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Using the full potential linear muffin-tin orbitals (FP-LMTO) method weexamine the pressure-dependence of superconductivity in the two metallic phasesof Boron: bct and fcc. Linear response calculations are carried out to examinethe phonon frequencies and electron-phonon coupling for various latticeparameters, and superconducting transition temperatures are obtained from theEliashberg equation. In both bct and fcc phases the superconducting transitiontemperature T$_c$ is found to decrease with increasing pressure, due tostiffening of phonons with an accompanying decrease in electron-phononcoupling. This is in contrast to a recent report, where T$_c$ is found toincrease with pressure. Even more drastic is the difference between themeasured T$_c$, in the range 4-11 K, and the calculated values for both bct andfcc phases, in the range 60-100 K. The calculation reveals that the transitionfrom the fcc to bct phase, as a result of increasing volume or decreasingpressure, is caused by the softening of the X-point transverse phonons. Thisphonon softening also causes large electron-phonon coupling for high volumes inthe fcc phase, resulting in coupling constants in excess of 2.5 and T$_c$nearing 100 K. We discuss possible causes as to why the experiment might haverevealed T$_c$'s much lower than what is suggested by the present study. Themain assertion of this paper is that the possibility of high T$_c$, in excessof 50 K, in high pressure pure metallic phases of boron cannot be ruled out,thus substantiating the need for further experimental investigations of thesuperconducting properties of high pressure pure phases of boron.Comment: 16 pages, 8 figures, 1 Tabl

Superconductivity in boron under pressure: A full-potential linear muffin-tin orbitals study