Abstract
We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function \ensuremath{\Psi}($x$) of the quantum state, changing the electron's energy by an amount proportional to $|{\ensuremath{\Psi}(x)|}^{2}$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.
Highlights
As electronic devices become smaller, quantum mechanical effects become central to their operation
Few electron quantum dots made from GaAs/AlGaAs heterostructures that contain only a few electrons have welldefined quantum states that can be measured with Coulomb blockade spectroscopy [19,20] and coupled quantum dots can be used for quantum information processing
We propose a novel Scanning probe microscope (SPM) imaging technique that can extract the density profile of the wavefunction of an electron state in a quantum dot using a capacitive probe
Summary
As electronic devices become smaller, quantum mechanical effects become central to their operation. We propose an imaging technique to measure the energy levels of an electron inside a nanostructure and to extract the density profile of the electronic wavefunctions using a cooled SPM. Using first-order perturbation theory, the density profile |ΨN(x)|2 of the electronic wavefunction can be extracted from the energy map ΔEN(xtip), which is measured using Coulomb blockade spectroscopy. This imaging technique could be used to study the transition between the Wigner Crystal and the Luttinger Liquid states predicted by Qian et al (2010) in Ref. 30. The imaging technique we propose in this paper combines Coulomb blockade transport measurements with a weakly perturbing SPM tip to perform energy level spectroscopy and wavefunction diagnostics with the same system
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