  We present an extensive experimental and theoretical study of the proximity
effect in InAs nanowires connected to superconducting electrodes. We fabricate
and investigate devices with suspended gate-controlled nanowires and
nonsuspended nanowires, with a broad range of lengths and normal-state
resistances. We analyze the main features of the current-voltage
characteristics: the Josephson current, excess current, and subgap current as
functions of length, temperature, magnetic field, and gate voltage, and compare
them with theory. The Josephson critical current for a short-length device, L =
30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes
close to the theoretically expected value. The critical current in all other
devices is typically reduced compared to the theoretical values. The excess
current is consistent with the normal resistance data and agrees well with the
theory. The subgap current shows a large number of structures; some of them are
identified as subharmonic gap structures generated by multiple Andreev
reflection. The other structures, detected in both suspended and nonsuspended
devices, have the form of voltage steps at voltages that are independent of
either the superconducting gap or length of the wire. By varying the gate
voltage in suspended devices, we are able to observe a crossover from typical
tunneling transport at large negative gate voltage, with suppressed subgap
current and negative excess current, to pronounced proximity junction behavior
at large positive gate voltage, with enhanced Josephson current and subgap
conductance as well as a large positive excess current.
