Raising the superconducting $T_{\mathrm{c}}$ of gallium: in-situ characterization of the transformation of $\alpha$-Ga into $\beta$-Ga

Abstract

Gallium (Ga) displays several metastable phases. Superconductivity is strongly enhanced in the metastable $\beta$-Ga with a critical temperature $T_{\mathrm{c}}=6.04(5)\mathrm{K}$, while stable $\alpha$-Ga has a much lower $T_{\mathrm{c}}<1.2\mathrm{K}$. Here we use a membrane-based nanocalorimeter to initiate the transition from $\alpha$-Ga to $\beta$-Ga on demand, as well as study the specific heat of the two phases on one and the same sample. The in-situ transformation is initiated by bringing the temperature to about $10\mathrm{K}$ above the melting temperature of $\alpha$-Ga. After such treatment, the liquid supercools down to $232\mathrm{K}$, where $\beta$-Ga solidifies. We find that $\beta$-Ga is a strong-coupling type-I superconductor with $\Delta (0)/k_{\mathrm{B}}{T}_{\mathrm{c}}=2.00(5)$ and a Sommerfeld coefficient ${\gamma }_{\mathrm{n}}=1.53(4)mJ/mol{\mathrm{K}}^2$, 2.55 times higher than that in the $\alpha$ phase. The results allow a detailed comparison of fundamental thermodynamic properties between the two phases.