Superconductivity of $\beta$-Gallium

TL;DR

This study investigates the reasons behind the higher superconducting transition temperature of metastable $eta$-Gallium compared to stable $eta$-Gallium by analyzing their electronic and phononic properties.

Contribution

It provides a detailed theoretical analysis linking structural differences to the enhanced superconductivity in the $eta$ phase of gallium.

Findings

$eta$-Ga has a higher $T_c$ (~6K) than $eta$-Ga (~0.9K).

Structural motifs influence the density of states and electron-phonon coupling.

Arrays of Ga chains in $eta$-Ga promote stronger electron-phonon interactions.

Abstract

Elemental gallium can exist in several phases under ambient conditions. The stable $\alpha$ phase has a superconducting transition temperature, $T_c$, of 0.9~K. By contrast, the $T_c$ of the metastable $\beta$ phase is around 6~K. To understand the significant improvement in $T_c$ in the $\beta$ phase, we first calculate the electronic structure, phonon dispersion, and the electron-phonon coupling of gallium in the $\alpha$ and $\beta$ phase. Next, we solve the Eliashberg equations to obtain the superconducting gaps and the transition temperatures. Using these results, we relate the increased $T_c$ in the $\beta$ phase to structural differences between the phases that affect the electronic and phonon properties. The structure motif of the $\alpha$ phase is Ga$_2$ dimers, which form strong covalent bonds leading to bonding and antibonding states that suppress the density of states at the Fermi level. The $\beta$-Ga structure consists of arrays of Ga chains that favor strong coupling between the lattice vibrations and the electronic states near the Fermi level. The increased density of states and strong coupling to the phonons for the $\beta$-Ga chains compared to the $\alpha$ Ga$_2$ dimers enhance superconductivity in the $\beta$-Ga phase.