We study the conductivity of graphene with a smooth but particle-hole- asymmetric disorder potential. Using perturbation theory for the weak-disorder regime and numerical calculations, we investigate how the particle-hole asymmetry shifts the position of the minimal conductivity away from the Dirac point ɛ=0. We find that the conductivity minimum is shifted in opposite directions for weak and strong disorder. For large disorder strengths, the conductivity minimum appears close to the doping level for which electron and hole doped regions (“puddles”) are equal in size.
