Interference features in scanning gate conductance maps of quantum point contacts with disorder

TL;DR

This paper investigates interference features in conductance maps of disordered quantum point contacts using scanning gate microscopy, revealing new elliptical and funnel-shaped interference patterns and providing a model to locate impurities.

Contribution

It introduces a detailed analysis of interference fringes in disordered QPCs, including the first description of funnel-shaped features and a simple model for impurity localization.

Findings

Interference fringes are temperature stable far from the QPC.

Funnel-shaped features accompany branch splitting.

Elliptical fringes depend on tip voltage and temperature.

Abstract

We consider quantum point contacts (QPCs) defined within disordered two-dimensional electron gases as studied by scanning gate microscopy. We evaluate the conductance maps in the Landauer approach and wave function picture of electron transport for samples with both low and high electron mobility at finite temperatures. We discuss the spatial distribution of the impurities in the context of the branched electron flow. We reproduce the surprising temperature stability of the experimental interference fringes far from the QPC. Next, we discuss -- previously undescribed -- funnel-shaped features that accompany splitting of the branches visible in previous experiments. Finally, we study elliptical interference fringes formed by an interplay of scattering by the point-like impurities and by the scanning probe. We discuss the details of the elliptical features as functions of the tip voltage and the temperature, showing that the first interference fringe is very robust against the thermal widening of the Fermi level. We present a simple analytical model that allows for extraction of the impurity positions and the electron gas depletion radius induced by the negatively charged tip of the atomic force microscope, and apply this model on experimental scanning gate images showing such elliptical fringes.