Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

Abstract

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter $w$ related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on Landauer approach and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter $w$ and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low energy band structure.

Extended version of v1, 8 pages, 4 figures

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Cited by in corpus (7)

• Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
• Broken-symmetry $\nu =0$ quantum Hall states in bilayer graphene: Landau level mixing and dynamical screening
• Spontaneous Layer-Pseudospin Domain Walls in Bilayer Graphene
• Conductance anomaly near the Lifshitz transition in strained bilayer graphene
• Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation
• Electron-electron interactions in non-equilibrium bilayer graphene
• Finite-size effects on the minimal conductivity in graphene with Rashba spin-orbit coupling