The Interplay of Charge and Spin in Quantum Dots: The Ising Case

The physics of quantum dots is succinctly depicted by the {\it Universal Hamiltonian}, where only zero mode interactions are included. In the case where the latter involve charging and isotropic spin-exchange terms, this would lead to a non-Abelian action. Here we address an Ising spin-exchange interaction, which leads to an Abelian action. The analysis of this simplified yet non-trivial model shed some light on a more general case of charge and spin entanglement. We present a calculation of the tunneling density of states and of the dynamic magnetic susceptibility. Our results are amenable to experimental study and may allow for an experimental determination of the exchange interaction strength.Comment: 11 pages, 7 figure

Self-sustained oscillations in nanoelectromechanical systems induced by Kondo resonance

We investigate instability and dynamical properties of nanoelectromechanical systems represented by a single-electron device containing movable quantum dot attached to a vibrating cantilever via asymmetric tunnel contact. The Kondo resonance in electron tunneling between source and shuttle facilitates self-sustained oscillations originated from strong coupling of mechanical and electronic/spin degrees of freedom. We analyze stability diagram for two-channel Kondo shuttling regime due to limitations given by the electromotive force acting on a moving shuttle and find that the saturation amplitude of oscillation is associated with the retardation effect of Kondo-cloud. The results shed light on possible ways of experimental realization of dynamical probe for the Kondo-cloud by using high tunability of mechanical dissipation as well as supersensitive detection of mechanical displacement

Shuttle-promoted nano-mechanical current switch

We investigate electron shuttling in three-terminal nanoelectromechanocal device built on a movable metallic rod oscillating between two drains. The device shows a double-well shaped electromechanical potential tunable by a source-drain bias voltage. Four stationary regimes controllable by the bias are found for this device: (i) single stable fixed point, (ii) two stable fixed points, (iii) two limiting cycles, and (iv) single limiting cycle. In the presence of perpendicular magnetic field the Lorentz force makes possible switching from one electromechanical state to another. The mechanism of tunable transitions between various stable regimes based on the interplay between voltage controlled electromechanical instability and magnetically controlled switching is suggested. The switching phenomenon is implemented for achieving both a reliable \emph{active} current switch and sensoring of small variations of magnetic field.Comment: 11 pages, 4 figure

U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Sch\"on approaches

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Sch\"on approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).Comment: Contribution for Leonid Keldysh 85 Festschrif