Tunneling study of Fermi-liquid effects in amorphous gallium

The Fermi-liquid parameter $G_0$ has been determined in amorphous gallium. Al/${\mathrm{Al}}_2$ ${\mathrm{O}}_3$/a-Ga tunnel junctions were used to observe the renormalization caused by Fermi-liquid interactions of the spin splitting of the a-Ga superconducting density of states in a magnetic field. This was done by fitting the dynamic tunneling conductance to the theory of Rainer. Excellent agreement was found with this theory, and the results were consistent with critical-field measurements made on the same films. A large renormalization was observed ($G_0$=0.81±0.14), as expected for this strongly coupled material. Correlation effects were also seen. The spin-orbit scattering rate $b_{\mathrm{SO}}$ was found to be 0.18±0.03.