Influence of lithium doping on the thermodynamic properties of graphene based superconductors

It has been recently observed that the conventional electron-phonon mediated superconducting phase in graphene can be easily induced by doping its surface with the lihitum adatoms. Due to the emerging interest in this field of research we present our theoretical discussion of the thermodynamic properties of this novel structures within the strong-coupling limit. We show, that together with the increase of the adatom doping, from one (LiC$_{6}$) to two (Li$_{2}$C$_{6}$) lithium atoms per unit cell, the critical temperature ($T_C$) changes from 8.55 K to 21.83 K. Such trend is also observed for other thermodynamic properties which moreover differ from the predictions of the Bardeen-Cooper-Schrieffer theory. In particular, the zero-temperature energy gap to the critical temperature ratio: R$_{\Delta}^{{\rm LiC}_6}$=3.72 and R$_{\Delta}^{{\rm Li}_{2}{\rm C}_6}$=4.21; the ratio of the specific heat for superconducting and the normal state: R$_{\rm C}^{{\rm LiC}_6}$=1.47 and R$_{\rm C}^{{\rm Li}_{2}{\rm C}_6}$=1.79; and the parameter connected with the zero-temperature thermodynamic critical field: R$_{\rm H}^{{\rm LiC}_6}$=0.167 and R$_{\rm H}^{{\rm Li}_{2}{\rm C}_6}$=0.144. Finally the electron effective mass at $T_c$ is calculated to be: $(1.62m_e)_{{\rm LiC}_6}$ and $(2.48m_e)_{{\rm Li}_{2}{\rm C}_6}$.