6 which operates with the quasiparticles corresponding to the eigenstates of the normal-state Hamiltonian [spinors ˆ a$_{↑}$ and ˆ a$_{↓}$ in Eq. (11)]. All essential properties are then derived based on the quasiparticle energy spectrum. The Fermi-liquid approach (with some variations) was used in Refs. 6,8–11. The dilemma of “intra-sublattice inter- action only” vs. “interaction between true quasiparticles of the normal graphene” was also discussed in connection with other collective modes in graphene $^{19}$. In general, this dilemma can be resolved only on the basis of the de- tailed microscopic analysis of the particular interaction mechanism. Nevertheless, the main outcome of our analysis is that the superconducting behaviors calculated within the two aforementioned approaches are qualitatively very similar, though intra-sublattice interaction requires a more in- volved algebra (4-fold matrices rather than 2-fold matri- ces in the Fermi-liquid approach). Quantitatively, how- ever, Eq. (32) is slightly different from the result of Ref. 10. In particular, the current in the limit µ ≫ | Δ | , Eq. (33), is twice as large as in Ref. 10. This factor 2 ap- pears simply because the model with two times smaller number of the degrees of freedom (only one valley with a Dirac cone in the Brillouin zone) has been considered in the cited paper. For large µ , there should otherwise be no difference in the superconducting properties, since the both models practically coincide with that for usual su- perconductors. However, the low- µ limit differs already by factor 4. The latter is obviously a manifestation of a more subtle difference between these two models. Apart from this numerical difference, the global fea- tures of the superconducting graphene are insensitive to the choice of the pairing model. The main message of Ref. 10 is confirmed that the supercurrent and the su- perconducting electron density are finite at any doping level for all temperatures below the critical temperature; in particular, they do not disappear in the limit µ = 0 contrary to the claim of Ref. 7. We have in fact shown that the low-doping limit µ → 0, being degenerate in the excitation energies, is not any special in the sense of the supercurrent: The supercurrent obtained within the linear approximation in the gradient of the order param- eter phase, k ≪ | Δ | /v$_{F}$ , is the same irrespectively of the relation between v$_{F}$k and µ . The crucial difference be- tween the superconducting graphene and the usual BCS superconductor is that the supercurrent density in the low-doping limit at T = 0 is proportional to the order parameter Δ rather than to the total electron density. This work was supported by the grant of the Israel Academy of Sciences and Humanities, by the Russian Foundation for Basic Research under grant 09-02-00573- a, by the Program “Quantum Macrophysics” of the Rus- sian Academy of Sciences, and by the Academy of Fin- land Centers of Excellence Program. NBK thanks for As we already mentioned in the Introduction, the present paper studies the model 7,12 that assumes Cooper pairing between electrons (holes) belonging to the same sublattice in the configurational space. This is evident, in fact, from the self-consistency equation Eq. (3), which contains the scalar product of the spinors ˆ u and ˆ v . How- ever, other scenarios of the superconducting pairing are possible, as well. In particular, one can use the ap- proach which is based on the Landau Fermi-liquid theory Acknowledgments IV. DISCUSSION AND COMPARISON which is the same result as in the linear approximation, Eq. (34). Consider low temperatures, T ≪ | Δ | . The first term vanishes and we obtain It does not depend on µ . Now we insert all four solutions into the expression Eq. (5) for the current. Removing the divergence by subtracting the current in the normal state we find which agrees with Eq. (21). and C$_{11}$ = C$_{33}$ = C$_{22}$ = C$_{44}$ = 1 , C$_{13}$ = C$_{31}$ = C$_{24}$ = C$_{42}$ = 0 which agrees with the result of the linear ap- proximation in k . The coefficients C$_{ik}$ taken for v$_{F}$k ≪ µ coincide with Eqs. (24)-(25) in the limit µ ≪ E . In the limit µ = 0 we have The coefficients obey the normalization | C (0) 11 | $^{2}$+ | C (0) 13 | 2 = | C (0) 33 | 2 + | C (0) 31 | 2 = 1. In the same way we find δE$_{2}$$_{,}$$_{4}$ = ± ˜ E$_{2}$ . The energy correction ˜ E$_{2}$ and the coefficients C (0) 22 = C (0) 44 and C (0) 24 = C (0) 42 are obtained from ˜ E$_{1}$ , C (0) 11 , and C (0) 13 , respectively, by replacing p → − p . For k/p ≪ µ/ | Δ | we have and C (0) 11 = C (0) 33 = 1 √$_{2}$ √ 1 + µv$_{F}$ p E 0 − E$_{D}$ ˜ E$_{1}$ , (40) C (0) 13 = C (0) 31 = i sign([ p × k ] z ) √$_{2}$ √ 1 − µv$_{F}$ p E 0 − E$_{D}$ ˜ E$_{1}$ . (41) ˜ E$_{1}$$_{,}$$_{2}$ = µv$_{F}$ p E$_{0}$ ∓ E$_{D}$ ˜ E$_{1}$ = ˜ E$_{2}$ ≡ ˜ E = ( v$_{F}$ p/E$_{0}$ ) √ E 2 D + k $^{2}$| Δ | $^{2}$/ 4 p 2 j = ev 2 $_{F}$k ∫ ∞ 0 p dp 2 π [ − ( 1 + | Δ | 2 E 2 0 ) d dE$_{0}$ tanh E$_{0}$ 2 T + 1 v$_{F}$p − v 2 $_{F}$p 2 E 3 0 tanh E$_{0}$ 2 T ] . (42) j = ev 2 $_{F}$k ∫ ∞ 0 p dp 2 π [ 1 v$_{F}$ p − v 2 $_{F}$p 2 E 3 0 ] = e | Δ | k π (43)