Rotational levels in quantum dots

Low energy spectra of isotropic quantum dots are calculated in the regime of low electron densities where Coulomb interaction causes strong correlations. The earlier developed pocket state method is generalized to allow for continuous rotations. Detailed predictions are made for dots of shallow confinements and small particle numbers, including the occurance of spin blockades in transport.Comment: RevTeX, 10 pages, 2 figure

Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement

Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with l_{2}/l_1 \sim l_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particle localization lengths and the exponent $\gamma$ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all ($l_{2} \approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for publication in Phys. Rev.

Breit-Wigner width for two interacting particles in one-dimensional random potential

For two interacting particles (TIP) in one-dimensional random potential the dependence of the Breit-Wigner width $\Gamma$, the local density of states and the TIP localization length on system parameters is determined analytically. The theoretical predictions for $\Gamma$ are confirmed by numerical simulations.Comment: 10 pages Latex, 4 figures included. New version with extended numerical results and discussions of earlier result

Interaction-induced delocalization of two particles in a random potential: Scaling properties

The localization length $\xi_2$ for coherent propagation of two interacting particles in a random potential is studied using a novel and efficient numerical method. We find that the enhancement of $\xi_2$ over the one-particle localization length $\xi_1$ satisfies the scaling relation $\xi_2/\xi_1=f(u/\Delta_\xi)$, where $u$ is the interaction strength and $\Delta_{\xi}$ the level spacing of a wire of length $\xi_1$. The scaling function $f$ is linear over the investigated parameter range. This implies that $\xi_2$ increases faster with $u$ than previously predicted. We also study a novel mapping of the problem to a banded-random-matrix model.Comment: 5 pages and two figures in a uuencoded, compressed tar file; uses revtex and psfig.sty (included); substantial revision of a previous version of the paper including newly discovered scaling behavio

Absence of bimodal peak spacing distribution in the Coulomb blockade regime

Using exact diagonalization numerical methods, as well as analytical arguments, we show that for the typical electron densities in chaotic and disordered dots the peak spacing distribution is not bimodal, but rather Gaussian. This is in agreement with the experimental observations. We attribute this behavior to the tendency of an even number of electrons to gain on-site interaction energy by removing the spin degeneracy. Thus, the dot is predicted to show a non trivial electron number dependent spin polarization. Experimental test of this hypothesis based on the spin polarization measurements are proposed.Comment: 13 pages, 3 figures, accepted for publication in PRL - a few small change

Chaos Thresholds in finite Fermi systems

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slater-determinant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.Comment: 9 pages, REVTEX, 2 eps figures. Enlarged versio

Suppression of Ground-State Magnetization in Finite-Sized Systems Due to Off-Diagonal Interaction Fluctuations

We study a generic model of interacting fermions in a finite-sized disordered system. We show that the off-diagonal interaction matrix elements induce density of states fluctuations which generically favor a minimum spin ground state at large interaction amplitude, $U$. This effect competes with the exchange effect which favors large magnetization at large $U$, and it suppresses this exchange magnetization in a large parameter range. When off-diagonal fluctuations dominate, the model predicts a spin gap which is larger for odd-spin ground states as for even-spin, suggesting a simple experimental signature of this off-diagonal effect in Coulomb blockade transport measurements.Comment: Final, substantially modified version of the article. Accepted for publication in Physical Review Letter

Nonequilibrium excitations in Ferromagnetic Nanoparticles

In recent measurements of tunneling transport through individual ferromagnetic Co nanograins, Deshmukh, Gu\'eron, Ralph et al. \cite{mandar,gueron} (DGR) observed a tunneling spectrum with discrete resonances, whose spacing was much smaller than what one would expect from naive independent-electron estimates. In a previous publication, \cite{prl_kleff} we had suggested that this was a consequence of nonequilibrium excitations, and had proposed a ``minimal model'' for ferromagnetism in nanograins with a discrete excitation spectrum as a framework for analyzing the experimental data. In the present paper, we provide a detailed analysis of the properties of this model: We delineate which many-body electron states must be considered when constructing the tunneling spectrum, discuss various nonequilibrium scenarios and compare their results with the experimental data of Refs. \cite{mandar,gueron}. We show that a combination of nonequilibrium spin- and single-particle excitations can account for most of the observed features, in particular the abundance of resonances, the resonance spacing and the absence of Zeeman splitting.Comment: 13 pages, 10 figure

Non-equilibrium transport through a vertical quantum dot in the absence of spin-flip energy relaxation

We investigate non-equilibrium transport in the absence of spin-flip energy relaxation in a few-electron quantum dot artificial atom. Novel non-equilibrium tunneling processes involving high-spin states which cannot be excited from the ground state because of spin-blockade, and other processes involving more than two charge states are observed. These processes cannot be explained by orthodox Coulomb blockade theory. The absence of effective spin relaxation induces considerable fluctuation of the spin, charge, and total energy of the quantum dot. Although these features are revealed clearly by pulse excitation measurements, they are also observed in conventional dc current characteristics of quantum dots.Comment: accepted for publication in Phys. Rev.Let