Scanning gate microscopy of nonretracing electron-hole trajectories in a normal-superconductor junction

We theoretically study scanning gate microscopy (SGM) of electron and hole trajectories in a quantum point contact (QPC) embedded in a normal-superconductor (NS) junction. At zero voltage bias, the electrons and holes transported through the QPC form angular lobes and are subject to self-interference, which marks the SGM conductance maps with interference fringes analogously as in normal systems. We predict that for an NS junction at nonzero bias, a beating pattern is to occur in the conductance probed with the use of the SGM technique owing to a mismatch of the Fermi wave vectors of electrons and holes. Moreover, the SGM technique exposes a pronounced disturbance in the angular conductance pattern, as the retroreflected hole does not retrace the electron path due to wave vector difference.