Theoretical Study of Electron-Phonon Superconductivity

This theoretical study of superconductivity examines some of the limiting factors that constrain the Tc of conventional, phonon-mediated superconductors. For materials with wide-bandwidth metallic states, electronic instabilities that are theoretically challenging to deal with can be avoided. In this case, structural instability can still result from phonon softening caused by strong electron-phonon coupling of electrons at the Fermi level. Superconductivity is also limited by the total electron-phonon coupling available within a material given the hypothetical ability to arbitrarily dope the material. This limit is studied by deriving a generalization of the McMillan-Hopfield parameter, h&d5; (E), which measures the strength of electron-phonon coupling including anisotropy effects and rigid-band doping of the Fermi level to E. I examine these bounds for some covalent superconductors including MgB2, where Tc has reached the limit set by total electron-phonon coupling strength, and boron-doped diamond, which is far from any bounds. To consider the possibility of increasing the Tc of boron-doped diamond, calculations of electron-phonon coupling are performed for boron-doped diamond structures without electronically compensating defects over a wide range of boron concentration. The effects of boron substitutional disorder are incorporated through the use of randomly generated supercells, leading to a disorder-broadened distribution of results. After averaging over disorder, this study predicts a maximum bulk Tc near 55 K for boron concentrations between 20% -- 30%, assuming the validity of the simple structural model used and a Coulomb pseudopotential of micro* = 0.12. Considering only the largest electron-phonon coupling values of the distribution, superconductivity may still percolate through the material at higher temperatures, up to 80 K, through the regions of large coupling. A synthesis path is proposed to experimentally access higher levels of boron concentration in diamond. This path requires two non-equilibrium steps---the chemical vapor deposition growth of boron-carbon graphite and a high pressure treatment to cause a graphite-to-diamond transition at temperatures low enough to avoid boron-carbon phase separation. A prediction of a thermodynamically stable superconductor is more straight-forward to experimentally test than a material requiring complicated non-equilibrium synthesis. Calculations suggest that Be2Bx, C 1-x, will form in the anti-fluorite structure for 0 0.4, superconductivity is predicted in this structure with a Tc between 5 K and 13 K. The uncertainty in this prediction is because with an electron-phonon coupling of lambda ≈ 0.5, the material remains in the weak-coupling regime of superconductivity where Tc is sensitive to small variations in lambda and mu*. Finally, I examine the electron-phonon coupling in a class of covalent materials by performing calculations on a set of molecular units from which they might be composed. By considering coupling to states at energies in the vicinity of the Fermi energy, one develops a picture of how couplings might be affected as these units are connected to form extended systems. Guided by this study of molecular fragments, I construct two examples of hypothetical covalent superconductors each with a transition temperature estimated to be 380 K within Eliashberg theory. These hypothetical materials enter the regime of narrow-bandwidth metals...