Interaction-induced metallic state in graphene on hexagonal boron nitride

The Coulomb interaction is widely known to enhance the effective mass of interacting particles and therefore tends to favor a localized state at commensurate filling. Here, we will show that, in contrast to this consensus, in a van der Waals heterostructure consisting of graphene and hexagon boron nitride (h-BN), the onsite Coulomb repulsion will at first destroy the localized state. This is due to the fact that the onsite Coulomb repulsion tends to suppress the asymmetry between neighboring carbons induced by h-BN substrate. We corroborate this surprising phenomenon by solving a tight-binding model with onsite Coulomb repulsion treated within coherent potential approximation, where hopping parameters are derived from density functional theory calculations based on the graphene/h-BN heterostructure. Our results indicate that both gapless and gapped states observed experimentally in graphene/h-BN heterostructures can be understood after a realistic value of the onsite Coulomb repulsion, as well as different interlayer distances, is taken into account. Finally, we propose ways to enhance the gapped state which is essential for potential application of graphene to next-generation electronics. Furthermore, we argue that band gap suppressed by many-body effect should happen in other van der Waals heterostructures.

Figure 1

Comparison between band structures of graphene/h-BN heterostructure calculated from density functional theory (DFT) and the derived tight-binding model (1) at $U=0$ for AB-N stack with interlayer distance of $d_0=3.022$ Å. (b) is a blowup of (a) around the Fermi level. Solid (red) lines are the band structure from DFT calculations while dashed (black) ones are from the derived tight-binding model.

Figure 2

Densities of states (DOS) for three different values of $U$ with interlayer distance of $d_0=3.022$ Å. Inset is the blowup of DOS around the Fermi level.

Figure 3

Partial densities of states (DOS) for three different values of $U$ with interlayer distance of $d_0=3.022$ Å. (a) $U=1.0$ eV, (b) $U=5.0$ eV, and (c) $U=10.0$ eV. Insets are the blowups of DOS around the Fermi level. ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are the carbons of different sublattices. B and N denote boron and nitrogen, respectively.

Figure 4

Evolution of gap size as a function of onsite Coulomb repulsion for several different interlayer distances in the unit of equilibrium distance $d_0=3.022$ Å. Insets show the most stable lattice configuration with lowest total energy, called AB-N stack where one carbon is above boron and the other centered above a h-BN hexagon. The upper panel is a side view while the lower one is a top view. ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are the carbons of different sublattices. B and N denote boron and nitrogen, respectively.

Figure 5

Difference of occupation number between two nearest neighbor carbons $\mathrm{\Delta }{n}_c$ as a function of $U$ for several different interlayer distances in the unit of equilibrium distance $d_0=3.022$ Å. Insets are cartoons for the graphene layer where larger dots denote charge-richer sites while smaller ones indicate charge-poorer sites. (a) and (b) represent the case of a smaller U region where interlayer hybridizations play dominant roles and a larger U region where local potentials dominate the charge distributions, respectively. ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are the carbons of different sublattices.

Figure 6

Imaginary part of total self-energy of two neighboring carbons $Im{\mathrm{\Sigma }}_C$ for several values of $U$ with an interlayer distance of $d_0=3.022$ Å.

Figure 7

Phase diagram in the plane of interaction in the unit of eV and interlayer distance in the unit of equilibrium distance $d_0=3.022$ Å. Lines are guidance for the eyes. Insets are two metastable lattice configurations denoted by AB-B stack with one carbon over nitrogen and the other centered above an h-BN hexagon (left two panels) and AA stack with one carbon over boron and the other over nitrogen (right two panels), respectively. Upper panels are side views while lower panels are top views. The most stable lattice configuration is shown in the insets of Fig. 4. ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ are the carbons of different sublattices. B and N denote boron and nitrogen, respectively.

Figure 8

(a) and (b) are the spectral functions along $\mathrm{\Gamma }-K-M$ line in the Brillouin zone at $U=3$ eV for two different interlayer distances of $0.9d_0$ and $1.1d_0$ with $d_0=3.022$ Å, respectively.