Conductivity scaling and the effects of symmetry-breaking terms in bilayer graphene Hamiltonian

We study the ballistic conductivity of bilayer graphene in the presence of symmetry-breaking terms in an effective Hamiltonian for low-energy excitations, such as the trigonal-warping term (gamma(3)), the electron-hole symmetry-breaking interlayer hopping (gamma(4)), and the staggered potential (delta(AB)). Earlier, it was shown that for gamma(3) not equal 0, in the absence of remaining symmetry-breaking terms (i.e., gamma(4) = delta(AB) = 0), the conductivity (sigma) approaches the value of 3 sigma(0) for the system size L -> infinity[with sigma(0) = 8e(2)/(pi h) being the result in the absence of trigonal warping, gamma(3) = 0]. We demonstrate that gamma(4) not equal 0 leads to the divergent conductivity (sigma -> infinity) if gamma(3) not equal 0, or to the vanishing conductivity (sigma -> 0) if gamma(3) = 0. For realistic values of the tight-binding model parameters, gamma(3) = 0.3 eV, gamma(4) = 0.15 eV (and delta(AB) = 0), the conductivity values are in the range sigma/sigma(0) approximate to 4 - 5 for 100 nm < L < 1 mu m, in agreement with existing experimental results. The staggered potential (delta(AB) not equal 0) suppresses zero-temperature transport, leading to sigma -> 0 for L -> infinity. Although sigma = sigma (L) is no longer universal, the Fano factor approaches the pseudodiffusive value (F -> 1/3 for L -> infinity) in any case with nonvanishing sigma (otherwise, F -> 1), signaling the transport is ruled by evanescent waves. Temperature effects are briefly discussed in terms of a phenomenological model for staggered potential delta(AB) = delta(AB)(T) showing that, for 0 < T <= T-c approximate to 12 K and delta(AB)(0) = 1.5 meV, sigma (L) is noticeably affected by T for L greater than or similar to 100 nm.