All Publications

We propose a realization of mechanically tunable Ruderman-Kittel-Kasuya-Yosida interaction in a double quantum dot nanoelectromechanical device. The coupling between spins of two quantum dots suspended above a metallic plate is mediated by conduction electrons. We show that the spin-mechanical interaction can be driven by a slow modulation of charge density in the metallic plate. We propose to use Stückelberg oscillations as a sensitive tool for detection of the spin and charge states of the coupled quantum dots. Theory of mechanical back action induced by a dynamical spin-spin interaction is discussed.

We investigate thermoelectric transport through a SU(N) quantum impurity in the Kondo regime. The strong-coupling fixed-point theory is described by the local Fermi-liquid paradigm. Using Keldysh technique we analyze the electric current through the quantum impurity at both finite bias voltage and finite temperature drop across it. The theory of a steady state at zero current provides a complete description of the Seebeck effect. We find pronounced nonlinear effects in temperature drop at low temperatures. We illustrate the significance of the nonlinearities for enhancement of thermopower by two examples of SU(4) symmetric regimes characterized by a filling factor m: (i) particle-hole symmetric at m=2 and (ii) particle-hole nonsymmetric at m=1. We analyze the effects of potential scattering and coupling asymmetry on the transport coefficients. We discuss connections between the theory and transport experiments with coupled quantum dots and carbon nanotubes.

We investigate the interplay between the magnetic and the superconducting degrees of freedom in unconventional multi-band superconductors such as iron pnictides. For this purpose a dynamical mode-mode coupling theory is developed based on the coupled Bethe-Salpeter equations. In order to investigate the region of the phase diagram not too far from the tetracritical point where the magnetic spin density wave, (SDW) and superconducting (SC) transition temperatures coincide, we also construct a Ginzburg-Landau functional including both SC and SDW fluctuations in a critical region above the transition temperatures. The fluctuation corrections tend to suppress the magnetic transition, but in the superconducting channel the intraband and interband contribution of the fluctuations nearly compensate each other.

Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the perturbative diagrammatic expansion is generated by Wick's theorem, and (ii) Dyson's collapse argument implying that the expansion in powers of coupling constant is divergent. We show that for arbitrary classical lattice models both problems can be solved/circumvented by reformulating the high-temperature expansion (more generally, any discrete representation of the model) in terms of Grassmann integrals. Discrete variables residing on either links, plaquettes, or sites of the lattice are associated with the Grassmann variables in such a way that the partition function (as well as all correlation functions) of the original system and its Grassmann-field counterpart are identical. The expansion of the latter around its Gaussian point generates Feynman diagrams. Our work paves the way for studying lattice gauge theories by treating bosonic and fermionic degrees of freedom on equal footing.

We show that nanomechanical vibrations in a magnetic shuttle device can be strongly affected by external microwave irradiation through photo-assisted electronic spin-flip transitions. Mechanical consequences of these spin flips are due to a spin-dependent magnetic force, which may lead to a nanomechanical instability in the device. We derive a criterion for the instability to occur and analyze different regimes of nanomechanical oscillations. Possible experimental realizations of the spin-mediated photomechanical instability and detection of the device backaction are discussed.

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira–Leggett and Ambegaokar–Eckern–Schön approaches. Here, we recall the differences between them and explain the consequences of applying each to a zero-dimensional spin (having an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).

We investigate electron shuttling in three-terminal nanoelectromechanical 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 limit cycles, and (iv) single limit 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 active current switch and sensoring of small variations of magnetic field.

We show that a thermoelectric transport through a quantum dot-single-mode quantum point contact nanodevice demonstrating pronounced fingerprints of nonFermi liquid (NFL) behavior in the absence of external magnetic field is protected from magnetic field NFL destruction by strong spin-orbit interaction (SOI). The mechanism of protection is associated with the appearance of additional scattering processes due to lack of spin conservation in the presence of both SOI and small Zeeman field. The interplay between in-plane magnetic field B - and SOI is controlled by the angle between B - and B - SOI. We predict strong dependence of the thermoelectric coefficients on the orientation of the magnetic field and discuss a window of parameters for experimental observation of NFL effects.

The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

A single-electron tunneling (SET) device with a nanoscale central island that can move with respect to the bulk source- and drain electrodes allows for a nanoelectromechanical (NEM) coupling between the electrical current through the device and mechanical vibrations of the island. Although an electromechanical "shuttle" instability and the associated phenomenon of single-electron shuttling were predicted more than 15 years ago, both theoretical and experimental studies of NEM-SET structures are still carried out. New functionalities based on quantum coherence, Coulomb correlations and coherent electron-spin dynamics are of particular current interest. In this article we present a short review of recent activities in this area.

Recent experimental and numerical studies of the critical-temperature exponent φ for the superfluid-Bose-glass universality in three-dimensional systems report strong violations of the key quantum critical relation, φ=νz, where z and ν are the dynamic and correlation-length exponents, respectively; these studies question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal-fluid transition-temperature dependence on the chemical potential (or the magnetic field, in spin systems), Tca∝(μ-μc)φ, was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the φ=νz law [with φ=2.7(2), z=3, and ν=0.88(5)] holds true, resolving the φ-exponent "crisis." © 2014 American Physical Society.

We analytically and numerically compute three equilibrium Fermi-liquid coefficients of the fully screened N-channel Kondo model, namely cB, cT, and c, characterizing the magnetic field and temperature dependence of the resisitivity, and the curvature of the equilibrium Kondo resonance, respectively. We present a compact, unified derivation of the N dependence of these coefficients, combining elements from various previous treatments of this model. We numerically compute these coefficients using the numerical renormalization group, with non-Abelian symmetries implemented explicitly, finding agreement with Fermi-liquid predictions on the order of 5% or better. © 2014 American Physical Society.

A single-electron tunneling (SET) device with a nanoscale central island that can move with respect to the bulk source- and drain electrodes allows for a nanoelectromechanical (NEM) coupling between the electrical current through the device and mechanical vibrations of the island. Although an electromechanical "shuttle" in-stability and the associated phenomenon of single-electron shuttling were predicted more than 15 years ago, both theoretical and experimental studies of NEM-SET structures are still carried out. New functionalities based on quantum coherence, Coulomb correlations and coherent electron-spin dynamics are of particular current interest. In this article we present a short review of recent activities in this area.

We investigate the instability and dynamical properties of nanoelectromechanical systems represented by a single-electron device containing movable quantum dots attached to a vibrating cantilever via asymmetric tunnel contacts. The Kondo resonance in electron tunneling between the source and shuttle facilitates self-sustained oscillations originating from the strong coupling of mechanical and electronic/spin degrees of freedom. We analyze a stability diagram for the two-channel Kondo shuttling regime due to limitations given by the electromotive force acting on a moving shuttle, and find that the saturation oscillation amplitude is associated with the retardation effect of the Kondo cloud. The results shed light on possible ways to experimentally realize the Kondo-cloud dynamical probe by using high mechanical dissipation tunability as well as supersensitive detection of mechanical displacement. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

We propose a universal approach to the Landau-Zener problem in a three-level system. The problem is formulated in terms of Gell-Mann operators which generate SU(3) algebra and map the Hamiltonian on the effective anisotropic pseudospin 1 model. The vector Bloch equation for the density matrix describing the temporal evolution of the three-level crossing problem is also derived and solved analytically for the case where the diabatic states of the SU(3) Hamiltonian form a triangle. This analytic solution is in excellent quantitative agreement with the numerical solution of the Schrödinger equation for a 3-level crossing problem. The model demonstrates oscillation patterns which radically differ from the standard patterns for the two-level Landau-Zener problem. The triangle works as an interferometer and the interplay between two paths results in formation of "beats" and "steps" pattern in the time-dependent transition probability. The characteristic time scales describing the "beats" and "steps" depend on a dwell time in the triangle. These scales are related to the geometric size of the interferometer. The possibilities of the experimental realization of this effect in triple quantum dots and in two-well traps for cold gases are discussed. © Copyright EPLA, 2013.

We investigate the Landau-Zener transition in two- and three-level systems subject to a classical Gaussian noise. Two complementary limits of the noise being fast and slow compared to characteristic Landau-Zener tunnel times are discussed. The analytical solution of a density matrix (Bloch) equation is given for a long-time asymptotic of transition probability. It is demonstrated that the transition probability induced or assisted by the fast noise can be obtained through a procedure of Bloch's equation averaging with further reducing it to a master equation. In contrast to the case of fast noise, the transition probability for LZ transition induced, or assisted, by the slow classical noise can be obtained by averaging the solution of Bloch's equation over the noise realization. As a result, the transition probability is described by the activation Arrhenius law. The approximate solution of the Bloch's equation at finite times is written in terms of Fresnel's integrals and interpreted in terms of interference pattern. We discuss consequences of a local isomorphism between SU(2) and SO(3) groups and connections between Schrödinger and Bloch descriptions of spin dynamics. Based on this isomorphism, we establish the relations between S=1/2 and 1 transition probabilities influenced by the noise. A possibility to use the slow noise as a probe for tunnel time is discussed. © 2013 American Physical Society.

We consider the electromechanical properties of a single-electronic device consisting of a movable quantum dot attached to a vibrating cantilever, forming a tunnel contact with a nonmovable source electrode. We show that the resonance Kondo tunneling of electrons amplifies exponentially the strength of nanoelectromechanical (NEM) coupling in such a device and make the latter insensitive to mesoscopic fluctuations of electronic levels in a nanodot. It is also shown that the study of a Kondo-NEM phenomenon provides additional (as compared with standard conductance measurements in a nonmechanical device) information on retardation effects in the formation of a many-particle cloud accompanying the Kondo tunneling. A possibility for superhigh tunability of mechanical dissipation as well as supersensitive detection of mechanical displacement is demonstrated. © 2013 American Physical Society.

The inclusion of charging and spin-exchange interactions within the universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution to the problem, in particular, in the vicinity of the Stoner instability. We calculate the tunneling density of states and the spin susceptibility. We demonstrate that near the Stoner instability the spin susceptibility follows a Curie law with an effective spin. The latter depends logarithmically on temperature due to the statistical fluctuations of the single-particle levels. Near the Stoner instability the tunneling density of states exhibits a nonmonotonous behavior as a function of the tunneling energy, even at temperatures higher than the exchange energy. This is due to enhanced spin correlations. Our results could be tested in quantum dots made of nearly ferromagnetic materials. © 2012 American Physical Society.

Group theoretical concepts elucidate fundamental physical phenomena, including excitation spectra of quantum systems and complex geometrical structures such as molecules and crystals. These concepts are extensively covered in numerous textbooks. The aim of the present monograph is to illuminate more subtle aspects featuring group theory for quantum mechanics, that is, the concept of dynamical symmetry. Dynamical symmetry groups complement the conventional groups: their elements induce transitions between states belonging to different representations of the symmetry group of the Hamiltonian. Dynamical symmetry appears as a hidden symmetry in the hydrogen atom and quantum rotator problem, but its main role is manifested in nano and meso systems. Such systems include atomic clusters, large molecules, quantum dots attached to metallic electrodes, etc. They are expected to be the building blocks of future quantum electronic devices and information transmitting algorithms. Elucidation of the electronic properties of such systems is greatly facilitated by applying concepts of dynamical group theory.

We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak-almost not resolvable-sensitivity of the critical interaction to the strength of (weak) disorder. © 2011 American Physical Society.