Eur. Phys. J. B (2015) 88: 157
https://doi.org/10.1140/epjb/e2015-60198-x

Regular Article

Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

¹ P.L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, 119334 Moscow, Russia
² National Research University, Higher School of Economics, 109028 Moscow, Russia
³ L.V. Kirensky Institute of Physics, Siberian Branch of Russian Academy of Sciences, 660036 Krasnoyarsk, Russia
⁴ M.F. Reshetnev Siberian State Aerospace University, 660014 Krasnoyarsk, Russia

^a e-mail: kmax@iph.krasn.ru

Received: 11 March 2015
Received in final form: 13 May 2015
Published online: 15 June 2015

Abstract

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in bilayer doped graphene is studied disregarding of the effect of the van der Waals potential of the substrate and impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p + ip-, and d + id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.