Gapped Bilayer Graphene: A Tunable Strongly Correlated Band Insulator

We introduce the notion of the strongly correlated band insulator (SCI), where the lowest energy excitations are collective modes (excitons) rather than the single particles. We construct controllable $1/N$ expansion for SCI to describe their observable properties. A remarkable example of the SCI is bilayer graphene which is shown to be tunable between the SCI and usual weak coupling regime.

Figure 1

One- (I) and two-particle spectra (II) in the insulator. (a) Noninteracting particles; (b) the weak coupling; (c) SCI; Particle-hole symmetry is implied for simplicity.

Figure 2

(a) Resummation of the leading $N$ loops leads to the RPA screening of the interaction potential. (b) Asymptotic regions for the polarization operator. (c) The leading-order self energy correction. (d) Resummation of the leading logarithm using Ward-Takahashi identity (e).

Figure 3

The energy-dependent electron spectral weight $A(ϵ)$, representing the ARPES line shape near the $K$ point of the Brillouin zone of BLG at different values of the coupling constant $\kappa$. For clarity, the curves corresponding to ten equidistant values of $\kappa =4,8,12,\dots ,40$ are vertically offset and the quasiparticle peak is artificially broadened and scaled down by a factor of 100.

Figure 4

The energy levels of the exciton in units of $u_0$ for $N=4$. Hatched region is the two-exciton continuum. Side panels are the sketches of the absorption (left) and Raman spectrum (right). Bottom table contains the oscillator strengths of the transitions in units of the strongest line, ${\overrightarrow{e}}_{i,o}$ are the complex polarization vectors for the incoming (i) and outgoing (o) light, $\Omega$ is the base line frequency, and ${\gamma }_1\simeq 0.2\mathrm{eV}$. The coefficient ${\nu }_3\simeq ({\mathcal{E}}_{\mathrm{LiTr}}/u{)}^2$ is not zero only due to the trigonal warping of the spectrum, where ${\mathcal{E}}_{\mathrm{LiTr}}\simeq 1\mathrm{meV}$ is the energy of the Lifshitz transition in gapless, $u_0=0$, BLG [7, 8].