Anisotropic minimal conductivity of graphene bilayers

Details Anisotropic minimal conductivity of graphene bilayers Anisotropic minimal conductivity of graphene bilayers

2008-04-17

arxiv.org/abs/0804.2748v1

Phys. Rev. B 79, 073401 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevB.79.073401

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 $\Delta \theta\sim \ell/L$.

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