Critical dimension of inhomogeneous gap states in nonequilibrium superconductors under large injection of quasiparticles via tunneling

Inhomogeneous energy-gap states in nonequilibrium Pb-In alloy films have been studied under high-energy injection of quasiparticles via tunneling. Two types of configuration of double tunnel junctions (Pb-In-Pb-In-Pb) have been used in the experiment: In the first configuration, $T_{\mathrm{I}}$, geometrical dimensions of both injectors and detectors of the junctions were changed precisely and quasicontinuously. The second configuration, $T_{\mathrm{II}}$, consisted of a long inline injector and very narrow multiple detectors. For samples with $T_{\mathrm{I}}$ configuration, coexistence of two different energy gaps was observed only in samples with dimensions above a critical sample size of about 25 × 25 μ${\mathrm{m}}^2$, while in samples with dimensions below the critical size a first-order transition from the superconducting state with a broad but reduced energy gap to the normal state was observed. The results indicate that the inhomogeneous energy-gap state possesses a critical characteristic dimension with a macroscopic size in nonequilibrium superconductors. Spatial structures of the inhomogeneous gap state were measured by using samples with $T_{\mathrm{II}}$ configuration. The spatial structure was found to be affected dominantly by the macroscopic sample boundary. These inhomogeneous gap states are discussed by current theories of nonequilibrium instabilities.