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(a) Schematic of p-n pairing (illustrated by wavy lines) between electron-like carriers of spin in the Dirac cone conduction band of the K-valley and hole-like carriers of opposite spin in the valance band of the -valley. The pairing can be realized in a ferromagnetic monolayer graphene (b, upper panel) with an exchange field h exceeding its chemical potential μ, or between layers of a double layer graphene (b, lower panel) with a difference in the chemical potentials (controlled by a perpendicular electric field ) of the two layers exceeding their mean value . The zero-temperature phase diagram of graphene-based ferromagnetic superconductivity showing dependence on h and μ for s-wave (c)and p+ip-wave (d) pairing symmetry. The superconducting region consists of three phases of BCS, Sarma and p-n pairing. The dashed line in (c) and (d) indicates the instability boundary for BCS phase separating stable BCS states (left side) with the unstable (right side) ones. The S to N transition on these lines is first order. While the solid line in (d) indicates a second order S-N transition.
The plot of quasi-particle excitation spectrum versus in the superconducting state. The dispersions correspond to the regimes of (a) BCS pairing with no effective Fermi surface for both branches l = ±1, (b) Sarma pairing with two effective Fermi surfaces for the branch l = –1 but no Fermi surface for the other branch l = 1, and (c) p-n pairing with single Fermi surface in each branch l = ±1.
(a) Nonzero solutions of s-wave pairing gap equation versus exchange field h for different levels of doping μ. We have set . (b) Difference in thermodynamic potentials of N and S states versus h calculated at the same values of μ as in (a).
The same as in Fig. 3, but for p+ip-wave symmetry. Here, we have set .
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