Magnetically induced chessboard pattern in the conductance of a Kondo quantum dot

We quantitatively describe the main features of the magnetically induced conductance modulation of a Kondo quantum dot -- or chessboard pattern -- in terms of a constant-interaction double quantum dot model. We show that the analogy with a double dot holds down to remarkably low magnetic fields. The analysis is extended by full 3D spin density functional calculations. Introducing an effective Kondo coupling parameter, the chessboard pattern is self-consistently computed as a function of magnetic field and electron number, which enables us to quantitatively explain our experimental data.Comment: 4 pages, 3 color figure

Rashba-control for the spin excitation of a fully spin polarized vertical quantum dot

Far infrared radiation absorption of a quantum dot with few electrons in an orthogonal magnetic field could monitor the crossover to the fully spin polarized state. A Rashba spin-orbit coupling can tune the energy and the spin density of the first excited state which has a spin texture carrying one extra unit of angular momentum. The spin orbit coupling can squeeze a flipped spin density at the center of the dot and can increase the gap in the spectrum.Comment: 4 pages, 5 figure

Gauge invariant grid discretization of Schr\"odinger equation

Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that obtained by a straightforward discretization of the continuous Hamiltonian by means of balanced difference methods, and with a tight-binding Hamiltonian. The proposed Hamiltonian and the balanced difference one are used to compute the energy spectrum of a charged particle in a two-dimensional parabolic potential in the presence of a perpendicular, constant magnetic field. With this example we point out how a "naive" discretization gives rise to an explicit breaking of the gauge invariance and to large errors in the computed eigenvalues and corresponding probability densities; in particular, the error on the eigenfunctions may lead to very poor estimates of the mean values of some relevant physical quantities on the corresponding states. On the contrary, the proposed discretized Hamiltonian allows a reliable computation of both the energy spectrum and the probability densities.Comment: 7 pages, 4 figures, discussion about tight-binding Hamiltonians adde

Effect of confinement potential shape on exchange interaction in coupled quantum dots

Exchange interaction has been studied for electrons in coupled quantum dots (QD's) by a configuration interaction method using confinement potentials with different profiles. The confinement potential has been parametrized by a two-centre power-exponential function, which allows us to investigate various types of QD's described by either soft or hard potentials of different range. For the soft (Gaussian) confinement potential the exchange energy decreases with increasing interdot distance due to the decreasing interdot tunnelling. For the hard (rectangular-like) confinement potential we have found a non-monotonic behaviour of the exchange interaction as a function of distance between the confinement potential centres. In this case, the exchange interaction energy exhibits a pronounced maximum for the confinement potential profile which corresponds to the nanostructure composed of the small inner QD with a deep potential well embedded in the large outer QD with a shallow potential well. This effect results from the strong localization of electrons in the inner QD, which leads to the large singlet-triplet splitting. Implications of this finding for quantum logic operations have been discussed.Comment: 16 pages, including 11 figure

Chaos in Quantum Dots: Dynamical Modulation of Coulomb Blockade Peak Heights

The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in this case the conductance has a peak. In a small grain with quantized electron states, referred to as a quantum dot, the magnitude of the conductance peak is directly related to the magnitude of the wavefunction near the contacts to the dot. Since dots are generally irregular in shape, the dynamics of the electrons is chaotic, and the characteristics of Coulomb blockade peaks reflects those of wavefunctions in chaotic systems. Previously, a statistical theory for the peaks was derived by assuming these wavefunctions to be completely random. Here we show that the specific internal dynamics of the dot, even though it is chaotic, modulates the peaks: because all systems have short-time features, chaos is not equivalent to randomness. Semiclassical results are derived for both chaotic and integrable dots, which are surprisingly similar, and compared to numerical calculations. We argue that this modulation, though unappreciated, has already been seen in experiments.Comment: 4 pages, 3 postscript figs included (2 color), uses epsf.st

Towards an Explanation of the Mesoscopic Double-Slit Experiment: a new model for charging of a Quantum Dot

For a quantum dot (QD) in the intermediate regime between integrable and fully chaotic, the widths of single-particle levels naturally differ by orders of magnitude. In particular, the width of one strongly coupled level may be larger than the spacing between other, very narrow, levels. In this case many consecutive Coulomb blockade peaks are due to occupation of the same broad level. Between the peaks the electron jumps from this level to one of the narrow levels and the transmission through the dot at the next resonance essentially repeats that at the previous one. This offers a natural explanation to the recently observed behavior of the transmission phase in an interferometer with a QD.Comment: 4 pages, 2 figures, Journal versio

Semiclassical Theory of Coulomb Blockade Peak Heights in Chaotic Quantum Dots

We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate the peak height distributions and the correlation functions. We demonstrate that the corrections to the corresponding results of the standard statistical theory are non-universal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For non-zero temperature, the correlation function obtained theoretically is in good agreement with that measured experimentally.Comment: 5 color eps figure

Wigner Crystallization in a Quasi-3D Electronic System

When a strong magnetic field is applied perpendicularly (along z) to a sheet confining electrons to two dimensions (x-y), highly correlated states emerge as a result of the interplay between electron-electron interactions, confinement and disorder. These so-called fractional quantum Hall (FQH) liquids form a series of states which ultimately give way to a periodic electron solid that crystallizes at high magnetic fields. This quantum phase of electrons has been identified previously as a disorder-pinned two-dimensional Wigner crystal with broken translational symmetry in the x-y plane. Here, we report our discovery of a new insulating quantum phase of electrons when a very high magnetic field, up to 45T, is applied in a geometry parallel (y-direction) to the two-dimensional electron sheet. Our data point towards this new quantum phase being an electron solid in a "quasi-3D" configuration induced by orbital coupling with the parallel field

Noninvasive fractal biomarker of clock neurotransmitter disturbance in humans with dementia

Human motor activity has a robust, intrinsic fractal structure with similar patterns from minutes to hours. The fractal activity patterns appear to be physiologically important because the patterns persist under different environmental conditions but are significantly altered/reduced with aging and Alzheimer's disease (AD). Here, we report that dementia patients, known to have disrupted circadian rhythmicity, also have disrupted fractal activity patterns and that the disruption is more pronounced in patients with more amyloid plaques (a marker of AD severity). Moreover, the degree of fractal activity disruption is strongly associated with vasopressinergic and neurotensinergic neurons (two major circadian neurotransmitters) in postmortem suprachiasmatic nucleus (SCN), and can better predict changes of the two neurotransmitters than traditional circadian measures. These findings suggest that the SCN impacts human activity regulation at multiple time scales and that disrupted fractal activity may serve as a non-invasive biomarker of SCN neurodegeneration in dementia