Abstract
A study of possible superconducting phases of graphene has been constructed in detail. A realistic tight binding model, fit to ab initio calculations, accounts for the Li-decoration of graphene with broken lattice symmetry, and includes s and d symmetry Bloch character that influences the gap symmetries that can arise. The resulting seven hybridized Li-C orbitals that support nine possible bond pairing amplitudes. The gap equation is solved for all possible gap symmetries. One band is weakly dispersive near the Fermi energy along Γ → M where its Bloch wave function has linear combination of {d}_{{x}^{2}-{y}^{2}} and dxy character, and is responsible for {d}_{{x}^{2}-{y}^{2}} and dxy pairing with lowest pairing energy in our model. These symmetries almost preserve properties from a two band model of pristine graphene. Another part of this band, along K → Γ, is nearly degenerate with upper s band that favors extended s wave pairing which is not found in two band model. Upon electron doping to a critical chemical potential μ1 = 0.22 eV the pairing potential decreases, then increases until a second critical value μ2 = 1.3 eV at which a phase transition to a distorted s-wave occurs. The distortion of d- or s-wave phases are a consequence of decoration which is not appear in two band pristine model. In the pristine graphene these phases convert to usual d-wave or extended s-wave pairing.
Highlights
Two dimensional superconducting phases have become of great interest since the discovery of the high temperature superconducting (HTS) cuprates and subsequent finding of Fe-pnictide and -chalcogenide HTSs
Experimental evidence for a superconducting gap in Li-decorated monolayer graphene around 6 K has been reported by Ludbrook et al based on angle-resolved photoemission spectroscopy5 (ARPES)
Profeta et al.15 calculated on the basis of density functional theory for superconductors that decoration by electron donating atoms such as Ca and Li will make single layer graphene superconducting, up to 8 K for the case of Li
Summary
A study of possible superconducting phases of graphene has been constructed in detail. Charge migration from such decorating atoms to the graphene layer will affect the C-C bonding, leading to contraction or expansion of the graphene hexagons that are centered by the decorating atoms, breaking the symmetry of C-C hopping integrals around the honeycomb loop. For two dimensional graphene-like structures effects, differences in nearest neighbour hopping integrals affect the band structure near the important Dirac point, which is folded back to the Γ point of the shrunken graphene superlattice investigated by Hou et al. and Long-Hua et al.18 For such systems not even the full analytic tight-binding band structure has yet been reported. IV the gap equations and approximate critical temperature These equations are solved analytically to establish the possible pairing symmetries and other properties of the superconducting states.
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