Conductance microscopy of quantum dots weakly or strongly coupled to the conducting channel

TL;DR

This paper investigates how conductance maps from scanning gate microscopy reveal local density of states in quantum dots, showing that weak coupling yields exact correspondence, while strong coupling only under specific conditions.

Contribution

It demonstrates the precise relationship between conductance maps and local density of states in quantum dots under different coupling regimes using wave function and perturbation theory.

Findings

Conductance maps for delta-like perturbations reproduce local density of states in weakly coupled dots.

Weak coupling is characterized by conductance varying between P-1 and P units of 2e^2/h.

Strong coupling only shows local density of states signatures at specific Fermi energy levels.

Abstract

We consider scanning gate conductance microscopy of an open quantum dot that is connected to the conducting channel using the wave function description of the quantum transport and a finite difference approach. We discuss the information contained in conductance ($G$) maps. We demonstrate that the maps for a delta-like potential perturbation exactly reproduce the local density of states for the quantum dot that is weakly coupled to the channel, i.e. when the connection of the channel to the dot transmits a single transport mode only. We explain this finding in terms of the Lippmann-Schwinger perturbation theory. We demonstrate that the signature of the weak coupling conditions is the conductance which for $P$ subbands at the Fermi level varies between $P-1$ and $P$ in units of ${2e^2}/{h}$. For stronger coupling of the quantum dot to the channel the $G$ maps resolve the local density of states only for very specific work points with the Fermi energy coinciding with quasi-bound energy levels.