Gate-induced gap in bilayer graphene suppressed by Coulomb repulsion

We investigate the effect of on-site Coulomb repulsion $U$ on the band gap of the electrically gated bilayer graphene by employing coherent potential approximation in the paramagnetic state, based on an ionic two-layer Hubbard model. We find that, while either the on-site Coulomb repulsion $U$ or the external perpendicular electric field $E$ alone will favor a gapped state in the bilayer graphene, competition between them will surprisingly lead to a suppression of the gap amplitude. Our results can be applied to understand the discrepancies of gap size reported from optical and transport measurements, as well as the puzzling features observed in angular resolved photoemission spectroscopic study.

Figure 1

Phase diagram in the $U/t-E$ plane. ${\gamma }_0=t=2.7$ eV, ${\gamma }_1=0.4$ eV, and ${\gamma }_3=0.3$ eV are fixed. An interaction-driven metallic state is sandwiched between two gapped states. Inset (a) is the cartoon for side view of bilayer graphene while inset (b) is the top view. The hoppings, interaction, and gate field are also illustrated in inset (a).

Figure 2

(a) Total density of states (DOS) for three different values of $U/t$ at a fixed value of electric field $E=3.0$ V/nm. The DOS at $U/t=0$ and $E=3.0$ V/nm is shown in dotted line. It is found that while the system is insulating at small or large value of $U/t$, it is metallic at intermediate value of $U/t$. The inset is a blowup of DOS around the Fermi level ($\omega =0$). (b) Imaginary parts of total self-energy for two different values of $U/t$ at $E=3.0$ V/nm corresponding to $\mathrm{\Delta }/t=0.378$.

Figure 3

(a) Optical conductivities at a fixed value of $E=3.0$ V/nm for a series of $U/t$. (b) Optical conductivities at a fixed value of $U/t=1.1$ for different perpendicular electric fields $E$. (c) Peak position and the gap amplitudes in the optical conductivity as a function of electric field $E$ at four different values of $U/t=0.5,0.9,1.0,1.1$.

Figure 4

Spectral function along $k_x$ direction around $K$ point in momentum space. The Lorentzian broadening factor of 40 meV is used in order to simulate the energy resolution in the angular resolved photoemission spectroscopic study. The dotted and dashed lines are the band dispersions of Bernal stacked and $AA$-stacking bilayer graphene, respectively, at $E=1.6$ V/nm and $U/t=0$.