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

TL;DR

This paper analyzes how local perturbations affect conductance in quantum point contacts using scattering theory, clarifying the roles of first and second-order corrections in scanning gate microscopy.

Contribution

It provides a detailed theoretical framework for interpreting conductance changes in scanning gate microscopy of quantum point contacts, emphasizing the significance of second-order effects.

Findings

First-order correction is suppressed on conductance plateaus.

Second-order correction is always negative and exhibits fringes.

Spatial decay of the second-order term matches experimental observations.

Abstract

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.