  Negative differential conductance (NDC) manifests as a significant
characteristic of various underlying physics and transport processes in hybrid
superconducting devices. In this work, we report the observation of
gate-tunable NDC outside the superconducting energy gap on two types of hybrid
semiconductor-superconductor devices, i.e., normal metal-superconducting
nanowire-normal metal and normal metal-superconducting nanowire-superconductor
devices. Specifically, we study the dependence of the NDCs on back-gate voltage
and magnetic field. When the back-gate voltage decreases, these NDCs weaken and
evolve into positive differential conductance dips; and meanwhile they move
away from the superconducting gap towards high bias voltage, and disappear
eventually. In addition, with the increase of magnetic field, the NDCs/dips
follow the evolution of the superconducting gap, and disappear when the gap
closes. We interpret these observations and reach a good agreement by combining
the Blonder-Tinkham-Klapwijk (BTK) model and the critical supercurrent effect
in the nanowire, which we call the BTK-supercurrent model. Our results provide
an in-depth understanding of the tunneling transport in hybrid
semiconductor-superconductor devices.
