This report is concerned with the properties of one and two dimensional semiconducting materials when brought into contact with a superconductor. Experimentally we study the 2D electron gas in an InGaAs/InAs heterostructure with aluminum grown in situ on the surface, and theoretically we show that a superconducting 1D nanowire can harbor Majorana bound states in the absence of spin–orbit coupling.

We fabricate and measure micrometer–sized mesoscopic devices demonstrating the inheritance of superconducting properties in the 2D electron gas.

By placing a quantum point contact proximal to the interface between the 2D electron gas and the aluminum, we are able to demonstrate quantization of conductance in units of 4e2/h indicative of perfect Andreev reflection at the interface. We show that the quantum point contact can be operated as a tunnel probe to locally measure the density of states in the electron gas, which shows dramatically suppressed conductance (a hard gap) for energies below the superconducting pair potential. By fabricating Josephson junctions where the 2D electron gas is flanked by two superconducting banks, we also study the supercurrent carrying properties of the 2D electron gas. When a voltage is passed through the Josephson junction, we observe multiple Andreev reflections and preliminary results point to a highly transmissive interface between the 2D electron gas and the superconductor.

In the theoretical section we demonstrate analytically and numerically, that in a 1D nanowire with a superconducting pairing potential, Majorana bound states can exist in the absence of spin–orbit coupling. Our proposal dispenses with spin–orbit coupling at the expense of a locally varying magnetic field. The presence of the topological state is demonstrated analytically by mapping our model onto a superconducting nanowire with topological properties. We deploy a numerical code using the scattering matrix approach to demonstrate the topological state for realistic parameters of a typical nanowire and magnetic fields generated from small permanent magnets.