Ja n 19 97 Statistics of conductance oscillations of a quantum dot in the Coulomb - blockade regime

The fluctuations and the distribution of the conductance peak spac-ings of a quantum dot in the Coulomb-blockade regime are studied and compared with the predictions of random matrix theory (RMT). The experimental data were obtained in transport measurements performed on a semiconductor quantum dot fabricated in a GaAs-AlGaAs heterostruc-ture. It is found that the fluctuations in the peak spacings are considerably larger than the mean level spacing in the quantum dot. The distribution of the spacings appears Gaussian both for zero and for non-zero magnetic field and deviates strongly from the RMT-predictions. Advanced nanofabrication techniques have made it possible to confine small numbers of electrons electrostatically within the two-dimensional electron gas (2DEG) of a semiconductor heterostructure [1, 2]. Both the electric charge and energy of such " quantum dots " are quantised and hence such structures are sometimes referred to as " artificial atoms " [3, 4]. In transport measurements the charging of these electron islands with single electrons leads to the observation of periodic conductance oscillations in the Coulomb-blockade regime [1]. These reflect the electrostatic coupling of the quantum dot to its environment and, additionally, they contain information about the eigenenergies and eigen-functions of the electrons in the dot. Due to irregularities in the electrostatic confinement potential and electron-electron interactions, the corresponding classical motion of the electrons in the quantum dot can be expected to be chaotic (nonintegrable) [5, 6, 7]. Consequently, recent experiments have considered the peak height distribution [8, 9], parametric conductance correlations [9] and level statistics [10] of a quantum dot in the Coulomb-blockade regime to test the concepts developed for the quantum mechanical description of classically chaotic systems (" quantum chaos " [11, 12]). In particular random matrix theory (RMT)