Effects of spin and exchange interaction on the Coulomb-blockade peak statistics in quantum dots

Mesoscopic Stoner Instability in Open Quantum Dots: Suppression of Coleman-Weinberg Mechanism by Electron Tunneling

The mesoscopic Stoner instability is an intriguing manifestation of symmetry breaking in isolated metallic quantum dots, underlined by the competition between single-particle energy and Heisenberg exchange interaction. Here we study this phenomenon in the presence of tunnel coupling to a reservoir. We analyze the spin susceptibility of electrons on the quantum dot for different values of couplings and temperature. Our results indicate the existence of a "quantum phase transition" at a critical value of the tunneling coupling, which is determined by the Stoner-enhanced exchange interaction. This quantum phase transition is a manifestation of the suppression of the Coleman-Weinberg mechanism of symmetry breaking, induced by coupling to the reservoir.

Mesoscopic stoner instability in metallic nanoparticles revealed by shot noise

We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallel magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe the mesoscopic Stoner instability.

Cotunneling current through a two-level quantum dot coupled to magnetic leads: the role of exchange interaction

The cotunneling current through a two-level quantum dot weakly coupled to ferromagnetic leads is studied in the Coulomb blockade regime. The cotunneling current is calculated analytically under simple but realistic assumptions as follows: (i) the quantum dot is described by the universal Hamiltonian, (ii) it is doubly occupied, and (iii) it displays a fast spin relaxation. We find that the dependence of the differential conductance on the bias voltage is significantly affected by the exchange interaction on the quantum dot. In particular, for antiparallel magnetic configurations in the leads, the exchange interaction results in the appearance of interference-type contributions from the inelastic processes to the cotunneling current. Such dependence of the cotunneling current on the tunneling amplitude phases should also occur in multi-level quantum dots weakly coupled to ferromagnetic leads near the mesoscopic Stoner instabilities.

Mesoscopic competition of superconductivity and ferromagnetism: conductance peak statistics for metallic grains

We investigate the competition between superconductivity and ferromagnetism in chaotic ultrasmall metallic grains in a regime where both phases can coexist. We use an effective Hamiltonian that combines a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange term. We study the transport properties of the grain in the Coulomb-blockade regime and identify signatures of the coexistence of pairing and exchange correlations in the mesoscopic fluctuations of the conductance peak spacings and peak heights.

Interacting quantum dot coupled to a kondo spin: a universal Hamiltonian study

We study a Kondo spin coupled to a mesoscopic interacting quantum dot that is described by the "universal Hamiltonian." The problem is solved numerically by diagonalizing the system Hamiltonian in a good-spin basis and analytically in the weak and strong Kondo coupling limits. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground-state spin (Stoner staircase), which is modified nontrivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The interplay between Kondo and ferromagnetic exchange correlations can be probed with experimentally tunable parameters.

Interplay of spin and charge channels in zero-dimensional systems

We study the interplay of charge and spin (zero-mode) channels in quantum dots. The latter affects the former in the form of a distinct signature on the differential conductance. We also obtain both longitudinal and transverse spin susceptibilities. All these observables, underlain by spin fluctuations, become accentuated as one approaches the Stoner instability. The nonperturbative effects of zero-mode interaction are described in terms of the propagation of gauge bosons associated with charge [U(1)] and spin [SU(2)] fluctuations in the dot, while transverse spin fluctuations are analyzed perturbatively.

Coherent versus sequential electron tunneling in quantum dots

Manifestations of quantum coherence in the electronic conductance through nearly closed quantum dots in the Coulomb-blockade regime are addressed. We show that quantum coherent tunneling processes explain some puzzling statistical features of the conductance peak heights observed in recent experiments at low temperatures. We employ the constant interaction model and the random matrix theory to model the quantum dot electronic interactions and its single-particle statistical fluctuations, taking full account of the finite decay width of the quantum dot levels.