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

Using the full-potential linear muffin-tin orbitals (FP-LMTO) method we examine the pressure dependence of superconductivity in the two metallic phases of boron (B), body-centered-tetragonal (bct) and fcc. Linear response calculations are carried out to examine the phonon frequencies and electron-phonon coupling for various lattice parameters, and superconducting transition temperatures are obtained from the isotropic Eliashberg equation. The fcc phase is found to be stable only at very high pressure (volume per atom < 21.3 bohrs(3)), estimated to be in excess of 360 GPa. The bct phase (volume per atom > 21.3 bohrs(3)) is stable at lower pressures in the range 210-360 GPa. In both bct and fcc phases the superconducting transition temperature T-c is found to decrease with increasing pressure, due to the stiffening of phonons with an accompanying decrease in electron-phonon coupling. This is in contrast to a recent report, where T-c is found to increase with pressure. Even more drastic is the difference between the measured T-c, in the range 4-11 K, and the calculated values for both bct and fcc phases, in the range 60-100 K. The calculation reveals that the transition from the fcc to bct phase, as a result of increasing volume or decreasing pressure, is caused by the softening of the X-point transverse phonons. This phonon softening also causes large electron-phonon coupling for high volumes in the fcc phase, resulting in coupling constants in excess of 2.5 and T-c nearing 100 K. Although it is possible that the method used somewhat overestimates the electron-phonon coupling, its success in studying several other systems, including MgB2, clearly suggests that the experimental work should be reinvestigated. We discuss possible causes as to why the experiment might have revealed T-c's much lower than what is suggested by the present study. The main assertion of this paper is that the possibility of high T-c, in excess of 50 K, in high pressure pure metallic phases of B cannot be ruled out, thus pointing to (substantiating) the need for further experimental investigations of the superconducting properties of high pressure pure phases of B.