Wave-function mapping conditions in open quantum dot structures

Abstract

We discuss the minimal conditions for wave function spectroscopy, in which resonant tunneling is the measurement tool. Two systems are addressed: resonant tunneling diodes, as a toy model, and open quantum dots. The toy model is used to analyze the crucial tunning between the necessary resolution in current-voltage characteristics and the breakdown of the wave functions probing potentials into a level splitting characteristic of double quantum wells. The present results establish a parameter region where the wavefunction spectroscopy by resonant tunneling could be achieved. In the case of open quantum dots, a breakdown of the mapping condition is related to a change into a double quantum dot structure induced by the local probing potential. The analogy between the toy model and open quantum dots show that a precise control over shape and extention of the potential probes is irrelevant for wave function mapping. Moreover, the present system is a realization of a tunable Fano system in the wave function mapping regime. PACS number(s) 73.40.Gk,73.21.Fg,73.21.La

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

“…Scanning gate microscopy (SGM) [1,2] is an experimental technique that probes the reaction of a confined electron system to perturbation introduced by the charge of the atomic force microscope tip that sweeps above the sample area. The SGM technique has been applied to a number of systems, including quantum point contacts [3][4][5][6][7][8][9][10][11], currents in the quantum Hall regime [12][13][14], quantum rings [1,[15][16][17][18][19][20], and quantum dots [2,[21][22][23][24][25]. The quantum dots that are studied with SGM include the closed ones [21], in which the transport is governed by the Coulomb blockade of the current.…”

“…In particular, the conductance maps of systems based on quantum point contacts are generally well correlated to the current flow at the Fermi level [3,5,[7][8][9][10][27][28][29]. For open quantum dots and quantum rings the SGM signal was attributed [1,[15][16][17]22] to the electron density at the Fermi level, called the local density of states (LDOS). According to the semi-classical WKB approximation the perturbation-due to the tip for instance-changes the electron wavelength locally.…”

Wave function mapping at Fano resonances and conductance switching in open quantum dots

“…For obtaining the LDOS, the method consist in a hybridization between the self-energy technique [6] and the recursive method [4]. The total Hamiltonian, H T , is a sum of four terms: the dot connected to the two point contacts regions, described by the H D , the left and rigth contact regions, H L and H R , respectively; as well as the coupling term between the contacts and the dot structure.…”

“…Such imaging procedure should be compared to the energy shift of the antiresonance at E 7 as a function of the perturbation position [4]. A complete imaging using such procedure is shown in Fig.…”

“…Open quantum dots (OQD) with highly transmitting channels are systems where single-particle resonances should be robust with respect to electron-electron interactions. An example of this type of system is described experimentally by Lundberg et al [3], OQDs with such characteristics are suitable for the wavefunction mapping of the quasi-bound states, based on shifts in energy of the resonances induced by AFM tip [4]. This procedure might be also useful for imaging of quantum billiard states [5].…”