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