Low-Field Metal-Insulator Transition in AB-Stacked Bilayer Graphene

Abstract

We investigate the interplay of in-plane magnetic and transverse electric fields in AB-stacked bilayer graphene. In prior work, we demonstrated that this configuration induces an insulator-metal (IM) transition with large impact on the magnetic response, albeit requiring impractically large magnetic fields. Here, we extend the analysis by incorporating previously neglected trigonal warping effects through interlayer skew couplings. In a restricted region of momentum space (on the order of 1/100 of the original Brillouin zone) trigonal warping produces a fine splitting of Dirac cones leading to a compensated semimetallic state in the absence of external fields. Application of a transverse electric field above a small threshold ($V_c\sim 0.6$ meV) reinstates the insulating gap, but this gap can be closed by a relatively small in-plane magnetic field, leading to an IM transition at a much smaller magnetic field ($\approx 10$ T) than previously predicted.

Figures (4)

• Figure 1: AB-stacked bilayer graphene lattice and band structure with trigonal warping. (a) Side view of the AB-stacked lattice showing relevant interlayer hopping terms. (b) Semi-metallic state at zero field with $E_F = 0.313~\mathrm{meV}$. (c) Semi-metallic state with displacement field slightly below the critical value. (d) Insulating state achieved by exceeding the critical displacement field.
• Figure 2: Density of states across the metal–insulator transition. (a) Insulating state for $V > V_c$ with vanishing DoS. (b) Semi-metallic state restored by in-plane magnetic field $\phi > \phi_c$. (c)$V$–$\phi$ phase diagram showing the critical magnetic field for gap closure, with cutoff at $25~\mathrm{T}$.
• Figure 3: Phase diagram showing the insulating (green) and metallic (blue) regions in the $(V,\Phi)$ plane. The low-field sector (this work) exhibits an insulator–metal (IM) boundary driven by a finite displacement $V$ and an in-plane flux $\Phi$; color axes are indicated on the left (meV) and right (eV). A crossover near $\sim137.5\,$T marks where the trigonal-warping picture breaks down; beyond this crossover one recovers the high-field regime discussed in Ref. PhysRevB.111.125130, where the unwarped model predicts a much larger critical field ($\sim1000\,$T).
• Figure 4: At displacement field $V>V_c$: $0.7$meV. Evolution of the indirect band-gap $E_g$ with respect to applied in-plane magnetic field strength $\phi$. Shows almost linearly decreasing nature with increasing magnetic field.