Electron paths and double-slit interference in the scanning gate microscopy

We analyze electron paths in a solid-state double-slit interferometer based on two-dimensional electron gas and mapping by scanning gate microscopy (SGM). A device with a quantum point source contact of a split exit and a drain contact for electron detection is considered. We study the SGM maps of source-drain conductance (G) as functions of the probe position, and we find that for a narrow drain, the classical electron paths are clearly resolved without any trace of double-slit interference. The latter is only present in the SGM maps of backscattering (R) probability. Double-slit interference is found in the G maps for a wider drain contact, but at the expense of a loss of information on the electron trajectories. We discuss the interplay of Young's interference and interference effects between various electron paths introduced by the tip and the electron detector. The stability of the G and R maps versus the geometry parameters of the scattering device is also discussed.