Imaging correlated wave functions of few-electron quantum dots: Theory and STS experiments

Massimo Rontani

Modena, Italy

Friday, 7 September 2007, 13:30
Seminar room F

Recent experiments have demonstrated that the regime of very few electrons in quantum dots (QDs) displays peculiar properties, different from the many-electron case: Among these, the non-universal behavior in transport interference experiments [1] and the manifestation of strong correlation effects in light scattering [2]. However, no direct observation of such effects in wave function images was obtained so far. Among the available techniques, scanning tunneling spectroscopy (STS) provides spectacular images of QD wave functions [3]. Experiments so far have shown maps of localized orbitals, that could be explained in terms of an independent-electron model.
In this paper we focus on QDs where we expect that electron-electron interaction may instead be relevant. We show that the wave function actually probed by STS is the space-resolved spectral density amplitude of the one-particle propagator (or quasi-particle wave function), which can considerably deviate from the independent-electron wave function, due to correlation effects [4]. To this aim we investigate, both experimentally and theoretically [5], STS wave function maps of single and freestanding strain-induced InAs QDs grown on GaAs(001). The sequence of measured wave functions cannot be explained in terms of single-electron orbitals. We compare the measured maps with those predicted by a numerical model which takes into account QD anisotropy and the full correlation effects, and we are able to separately identify ground- and excited-state wave functions corresponding to the injection of a first, second, and perhaps third electron into the QD. This interpretation is supported by the analysis of the measured differential conductance as a function of the stabilization current.
The quasi-particle wave function corresponding to the ground state -> ground state tunneling process N = 1 -> N = 2 displays a surprising two-peak charge modulation which is inconsistent with the simple picture of a doubly occupied s-like orbital. This effect, qualitatively reproduced by our simulations, is due to the destructive interference between different components of the correlated singlet wave function.

[1] M. Avinun-Kalish et al., Nature 436, 529 (2005).
[2] C. P. Garcia et al., Phys. Rev. Lett. 95, 266806 (2005).
[3] T. Maltezopoulos et al., Phys. Rev. Lett. 91, 196804 (2003).
[4] M. Rontani and E. Molinari, Phys. Rev. B 71, 233106 (2005).
[5] M. Rontani et al., J. Appl. Phys. 101, 081714 (2007); G. Maruccio et al., Nano Letters, in press (2007).