Anisotropic minimal conductivity of graphene bilayers

Abstract

Fermi line of bilayer graphene at zero energy is transformed into four separated points positioned trigonally at the corner of the hexagonal first Brillouin zone. We show that as a result of this trigonal splitting the minimal conductivity of an undoped bilayer graphene strip becomes anisotropic with respect to the orientation $\theta$ of the connected electrodes and finds a dependence on its length $L$ on the characteristic scale $\ell =\pi /\Delta k\simeq 50nm$ determined by the inverse of k-space distance of two Dirac points. The minimum conductivity increases from a universal isotropic value ${\sigma }_{\perp }^{min}=(8/\pi )e^2/h$ for a short strip $L\ll \ell$ to a higher anisotropic value for longer strips, which in the limit of $L\gg \ell$ varies from $(7/3){\sigma }_{\perp }^{min}$ at $\theta =0$ to $3{\sigma }_{\perp }^{min}$ over an angle range $\Delta \theta \sim \ell /L$.

4 pages, 2 figures

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• External gates and transport in biased bilayer graphene
• Lifshitz transition and thermoelectric properties of bilayer graphene
• Supercurrent reversal in Josephson junctions based on bilayer graphene flakes
• Trigonal warping, pseudodiffusive transport, and finite-system version of the Lifshitz transition in magnetoconductance of bilayer-graphene Corbino disks
• Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian
• Minimal conductivity and signatures of quantum criticality in ballistic graphene bilayer
• Magnetoconductance of the Corbino disk in graphene: Chiral tunneling and quantum interference in the bilayer case
• Effect of asymmetric Fermi velocity on trigonally warped spectrum of bilayer graphene
• Pseudodiffusive transmission of nodal Dirac fermions through a clean d-wave superconductor
• Finite-size effects on the minimal conductivity in graphene with Rashba spin-orbit coupling