Interplay of charge and spin in quantum dots: The Ising case
Nissan-Cohen B., Gefen Y., The physics of quantum dots is depicted succinctly by the universal Hamiltonian, where only zero-mode interactions are included. In the case in which 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 nontrivial model shed light on a more general case of charge and spin entanglement. We present a calculation of the tunneling density of states and dynamic magnetic susceptibility. We explain how the latter can be used for an experimental determination of the exchange interaction strength. © 2011 American Physical Society.
Thermodynamic properties of the superconductivity in quasi-two-dimensional Dirac electronic systems
Abah O., The thermodynamic properties of superconducting Dirac electronic systems is analyzed in the vicinity of quantum critical point. The system is characterized by a quantum critical point at zero doping, such that the critical temperature vanishes below some finite value of interaction strength. It is found that the specific heat jump of the system largely deviates from the conventional BCS theory value in the vicinity of quantum critical point. We investigated the region of applicability of the mean-field theory using the Ginzburg-Landau functional. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Asymmetric spin- 1 2 two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations
Aristov D.N., Brünger C., Assaad F.F., We consider asymmetric spin- 1 2 two-leg ladders with nonequal antiferromagnetic (AF) couplings J and κ J along legs (κ≤1) and ferromagnetic rung coupling, J. This model is characterized by a gap Δ in the spectrum of spin excitations. We show that in the large J limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at κ=1, admits a linear scaling for the spin gap Δ∼ J. The second class appears for a strong asymmetry of the coupling along legs, κ J J J and is characterized by two energy scales: the exponentially small spin gap Δ∼ J exp (- J / J), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ∼ J 2 / J. We report numerical results obtained by exact diagonalization, density-matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice. © 2010 The American Physical Society.
Spin and charge correlations in quantum dots: An exact solution
Burmistrov I., Gefen Y., 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 of the problem, in particular, in the vicinity of the Stoner instability point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the ac susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials. © 2010 Pleiades Publishing, Ltd.
Thermoelectric transport through a quantum dot: Effects of asymmetry in Kondo channels
Nguyen T., We consider effects of magnetic field on the thermopower and thermoconductance of a single-electron transistor based on a quantum dot strongly coupled to one of the leads by a single-mode quantum point contact. We show appearance of two new energy scales: Tmin∼|r| 2EC(B/BC)2 depending on a ratio of magnetic field B and the field BC corresponding to a full polarization of point contact and Tmax∼|r|2EC depending on a reflection amplitude r and charging energy EC. We predict that the behavior of thermoelectric coefficients is consistent with the Fermi-liquid theory at temperatures T≪Tmin while crossover from non-Fermi-liquid regime associated with a two-channel Kondo effect to Fermi-liquid single-channel Kondo behavior can be seen at Tmin
Kondo effect in complex quantum dots in the presence of an oscillating and fluctuating gate signal
We show how the charge input signal applied to the gate electrode in double and triple quantum dots may be converted to a pulse in the Kondo cotunneling current being a spin response of a nanodevice under a strong Coulomb blockade. The stochastic component of the input signal results in the infrared cutoff of Kondo transmission. The stochastization of the orbital component of the Kondo effect in triple quantum dots results in a noise-induced SU (4) →SU (2) quantum transition. © 2010 The American Physical Society.
Quantum tunneling through moving Kondo objects
Kikoin K., We show how the time-dependent modulation of charge input signal applied to the gate electrode in a double quantum dot may be converted to a pulse in the Kondo tunneling current, which is predominantly spin response of this nano-device in a strong Coulomb blockade regime. The stochastic component of the input signal reveals itself as the infrared cutoff of Kondo tunneling transmission. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Scalar and vector Keldysh models in the time domain
The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z 2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the vector Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed. © 2009 Pleiades Publishing, Ltd.
Spin and charge necklaces at commensurate filling
Kikoin K., The charge and spin properties of spin chains decorated with dimers and closed trimers (equilateral triangles) with commensurate partial filling (1/4 and 1/3, respectively) are considered. It is shown that due to the charge separation both systems prefer the ground state with even occupation per elementary cell, where the spin spectrum possesses the Haldane gap for negative spin exchange and magnon-like for positive coupling. The charge spectrum is always gapped. © 2009 IOP Publishing Ltd.
Spin and charge necklaces at commensurate filling
Kikoin K., The charge and spin properties of spin chains decorated with dimers and closed trimers (equilateral triangles) with commensurate partial filling (1/4 and 1/3, respectively) are considered. It is shown that due to the charge separation both systems prefer the ground state with even occupation per elementary cell, where the spin spectrum possesses the Haldane gap for negative spin exchange and magnon-like for positive coupling. The charge spectrum is always gapped. © 2009 IOP Publishing Ltd.
Spin gap and string order parameter in the ferromagnetic spiral staircase Heisenberg ladder: A quantum Monte Carlo study
Brünger C., Assaad F., Capponi S., Alet F., Aristov D., We consider a spin-1/2 ladder with a ferromagnetic rung coupling J⊥ and inequivalent chains. This model is obtained by a twist (θ) deformation of the ladder and interpolates between the isotropic ladder (θ=0) and the SU(2) ferromagnetic Kondo necklace model (θ=π). We show that the ground state in the (θ, J⊥) plane has a finite string order parameter characterizing the Haldane phase. Twisting the chain introduces a new energy scale, which we interpret in terms of a Suhl-Nakamura interaction. As a consequence we observe a crossover in the scaling of the spin gap at weak coupling from Δ/JJ⊥/J for θ<θc/8π/9 to Δ/J(J⊥/J)2 for θ>θc. Those results are obtained on the basis of large scale quantum Monte Carlo calculations. © 2008 The American Physical Society.
Phonon-assisted and magnetic field induced Kondo tunneling in single molecular devices
Kikoin K., We consider the Kondo tunneling induced by multiphonon emission/absorption processes in magnetic molecular complexes with low-energy singlet-triplet spin gap and show that the number of assisting phonons may be changed by varying the Zeeman splitting of excited triplet state. As a result, the structure of multiphonon Kondo resonances may be scanned by means of magnetic field tuning. © 2007 IOP Publishing Ltd.
Dynamical symmetries and quantum transport through nanostructures
We discuss the manifestation of dynamical symmetries in quantum transport through nanostructures. The dynamical symmetry SO(4) manifested in the singlet-triplet excitations is shown to be responsible for several exotic effects in nano-devices: non-equilibrium Kondo effect in T-shape Double Quantum Dots, phonon-induced Kondo effect in transition-metal-organic complexes, Kondo shuttling in Nano-Electro-mechanical Single Electron Transistor. We consider the interplay between charge U(1) and spin SU(2) fluctuations in the vicinity of Stoner instability point and a non-monotonic behavior of a Tunneling Density of States in metallic quantum dots. The experiments showing important role of dynamical symmetries in nanostructures are briefly reviewed. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.
Single-pole ladder at quarter filling
Aristov D.N., We study the ground state and excitation spectrum of a quasi-one- dimensional system consisting of a pole and rungs oriented in opposite directions ("centipede ladder," CL) at quarter filling. The spin and charge excitation spectra are found in the limits of small and large longitudinal hoppings t compared to the on-rung hopping rate t and exchange coupling I. At small t, the system with ferromagnetic on-rung exchange demonstrates instability against dimerization. Coherent propagation of charge-transfer excitons is possible in this limit. At large t, CL behaves like two-orbital Hubbard chain, but the gap opens in the charge excitation spectrum, thus reducing the symmetry from SU(4) to SU(2). The spin excitations are always gapless and their dispersion changes from quadratic magnonlike for ferromagnetic on-rung exchange to linear spinonlike for antiferromagnetic on-rung exchange in weak longitudinal hopping limit. © 2007 The American Physical Society.
Kondo effect in organometallic complexes with vibrating ligand shells
We investigate transport through a mononuclear rare-earth metal-organic shell complex with strong tunnel coupling between the shell and two electrodes. The ground state of this molecule is a singlet while the first excited state is a triplet. We show that modulation of the tunnel barrier due to a molecular distortion which couples to the tunneling induces the Kondo effect, provided the discrete vibrational energy compensates the singlet/triplet gap. We discuss also the possibility of tuning the phonon-induced Kondo tunneling by external magnetic field and the finite bias Kondo anomaly. © 2006 Elsevier B.V. All rights reserved.
Kondo shuttling in a nanoelectromechanical single-electron transistor
We investigate theoretically a mechanically assisted Kondo effect and electric charge shuttling in a nanoelectromechanical single-electron transistor. It is shown that the mechanical motion of the central island (a small metallic particle) with the spin results in a time-dependent tunneling width Γ (t) which leads to an effective increase of the Kondo temperature. The time-dependent oscillating Kondo temperature TK (t) changes the scaling behavior of the differential conductance, resulting in the suppression of transport in a strong-coupling and its enhancement in a weak-coupling regime. The conditions for fine-tuning of the Abrikosov-Suhl resonance and possible experimental realization of the Kondo shuttling are discussed. © 2006 The American Physical Society.
Kondo effect in a one-electron double quantum dot: Oscillations of the Kondo current in a weak magnetic field
Schröer D.M., Hüttel A.K., Eberl K., Ludwig S., We present transport measurements of the Kondo effect in a double quantum dot charged with only one or two electrons, respectively. For the one-electron case, we observe a surprising quasiperiodic oscillation of the Kondo conductance as a function of a small perpendicular magnetic field B50 mT. We discuss possible explanations of this effect and interpret it by means of a fine tuning of the energy mismatch of the single dot levels of the two quantum dots. The observed degree of control implies important consequences for applications in quantum information processing. © 2006 The American Physical Society.
Decoherence and dephasing in Kondo tunneling through double quantum dots
We describe the mechanism of charge-spin transformation in a double quantum dot (DQD) with even occupation, where a time dependent gate voltage vg (t) is applied to one of its two valleys, whereas the other one is coupled to the source and drain electrodes. The Kondo tunneling regime under strong Coulomb blockade may be realized when the spin spectrum of the DQD is formed by the ground state spin triplet and two singlet excitations. Charge fluctuations induced by vg (t) result in transitions within the spin multiplet characterized by the SO(5) dynamical symmetry group. In a weakly nonadiabatic regime the decoherence, dephasing, and relaxation processes affect Kondo tunneling. Each of these processes is caused by a special type of dynamical gauge fluctuations, so that one may discriminate between the decoherence in the ground state of a DQD and dephasing at finite temperatures. © 2006 The American Physical Society.
Kondo lattice without Nozières exhaustion effect
Kikoin K., We discuss the properties of layered Anderson/Kondo lattices with metallic electrons confined in 2D xy planes and local spins in insulating layers forming chains in the z direction. Each spin in this model possesses its own 2D Kondo cloud, so that the Nozières' exhaustion problem does not occur. The high-temperature perturbational description is matched to exact low-T Bethe-ansatz solution. The excitation spectrum of the model is gapless both in charge and spin sectors. The disordered phases and possible experimental realizations of the model are briefly discussed. © EDP Sciences.
Vibration-induced Kondo tunneling through metal-organic complexes with even electron occupation number
Kikoin K., We investigate transport through a mononuclear transition-metal complex with strong tunnel coupling to two electrodes. The ground state of this molecule is a singlet, while the first excited state is a triplet. We show that a modulation of the tunnel-barrier due to a molecular distortion which couples to the tunneling induces a Kondo-effect, provided the discrete vibrational energy compensates the singlet-triplet gap. We discuss the single-phonon and two-phonon-assisted cotunneling and possible experimental realization of the theory. © 2006 The American Physical Society.