Superconductivity in Boron under pressure - why are the measured T$_c$'s so low?

TL;DR

This study uses first-principles calculations to analyze the pressure dependence of superconductivity in boron phases, revealing a significant discrepancy between theoretical predictions of high T$_c$ and much lower experimental values, and suggesting high T$_c$ is possible in high-pressure phases.

Contribution

The paper provides detailed computational insights into the phonon and electron-phonon interactions in boron under pressure, challenging previous experimental results and emphasizing the potential for higher T$_c$ in pure boron phases.

Findings

Superconducting T$_c$ decreases with pressure in both phases.

Calculated T$_c$ values are much higher than experimental measurements.

Phonon softening at the X-point leads to phase transition and high electron-phonon coupling.

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: 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 Eliashberg equation. In both bct and fcc phases the superconducting transition temperature T$_c$ is found to decrease with increasing pressure, due to 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. 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 boron cannot be ruled out, thus substantiating the need for further experimental investigations of the superconducting properties of high pressure pure phases of boron.