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Weak localization and magnetoconductance of Dirac fermions under charged impurities in graphene

It has been found that the charged impurities with screened Coulomb potentials 1,2,3 are responsible for the observed carrier density dependence of the electric conductivity of graphene. 4 In a recent work, we have investigated the weak localization (WL) of electrons under the charged impurity scattering in graphene. 5 The description for the Cooperons under the finite-range scatters is different from that for the zero-range potentials as studied in the existing works. 6,7,8,9 In this paper, we present the details of the formalism for the WL of Dirac fermions under finite-range scatters in graphene. We also calculate the quantum inetrference correction (QIC) to the electric conductivity under a weak magnetic field and compare the result for the magnetoconductivity with the experimental measurements. The central problem of theoretically studying the weak localization of Dirac fermions under finite-range scatters is to solve the Bethe-Salpeter matrix equation for the Cooperons. With the self-consistent Born approximation (SCBA) to the single particle, we can obtain an explicit solution to the ground state of the singlet pseudospin Cooperons. By perturbation method, we will solve the Bethe-Salpeter matrix equation for all the singlet and triplet pseudospin Cooperons at long-wave length states. With the Cooperons, we derive the quantum interference correction to the electric conductivity that gives rise to WL effect.