdWh in the C$g$B configuration, and bulk h-BN with AB stacking. (b) PBE band structure of all considered structures. The band character is indicated by the atomic color code: pink for B, blue for N, and gray for C. The VBM is set to zero.

Figure 4

(a) PBE (black) and QP (red) band structure of the C$g$B heterostructure along the full path in the BZ, shown in Fig. 1. The VBM is set to zero. (b) QP band structure, in the vicinity of the path K-H (left) compared with that of bulk h-BN in the AB stacking (right). The shaded area indicates the gap between the h-BN-derived bands. The band character is indicated by the atomic color code: pink for B, blue for N, and gray for C. (c) Difference between the h-BN-derived gap in the vdWh and the gap in bulk h-BN, $\mathrm{\Delta }E$, computed from PBE (black) and $G_0{W}_0$ (red). ${\mathrm{\Delta }}_{\mathrm{p}}$ (green) represents the renormalization of the h-BN-derived gap in the vdWh due to dynamical screening effects.

Figure 5

In-plane component of the imaginary part of the macroscopic dielectric function of (a) graphene, (b) bulk h-BN in the AA stacking, and (c) vdWh in the B$g$B arrangement, computed including (BSE, solid line) and neglecting (IQPA, shaded area) excitonic effects. A Lorentzian broadening of 0.1 eV is applied to all spectra to mimic the excitation lifetime.

Figure 6

Central panel: In-plane component of the imaginary part of the macroscopic dielectric function of all considered semiconducting graphene/h-BN vdW heterostructures, computed from the BSE. A Lorentzian broadening of 0.1 eV is applied. Side panels: Schematic representation of the spatial distribution of the e-h pairs that dominate the regions (I, II, III) in the spectra. C, N, and B atoms are depicted in gray, blue, and pink, respectively.