Scanned gate microscopy of a one-dimensional quantum dot

TL;DR

This paper provides an analytical and numerical study of how a sharp conducting tip interacts electrostatically with a one-dimensional quantum wire in scanned gate microscopy, revealing conditions for imaging individual electrons.

Contribution

It offers a tractable analytical model for electrostatic interactions in SGM of 1D wires and identifies the spatial scale for electron imaging based on tip height.

Findings

Imaging of individual electrons is feasible when electron separation exceeds the tip's height.

The characteristic electrostatic coupling scale is equal to the tip height above the substrate.

Differences between weakly and strongly invasive SGM regimes are characterized.

Abstract

We analyze electrostatic interaction between a sharp conducting tip and a thin one-dimensional wire, e.g., a carbon nanotube, in a scanned gate microscopy (SGM) experiment. The problem is analytically tractable if the wire resides on a thin dielectric substrate above a metallic backgate. The characteristic spatial scale of the electrostatic coupling to the tip is equal to its height above the substrate. Numerical simulations indicate that imaging of individual electrons by SGM is possible once the mean electron separation exceeds this scale (typically, a few tens of nm). Differences between weakly and strongly invasive SGM regimes are pointed out.