# Partial local density of states from scanning gate microscopy

## TL;DR

This paper analytically demonstrates how partial local density of states can be extracted from scanning gate microscopy near quantum point contacts, highlighting the effects of transmission imperfections and tip parameters.

## Contribution

It provides a perturbative analytical framework for extracting partial local density of states from weakly invasive scanning gate microscopy measurements in quantum point contacts.

## Key findings

- Partial local density of states can be extracted on conductance plateaus.
- Deviations from perfect transmission significantly affect the extraction.
- Tip radius influences the accuracy of the local density of states measurement.

## Abstract

Scanning gate microscopy images from measurements made in the vicinity of quantum point contacts were originally interpreted in terms of current flow. Some recent work has analytically connected the local density of states to conductance changes in cases of perfect transmission, and at least qualitatively for a broader range of circumstances. In the present paper, we show analytically that in any time-reversal invariant system there are important deviations that are highly sensitive to imperfect transmission. Nevertheless, the unperturbed partial local density of states can be extracted from a weakly invasive scanning gate microscopy experiment, provided the quantum point contact is tuned anywhere on a conductance plateau. A perturbative treatment in the reflection coefficient shows just how sensitive this correspondence is to the departure from the quantized conductance value and reveals the necessity of local averaging over the tip position. It is also shown that the quality of the extracted partial local density of states decreases with increasing tip radius.