Putting unwanted surface states to good use: Large modulation of the superconducting state in a degenerate semiconductor by a gate

Continuous evolution of superconducting properties as a function of carrier density is difficult to investigate experimentally, unlike the properties of a ``gated'' semiconductor. This is because superconductors, in general, have carrier densities that are too high for a dielectric insulated gate (as in field-effect transistors) to work. Using an ionic liquid gate, we demonstrate that the modulation of carrier density can alter the superconducting transition temperature by up to 204 mK in epitaxial indium nitride on gallium nitride, accounting for $\ensuremath{\ge}10\mathrm{%}$ of the transition temperature in ungated conditions. Our devices are in the metallic regime, in the moderately clean limit (${k}_{F}l\ensuremath{\approx}3$--$6$) throughout the gate voltage range, and their properties are therefore not primarily governed by strong localization, granularity, etc. The primary determinants of the transition temperature in $\mathrm{In}\mathrm{N}$, which is a degenerate semiconductor, are carrier density, screening, and interaction, rather than disorder scattering. We show that the observed behavior is consistent with Bardeen-Cooper-Schrieffer s-wave superconductivity, as corroborated by the superconducting parameters we measure. Furthermore, we observe up to $60\mathrm{%}$ suppression of the supercurrent in our experiments. Both positive and negative gate voltages result in suppression of the critical current. Ionic liquid-gated $\mathrm{In}\mathrm{N}$ thus presents a platform in which s-wave superconductivity can be tuned at low carrier densities, almost 1000--10 000 times lower than in other systems such as niobium nitride. We point out potential areas where low carrier (superfluid) density can find useful applications.