What is measured in the scanning gate microscopy of a quantum point contact?

Rodolfo A. Jalabert, Wojciech Szewc, Steven Tomsovic, Dietmar Weinmann

Published 2010-07-15, updated 2010-10-12Version 2

The conductance change due to a local perturbation in a phase-coherent nanostructure is calculated. The general expressions to first and second order in the perturbation are applied to the scanning gate microscopy of a two-dimensional electron gas containing a quantum point contact. The first-order correction depends on two scattering states with electrons incoming from opposite leads and is suppressed on a conductance plateau; it is significant in the step regions. On the plateaus, the dominant second-order term likewise depends on scattering states incoming from both sides. It is always negative, exhibits fringes, and has a spatial decay consistent with experiments.