Finite-size effects on the minimal conductivity in graphene with Rashba spin–orbit coupling

• Using Landauer–Büttiker formalism, the minimal conductivity of monolayer graphene with Rashba spin–orbit couplings was obtained in continuum and tight binding models.
• Finite and infinite samples are considered.
• For finite samples depending on its orientation with respect to the electrodes, the conductivity can be suppressed compared to that obtained for infinite samples.
• This effect can be explained by a simple analysis of the boundary conditions.
• Owing to the spin–orbit interactions an oscillation of the conductivity is observed and explained as interference of states corresponding to different energy pockets of the low energy Fermi surface.

We study theoretically the minimal conductivity of monolayer graphene in the presence of Rashba spin–orbit coupling. The Rashba spin–orbit interaction causes the low-energy bands to undergo trigonal-warping deformation and for energies smaller than the Lifshitz energy, the Fermi circle breaks up into parts, forming four separate Dirac cones. We calculate the minimal conductivity for an ideal strip of length L and width W within the Landauer–Büttiker formalism in a continuum and in a tight binding model. We show that the minimal conductivity depends on the relative orientation of the sample and the probing electrodes due to the interference of states related to different Dirac cones. We also explore the effects of finite system size and find that the minimal conductivity can be lowered compared to that of an infinitely wide sample.