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

Abstract

Abstract. We perform a numerical simulation of mapping of charge confined in quantum dots by the scanning probe technique. We solve the few-electron Schrödinger equation with the exact diagonalization approach and evaluate the energy maps in function of the probe position. Next, from the energy maps we try to reproduce the charge density distribution using an integral equation given by the perturbation theory. The reproduced density maps are confronted with the original ones. The present study covers two-dimensional quantum dots of various geometries and profiles with the one-dimensional (1D) quantum dot as a limit case. We concentrate on large quantum dots for which strong electron-electron correlations appear. For circular dots the correlations lead to formation of Wigner molecules that in the presence of the tip appear in the laboratory frame. The unperturbed rotationally-symmetric charge density is surprisingly well reproduced by the mapping. We find in general that the size of the confined droplet as well as the spatial extent of the charge density maxima is underestimated for repulsive tip potential and overestimated for the attractive tip. In lower-symmetry quantum dots the Wigner molecules with single-electron islands nucleate for some electron numbers even in the absence of the tip. These charge densities are well resolved by the mapping. The single-electron islands appear in the laboratory frame provided that classical point charge density distribution is unique, in the 1D limit of confinement in particular. We demonstrate that for electron systems which possess a few equivalent classical configurations the repulsive probe switches between the configurations. In consequence the charge density evades mapping by the repulsive probe.

Imaging transition to fractional quantum Hall regime by Coulomb blockade microscopy

“…9) for N = 2 and N = 3 electrons in the square quantum dot possess more than one configurations of the lowest potential energy: with electrons occupying diagonal corners of the square for N = 2 and with one of the corners unoccupied for N = 3. In these conditions of a classical degeneracy 29 the system undergoes parity symmetry transformations in external magnetic field which For three [Fig. 11(d,e)] and two electrons (not shown) the density exhibits maxima at the corners of the potential, which are not resolved by the charge density mapping at high field.…”

“…The study of two-dimensional quantum dots in the absence of the magnetic field was given in our previous paper. 29 This paper is organized as follows: Section II explains the model and computational approach; Section III presents the results for an ideally circular parabolic quantum dot, for the quantum dot perturbed by a presence of a charged defect, as well as for confinement potential of a rectangular shape and flat profile near the minimum. Summary and conclusions are given in Section IV.…”

Pauli blockade microscopy of quantum dots

“…The method was also used to probe the states localized in quantum dots 3,4,8,[10][11][12]14,15 , where the potential of the tip switches on or off the Coulomb blockade 20 of the current flow. The technique was nicknamed a Coulomb blockade microscopy [21][22][23][24] .…”

Current noise as a probe for Wigner molecules

“…Ideas have been put forward for directly exploring density oscillations coupling a charged AFM tip to he dot and performing a transport experiment [52,53]: a shift in the linear conductance peaks is then produced proportional to the local electron density [52][53][54]. Also, a STM tip can be envisioned as a tool to investigate the Wigner regime, probing the local tunnelling density of states, which is a quantity sensitive to the formation of a Wigner molecule in the dot.…”