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The problem of supercurrent in superconducting graphene is revisited and the supercurrent is calculated within the mean-field model employing the two-component wave functions on a honeycomb lattice with pairing between different valleys in the Brillouin zone. We show that the supercurrent within the linear approximation in the order-parameter-phase gradient is always finite even if the doping level is exactly zero.
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Kopnin et al. (2010) studied this question.
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