  Hybrid superconductor/semiconductor devices constitute a powerful platform
where intriguing topological properties can be investigated. Here we present
fabrication methods and analysis of Josephson junctions formed by a
high-mobility InAs quantum-well bridging two Nb superconducting contacts. We
demonstrate supercurrent flow with transport measurements, critical temperature
of 8.1 K, and critical fields of the order of 3 T. Modulation of supercurrent
amplitude can be achieved by acting on two side gates lithographed close to the
two-dimensional electron gas. Low-temperature measurements reveal also
well-developed quantum Hall plateaus, showing clean quantization of Hall
conductance. Here the side gates can be used to manipulate channel width and
electron carrier density in the device. These findings demonstrate the
potential of these hybrid devices to investigate the coexistence of
superconductivity and Quantum Hall effect and constitute the first step in the
development of new device architectures hosting topological states of matter.
