Conductance enhancement in quantum-point-contact semiconductor-superconductor devices

We present numerical calculations of the conductance of an interface between a phase-coherent two-dimensional electron gas and a superconductor with a quantum point contact in the normal region. Using a scattering matrix approach we reconsider the geometry of De Raedt, Michielsen, and Klapwijk [Phys. Rev. B 50, 631 (1994)] which was studied within the time-dependent Bogoliubov–de Gennes formalism. We find that the factor-of-2 enhancement of the conductance $G_{\mathrm{NS}}$ compared to the normal state conductance $G_{\mathrm{N}}$ for ideal interfaces may be suppressed for interfaces with a quantum point contact with only a few propagating modes. The suppression is found to depend strongly on the position of the Fermi level. We also study the suppression due to a barrier at the interface and find an anomalous behavior caused by quasiparticle interference. Finally, we consider the limit of sequential tunneling and find a suppression of the factor-of-2 enhancement which may explain the absence of conductance enhancement in experiments on metal-superconductor structures.