On the scaling approach to electron-electron interactions in a chaotic quantum dot

A scaling theory is used to study the low energy physics of electron-electron interactions in a double quantum dot. We show that the fact that electrons are delocalized over two quantum dots does not affect the instability criterion for the description of electron-electron interactions in terms of a ``universal interaction Hamiltonian''.Comment: 4 pages, 3 figure

Ground-state energy and spin in disordered quantum dots

We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain proportional to level spacing. With increasing interaction strength, the even-odd alternation of addition energies disappears, and the probability of non-minimal spin increases, but never exceeds 50%. Within a two-orbital model, we show that the off-diagonal Coulomb matrix elements help stabilize a ground state of minimal spin.Comment: 10 pages, 2 figure

Quantum dots with two electrons: Singlet-triplet transitions

The magnetic character of the ground-state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is found that the coupling to the continuum of propagating states on the leads, in conjunction with the electron-electron interactions, may result in a delocalization of the bound state of the two electrons. This, in turn, reduces significantly the range of the Coulomb interaction parameters over which singlet-triplet transitions can be realized. It is also found that the coupling to the leads favors the singlet ground-state.Comment: 8 pages, submitted to Phys. Rev.

Spin and interaction effects in quantum dots: a Hartree-Fock-Koopmans approach

We use a Hartree-Fock-Koopmans approach to study spin and interaction effects in a diffusive or chaotic quantum dot. In particular, we derive the statistics of the spacings between successive Coulomb-blockade peaks. We include fluctuations of the matrix elements of the two-body screened interaction, surface-charge potential, and confining potential to leading order in the inverse Thouless conductance. The calculated peak-spacing distribution is compared with experimental results.Comment: 5 pages, 4 eps figures, revise

Interplay between pairing and exchange in small metallic dots

We study the effects of the mesoscopic fluctuations on the competition between exchange and pairing interactions in ultrasmall metallic dots when the mean level spacing is comparable or larger than the BCS pairing energy. Due to mesoscopic fluctuations, the probability to have a non-zero spin ground state may be non-vanishing and shows universal features related to both level statistics and interaction. Sample to sample fluctuations of the renormalized pairing are enlightened.Comment: 10 pages, 5 figure

Linear conductance in Coulomb-blockade quantum dots in the presence of interactions and spin

We discuss the calculation of the linear conductance through a Coulomb-blockade quantum dot in the presence of interactions beyond the charging energy. In the limit where the temperature is large compared with a typical tunneling width, we use a rate-equations approach to describe the transitions between the corresponding many-body states. We discuss both the elastic and rapid-thermalization limits, where the rate of inelastic scattering in the dot is either small or large compared with the elastic transition rate, respectively. In the elastic limit, we find several cases where a closed solution for the conductance is possible, including the case of a constant exchange interaction. In the rapid-thermalization limit, a closed solution is possible in the general case. We show that the corresponding expressions for the linear conductance simplify for a Hamiltonian that is invariant under spin rotations.Comment: 11 pages, no figures, revtex

Exchange and the Coulomb blockade: Peak height statistics in quantum dots

We study the effect of the exchange interaction on the Coulomb blockade peak height statistics in chaotic quantum dots. Because exchange reduces the level repulsion in the many body spectrum, it strongly affects the fluctuations of the peak conductance at finite temperature. We find that including exchange substantially improves the description of the experimental data. Moreover, it provides further evidence of the presence of high spin states (S>1) in such systems.Comment: 5 pages, 4 figures. Published version, title change

Mesoscopic interplay of superconductivity and ferromagnetism in ultra-small metallic grains

We review the effects of electron-electron interactions on the ground-state spin and the transport properties of ultra-small chaotic metallic grains. Our studies are based on an effective Hamiltonian that combines a superconducting BCS-like term and a ferromagnetic Stoner-like term. Such terms originate in pairing and spin exchange correlations, respectively. This description is valid in the limit of a large dimensionless Thouless conductance. We present the ground-state phase diagram in the fluctuation-dominated regime where the single-particle mean level spacing is comparable to the bulk BCS pairing gap. This phase diagram contains a regime in which pairing and spin exchange correlations coexist in the ground-state wave function. We discuss the calculation of the tunneling conductance for an almost-isolated grain in the Coulomb-blockade regime, and present measurable signatures of the competition between superconductivity and ferromagnetism in the mesoscopic fluctuations of the conductance.Comment: 6 pages, 3 figures, To be published in the proceedings of the NATO Advance Research Workshop "Recent Advances in Nonlinear Dynamics and Complex System Physics.

Diamagnetic Persistent Currents and Spontaneous Time-Reversal Symmetry Breaking in Mesoscopic Structures

Recently, new strongly interacting phases have been uncovered in mesoscopic systems with chaotic scattering at the boundaries by two of the present authors and R. Shankar. This analysis is reliable when the dimensionless conductance of the system is large, and is nonperturbative in both disorder and interactions. The new phases are the mesoscopic analogue of spontaneous distortions of the Fermi surface induced by interactions in bulk systems and can occur in any Fermi liquid channel with angular momentum $m$. Here we show that the phase with $m$ even has a diamagnetic persistent current (seen experimentally but mysterious theoretically), while that with $m$ odd can be driven through a transition which spontaneously breaks time-reversal symmetry by increasing the coupling to dissipative leads.Comment: 4 pages, three eps figure

Kondo effect induced by a magnetic field

We study peculiarities of transport through a Coulomb blockade system tuned to the vicinity of the spin transition in its ground state. Such transitions can be induced in practice by application of a magnetic field. Tunneling of electrons between the dot and leads mixes the states belonging to the ground state manifold of the dot. Remarkably, both the orbital and spin degrees of freedom of the electrons are engaged in the mixing at the singlet-triplet transition point. We present a model which provides an adequate theoretical description of recent experiments with semiconductor quantum dots and carbon nanotubes