Anisotropic minimal conductivity of graphene bilayers

TL;DR

This paper demonstrates that the minimal conductivity of undoped bilayer graphene becomes anisotropic due to trigonal splitting of the Fermi line, with the value depending on orientation and length, transitioning from a universal to an anisotropic regime.

Contribution

It reveals the anisotropic nature of minimal conductivity in bilayer graphene caused by trigonal splitting, detailing its dependence on orientation and length scales.

Findings

Minimal conductivity is anisotropic and depends on electrode orientation.

Conductivity increases from a universal value to higher anisotropic values with length.

The characteristic scale for this transition is approximately 50 nm.

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 $\ell=\pi/\Delta k\simeq 50 nm$ determined by the inverse of k-space distance of two Dirac points. The minimum conductivity increases from a universal isotropic value $\sigma^{min}_{\bot}=(8/\pi)e^2/h$ 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 $(7/3)\sigma^{min}_{\bot}$ at $\theta=0$ to $3\sigma^{min}_{\bot}$ over an angle range $\Delta \theta\sim \ell/L$.