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

TL;DR

This paper investigates how finite-size effects and Rashba spin-orbit coupling influence the minimal conductivity in graphene, revealing orientation-dependent variations and reductions in conductivity compared to infinite samples.

Contribution

It provides a theoretical analysis of minimal conductivity in graphene with Rashba coupling, including finite-size effects and orientation dependence, using Landauer-Büttiker formalism.

Findings

Minimal conductivity depends on sample orientation due to Dirac cone interference.

Finite system size can reduce the minimal conductivity compared to infinite samples.

Rashba spin-orbit coupling causes trigonal warping and Fermi circle breakup.

Abstract

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--B\"uttiker 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.