Extended Data Fig. 1: Self-consistency calculation.
From: High-energy quasiparticle injection into mesoscopic superconductors
Comparison of the spectroscopy fitting to the self-consistency relation for weak-coupling superconductors. This relation links the zero temperature gap to the critical temperature as Δ0 = 1.764kBTc, and the temperature dependence of the gap implicitly through the relation \(\,\text{ln}\,(2{e}^{\gamma }\hslash {\omega }_{D}/{k}_{\text{B}}{T}_{c}\pi )=\mathop{\int}\nolimits_{0}^{\hslash {\omega }_{D}}\,\text{tanh}\,(\sqrt{{\xi }^{2}+{{\Delta }}{(T)}^{2}}/2{k}_{\text{B}}T)/\sqrt{{\xi }^{2}+{{\Delta }}{(T)}^{2}}d\xi\) where γ is Euler’s constant, and ℏωD is the Debye energy. For weak coupling ℏωD ≫ kBT, so that Δ(T) is parametrized only by Tc23. Above we plot the titanium gap energy versus TQP extracted from the spectroscopy model (that is from the data of Fig. 1c-d). The data are within the range corresponding to Tc = 0.24 - 0.31 K, the grey region, obtained by solving the foregoing equation numerically for those two bounds. The conformity to the quasiparticle population to the self-consistency relation is therefore quite good, which further excludes an exotic dissipationless gate effect. The slight departure of the data from a typical BCS dependence may be due to variations in the non-equilibrium state due to the energy of the impinging electrons, which varies dramatically over this data set. The error bars are calculated as described in the methods section.
