Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-07-08
Phys. Rev. B 85, 041402(R) (2012) [5 pages]
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Extended version of v1, 8 pages, 4 figures
Scientific paper
10.1103/PhysRevB.85.041402
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.
Cserti József
Dávid Gyula
Oroszlany László
Rakyta Peter
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