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

Abstract

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 $(\text{volume per atom}<21.3\phantom{\rule{0.3em}{0ex}}{\text{bohrs}}^{3})$, estimated to be in excess of 360 GPa. The bct phase $(\text{volume per atom}>21.3\phantom{\rule{0.3em}{0ex}}{\text{bohrs}}^{3})$ 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 ${\mathrm{MgB}}_{2}$, 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.