Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a 2×2 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, and this directly affects the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on the 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.
|Journal||Physical Review B - Condensed Matter and Materials Physics|
|Publication status||Published - jan. 6 2012|
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics