Quantum-classical correspondence for local density of states and eigenfunctions of a chaotic periodic billiard

Classical-quantum correspondence for conservative chaotic Hamiltonians is investigated in terms of the structure of the eigenfunctions and the local density of states, using as a model a 2D rippled billiard in the regime of global chaos. The influence of the observed localized and sparsed states in the quantum-classical correspondence is discussed.Comment: 8 pages, 4 figure

Finite temperature effects in Coulomb blockade quantum dots and signatures of spectral scrambling

The conductance in Coulomb blockade quantum dots exhibits sharp peaks whose spacings fluctuate with the number of electrons. We derive the temperature-dependence of these fluctuations in the statistical regime and compare with recent experimental results. The scrambling due to Coulomb interactions of the single-particle spectrum with the addition of an electron to the dot is shown to affect the temperature-dependence of the peak spacing fluctuations. Spectral scrambling also leads to saturation in the temperature dependence of the peak-to-peak correlator, in agreement with recent experimental results. The signatures of scrambling are derived using discrete Gaussian processes, which generalize the Gaussian ensembles of random matrices to systems that depend on a discrete parameter -- in this case, the number of electrons in the dot.Comment: 14 pages, 4 eps figures included, RevTe

Statistics of Coulomb Blockade Peak Spacings within the Hartree-Fock Approximation

We study the effect of electronic interactions on the addition spectra and on the energy level distributions of two-dimensional quantum dots with weak disorder using the self-consistent Hartree-Fock approximation for spinless electrons. We show that the distribution of the conductance peak spacings is Gaussian with large fluctuations that exceed, in agreement with experiments, the mean level spacing of the non-interacting system. We analyze this distribution on the basis of Koopmans' theorem. We show furthermore that the occupied and unoccupied Hartree-Fock levels exhibit Wigner-Dyson statistics.Comment: 5 pages, 2 figures, submitted for publicatio

Quantum dots in magnetic fields: thermal response of broken symmetry phases

We investigate the thermal properties of circular semiconductor quantum dots in high magnetic fields using finite temperature Hartree-Fock techniques. We demonstrate that for a given magnetic field strength quantum dots undergo various shape phase transitions as a function of temperature, and we outline possible observable consequences.Comment: In Press, Phys. Rev. B (2001

Spin interactions and switching in vertically tunnel-coupled quantum dots

We determine the spin exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few Tesla, and perpendicular fields of the order of 10 Tesla for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken technique, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch on and off the spin coupling with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.Comment: 13 pages, 9 figure

Voltage-tunable singlet-triplet transition in lateral quantum dots

Results of calculations and high source-drain transport measurements are presented which demonstrate voltage-tunable entanglement of electron pairs in lateral quantum dots. At a fixed magnetic field, the application of a judiciously-chosen gate voltage alters the ground-state of an electron pair from an entagled spin singlet to a spin triplet.Comment: 8.2 double-column pages, 10 eps figure

Non-linear response of a Kondo system: Perturbation approach to the time dependent Anderson impurity model

Nonlinear tunneling current through a quantum dot (an Anderson impurity system) subject to both constant and alternating electric fields is studied in the Kondo regime. A systematic diagram technique is developed for perturbation study of the current in physical systems out of equilibrium governed by time - dependent Hamiltonians of the Anderson and the Kondo models. The ensuing calculations prove to be too complicated for the Anderson model, and hence, a mapping on an effective Kondo problem is called for. This is achieved by constructing a time - dependent version of the Schrieffer - Wolff transformation. Perturbation expansion of the current is then carried out up to third order in the Kondo coupling J yielding a set of remarkably simple analytical expressions for the current. The zero - bias anomaly of the direct current differential conductance is shown to be suppressed by the alternating field while side peaks develop at finite source - drain voltage. Both the direct component and the first harmonics of the time - dependent response are equally enhanced due to the Kondo effect, while amplitudes of higher harmonics are shown to be relatively small. A zero alternating bias anomaly is found in the alternating current differential conductance, that is, it peaks around zero alternating bias. This peak is suppressed by the constant bias. No side peaks show up in the differential alternating - conductance but their counterpart is found in the derivative of the alternating current with respect to the direct bias. The results pertaining to nonlinear response are shown to be valid also below the Kondo temperature.Comment: 55 latex pages 11 ps figure

Single-electron transport driven by surface acoustic waves: moving quantum dots versus short barriers

We have investigated the response of the acoustoelectric current driven by a surface-acoustic wave through a quantum point contact in the closed-channel regime. Under proper conditions, the current develops plateaus at integer multiples of ef when the frequency f of the surface-acoustic wave or the gate voltage Vg of the point contact is varied. A pronounced 1.1 MHz beat period of the current indicates that the interference of the surface-acoustic wave with reflected waves matters. This is supported by the results obtained after a second independent beam of surface-acoustic wave was added, traveling in opposite direction. We have found that two sub-intervals can be distinguished within the 1.1 MHz modulation period, where two different sets of plateaus dominate the acoustoelectric-current versus gate-voltage characteristics. In some cases, both types of quantized steps appeared simultaneously, though at different current values, as if they were superposed on each other. Their presence could result from two independent quantization mechanisms for the acoustoelectric current. We point out that short potential barriers determining the properties of our nominally long constrictions could lead to an additional quantization mechanism, independent from those described in the standard model of 'moving quantum dots'.Comment: 25 pages, 12 figures, to be published in a special issue of J. Low Temp. Phys. in honour of Prof. F. Pobel

Fano Resonances in Electronic Transport through a Single Electron Transistor

We have observed asymmetric Fano resonances in the conductance of a single electron transistor resulting from interference between a resonant and a nonresonant path through the system. The resonant component shows all the features typical of quantum dots, but the origin of the non-resonant path is unclear. A unique feature of this experimental system, compared to others that show Fano line shapes, is that changing the voltages on various gates allows one to alter the interference between the two paths.Comment: 8 pages, 6 figures. Submitted to PR