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

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.

17 pages, 12 figures

References in corpus (16)

• Imaging Magnetic Focusing of Coherent Electron Waves
• Unexpected features of branched flow through high-mobility two-dimensional electron gases
• On the imaging of electron transport in semiconductor quantum structures by scanning-gate microscopy: successes and limitations
• Probing decoherence through Fano resonances
• Imaging Electron Wave Functions Inside Open Quantum Rings
• Imaging Coulomb Islands in a Quantum Hall Interferometer
• Electron interferometer formed with a scanning probe tip and quantum point contact
• Local Density of States in Mesoscopic Samples from Scanning Gate Microscopy
• What is measured in the scanning gate microscopy of a quantum point contact?
• AFM probe for the signatures of Wigner correlations in the conductance of a one-dimensional quantum dot
• Measurement of the Tip-Induced Potential in Scanning Gate Experiments
• Imaging a 1-electron InAs quantum dot in an InAs/InP nanowire
• Direct measurement of the phase coherence length in a GaAs/GaAlAs square network
• Single electron charging of impurity sites visualized by scanning gate experiments on a quantum point contact
• Spatial mapping and manipulation of two tunnel-coupled quantum dots
• Non-linear Coulomb blockade microscopy of a correlated one-dimensional quantum dot

Cited by in corpus (3)

• Creating and Steering Highly Directional Electron Beams in Graphene
• Electron backscattering in a cavity: ballistic and coherent effects
• Multitip scanning gate microscopy for ballistic transport studies in systems with two-dimensional electron gas