We present recent achievements and predictions in the field of doping-induced superconductivity in column IV-based covalent semiconductors, with a focus on Bdoped diamond and silicon. Despite the amount of experimental and theoretical work produced over the last four years, many open questions and puzzling results remain to be clarified. The nature of the coupling (electronic correlation and/or phonon-mediated), the relationship between the doping concentration and the critical temperature (T C ), which determines the prospects for higher transition temperatures, as well as the influence of disorder and dopant homogeneity, are debated issues that will determine the future of the field. We suggest that innovative superconducting devices, combining specific properties of diamond or silicon, and the maturity of semiconductor-based technologies, will soon be developed.
1) IntroductionIt was probably the discovery of a superconducting transition around 40 K in the rather simple MgB 2 compound [1] that revived the interest for a specific class of superconducting materials, belonging to the so-called covalent metals [2] . These superconducting covalent systems (see box 1), including B-doped diamond [3] , silicon [4] , and silicon carbide [5,6] , Ba-doped silicon clathrates [7,8] , alkali-doped fullerenes [9,10] and the CaC 6 or YbC 6 intercalated graphites [11,12] , share the specificity of involving at least one relatively light element and of preserving strongly directional covalent bonds in their metallic state. The implications of this covalent character are important in superconductors in which Cooper pairs are coupled through phonons. The use of perturbation theory to study the renormalisation of the electron-electron repulsion by the electron-phonon interaction leads to the so-called Eliashberg equations [13] and to the celebrated McMillan formula [13] relating, in an approximate way, the superconducting transition temperature T C to an average phonon frequency ω ln , the electron-phonon coupling parameter λ ep and the screened and retarded Coulomb repulsion parameter µ*: Clearly, low atomic masses lead to high frequency phonon modes, which may enhance the ω ln prefactor and thus T C . This is the basis of the so-called isotope effect. Furthermore, strong covalent bonding will lead both to large phonon frequencies and a large electron-phonon coupling potential V ep =λ ep /N(E F ), with N(E F ) the density of states at the Fermi level, also contributing to enhance T C . Even within a phonon-mediated coupling scenario, these criteria do not necessarily warrant a large T C since increasing λ ep may also lead to a lattice instability, and a large electron-phonon potential V ep may be impaired by a low density N(E F ). However, these simple considerations, as well as more elaborate surveys and predictions of a larger T C [14][15][16] , have provided much incentive to study this class of materials.The most familiar covalent systems are certainly diamond and silicon. The former can be considered as the prototype insula...
