On the sample-dependent minimal conductivity in weakly disordered graphene

We present a unified understanding of the experimentally observed minimal dc conductivity in weakly disordered graphene. Firstly, based on linear response theory, we reveal that randomness or disorder inevitably induces momentum dependent corrections to the electron self-energy function, which naturally yields a sample-dependent minimal conductivity. Taking the long-ranged Gaussian and Coulomb potentials as examples, we derive the momentum dependent self-energy function within the Born approximation, and further validate it via numerical simulations using the large-scale Lanczos algorithm. The explicit momentum dependences of the self-energy on the intensity, concentration and range of potential are critically addressed. Therefore, our results provide a reasonable interpretation of the sample-dependent minimal conductivity observed in graphene samples.