Extracting the density profile of an electronic wave function in a quantum dot

Abstract

The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wavefunction Ψ(x) of the quantum state, changing the electron's energy by an amount proportional to |Ψ(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 wavefunction can be found along the length of the quantum dot.2

Charge density mapping of strongly-correlated few-electron two-dimensional quantum dots by the scanning probe technique

“…We first calculate the energy of N−electron system as a function of the tip position. The charge density extracted from the energy map n r is obtained under the assumption that the action of the tip is perturbative [6,11,12] …”

“…The study covers up to four electrons and quantum dots of various symmetries and profiles. We discuss the adequacy of the perturbative approach for extraction of the electron density [6,11,12] confined in quantum dots and the fidelity of charge images outside the perturbative regime. We find that the images obtained with repulsive (attractive) tip potential tend to overestimate (underestimate) the electron localization.…”

“…The effort on the extraction of the confined charge density by the scanning gate microscopy concerned mostly quasi one-dimensional (1D) quantum dots defined within a quantum wire [7,9,10,11,12,14,15]. Wigner molecules in 1D quantum dots [17] are relatively stable against external perturbations due to the fact that the electrons in one dimension cannot exchange their positions.…”

“…SGM covers both the open systems (quantum point contacts [2], resonant cavities [3], quantum rings [4]) in which the probe is used to read out the wave function at the Fermi level from the conductance perturbations as well as systems that are weakly coupled to the reservoirs, i.e. closed quantum dots [6,7,8,9,11,12,13,14,15]. For the latter, the current flows through the quantum dot only outside the Coulomb blockade conditions [16], i.e., when the chemical potential (µ N = E N − E N −1 ) of N confined electrons lies within the transport window defined by the Fermi levels of source and drain.…”

Probing Wigner correlations in a suspended carbon nanotube

“…On the experimental side, in 2D optical spectroscopy has been employed [3,4]; in 1D transport techniques based on momentum resolved tunneling between quantum wires [41,42,43], and on the magnetic properties of the Wigner molecule [44] have been used. Recently other experimental set ups for the detection of 1D Wigner molecules have been proposed [26,45,46,47,48,49,50]: the transport properties of 1D quantum dots perturbed by local probes such as AFM and STM tips have been demonstrated to be effective in the detection of the Wigner molecule. In many of the experimental realizations, quantum dots are however surrounded by metallic gates which unavoidably screen the Coulomb interactions, demoting the formation of the molecule itself.…”