We study a double quantum dot in the regime where each dot carries a spin-1/2. This system is described by the 2-impurity Kondo model, having a non-Fermi liquid fixed point for a critical value of the inter-impurity coupling. The Hamiltonian describing the vicinity of the critical point, including the relevant potential scattering perturbations, can be cast in quadratic form. This allows us to predict a universal scaling function for the finite temperature nonlinear conductance along the crossover from the critical point to the surrounding stable fixed points.
We develop a mapping of quantum steady-state nonequilibrium to an effective equilibrium and solve the problem using a quantum simulation technique. A systematic implementation of the nonequilibrium boundary condition in steady-state is made in the electronic transport on quantum dot structures. This formulation of quantum manybody problem in nonequilibrium enables the use of existing numerical quantum manybody techniques. The algorithm coherently demonstrates various transport behaviors from phonon-dephasing to I-V staircase and phonon-assisted tunneling.
We extend a perturbative, nonequilibrium renormalization group approach to multi-orbital systems and apply it for studying transport through two parallel quantum dots coupled electrostatically. In general, the conductance shows pronounced Kondoesque peaks at three voltages. One of these peaks disappears if, as in some experiments, one of the dots is decoupled from one of the two leads. For an asymmetric coupling to the leads, also negative differential conductances are possible. This is a genuine nonequilibrium effect, accompanying the Kondoesque peaks. Moreover, a criterion to distinguish spi…
Double quantum dots can provide an experimental realization of the 2 impurity Kondo model which exhibits a non-Fermi liquid quantum critical point (QCP) at a special value of its parameters. We generalize our recent study of double quantum dots in series \cite{Sela08} to a parallel configuration with an Aharonov-Bohm flux. We present an exact universal result for the finite temperature and finite voltage conductance $G[V,T]$ along the crossover from the QCP to the low energy Fermi liquid phase. Compared to the series configuration, here generically $G[V,T] \ne G[-V,T]$, leading to current rect…
We study a pseudo-spin-1/2 quantum dot in the cotunneling regime close to the particle-hole symmetric point. For a generic tunneling matrix we find a generic fixed point with interesting nonequilibrium properties, characterized by effective reservoirs with compensating spin orientation vectors weighted by the polarizations and the tunneling rates. At large bias voltage we study the magnetic field dependence of the dot magnetization and the current. The fixed point can be clearly identified by analyzing the magnetization of the dot. We characterize in detail the universal properties for the cas…
The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contribut…
We present a theory of zero-bias anomalies and dephasing rates for a Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage biased source and drain leads. We interpret our results in terms of the statistics of voltage fluctuations in the system.
Resonant electron transport through a mesoscopic region (quantum dot or single molecule) with electron-phonon interaction is considered at finite voltage. In this case the standard Landauer-Büttiker approach cannot be applied. Using the nonequilibrium Green function method we show that due to a nonequilibrium distribution function of electrons in the mesoscopic region, the inelastic scattering rate and spectral function of the dot become functions of the voltage and have to be calculated self-consistently.
Spin entanglement between two spatially separated electrons can be generated in nonequilibrium interacting quantum dots, coherently coupled to a common lead. In this system entangled two-electron states develop which are Werner states with an imbalance between singlet and triplet probabilities. We propose a multi-terminal, multiply-connected setup for the generation and detection of this imbalance. In particular, we identify a regime in which the formation of spin entanglement leads to a cancellation of Aharonov-Bohm oscillations.
We develop a low-energy nonequilibrium field theory for weakly interacting quantum dots. The theory is based on the Keldysh field integral in the spin channel of the quantum dot described by the single impurity Anderson Hamiltonian. The effective Keldysh action is a functional of the Hubbard-Stratonovich magnetization field decoupling the quantum dot spin channel. We expand this action up to the second order with respect to the magnetization field, which allows to describe nonequilibrium interacting quantum dots at low temperatures and weak electron-electron interactions,up to the contacts-dot…
We study the spin dynamics in charged quantum dots in the situation where the resident electron is coupled to only about 200 nuclear spins and where the electron spin splitting induced by the Overhauser field does not exceed markedly the spectral broadening. The formation of a dynamical nuclear polarization as well as its subsequent decay by the dipole-dipole interaction is directly resolved in time. Because not limited by intrinsic nonlinearities, almost complete nuclear polarization is achieved, even at elevated temperatures. The data suggest a nonequilibrium mode of nuclear polarization, di…
By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase i…
We report on capacitance-voltage spectroscopy of self-assembled InAs quantum dots under constant illumination. Besides the electronic and excitonic charging peaks in the spectrum reported earlier, we find additional resonances associated with nonequilibrium state tunneling unseen in C(V) measurements before. We derive a master-equation based model to assign the corresponding quantum state tunneling to the observed peaks. C(V) spectroscopy in a magnetic field is used to verify the model-assigned nonequilibrium peaks. The model is able to quantitatively address various experimental findings in C…
We develop a theory for charge and spin current between two canted magnetic leads flowing through a quantum dot with an arbitrary local interaction. For a noncollinear magnetic configuration, we calculate equilibrium and nonequilibrium current biased by voltage or temperature difference or pumped by magnetic dynamics. We are able to explicitly separate the equilibrium and nonequilibrium contributions to the current, both of which can be written in terms of the full retarded Green's function on the dot. Taking the specific example of a single-level quantum dot with a large on-site Coulomb inter…
We analyze the decoherence of charge states in double quantum dots due to cotunneling. The system is treated using the Bloch-Redfield generalized master equation for the Schrieffer-Wolff transformed Hamiltonian. We show that the decoherence, characterized through a relaxation $τ_{r}$ and a dephasing time $τ_ϕ$, can be controlled through the external voltage and that the optimum point, where these times are maximum, is not necessarily in equilibrium. We outline the mechanism of this nonequilibrium-induced enhancement of lifetime and coherence. We discuss the relevance of our results for recent …
We investigate the transient nonequilibrium dynamics of a molecular junction biased by a finite voltage and strongly coupled to internal vibrational degrees of freedom. Using two different, numerical exact techniques, diagrammatic Monte Carlo and the multilayer multiconfiguration time-dependent Hartree method, we show that the steady state current through the junction may depend sensitively on the initial preparation of the system, thus revealing signatures of bistability. The influence of the bias voltage and the transient dynamics on the phenomenon of bistability is analyzed. Furthermore, a …
We propose schemes for generating spatially-separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage, or in the steady state with applied bias voltage. In both cases so-called Werner states with spin singlet fidelity exceeding 1/2 are generated, which indicates entanglement.
We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a Gutzwiller's variational space, and applied to the study of the simple single-orbital Anderson impurity model at half filling, finding a good qualitative accord with the observed behavior in quantum dots for the expected regime of values of the bias. Beyond the purely theoretical interest in the formal definition of a variational principle in a nonequilibrium probl…
The optically induced polarization of localized electron spins in an ensemble of quantum dots (QDs) dephases due to the interaction with the surrounding nuclear spins. Despite this dephasing, the spins in the QDs can be controlled to respond coherently by applying periodic laser pulses, leading to a revival of the spin polarization before each pulse. This effect, known as spin mode locking, strongly depends on an emerging selection of certain polarizations of the nuclear spin bath which is driven to a steady state far from equilibrium. We investigate the influence of the nuclear composition in…
We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state. The structure is described by a two-level spinless Anderson model where the levels are coupled to two leads held at different chemical potentials. The problem is solved by a numerically exact hierarchical master equation technique and the results are compared to approximate ones obtained from Born-Markov theory. The methods allow us to study the time evolut…
Recent developments on studies of transport through quantum dots obtained by applying the time-dependent density matrix renormalization group method are summarized. Some new aspects of Kondo physics which appear in nonequilibrium steady states are discussed both for the single dot case and for the serially coupled double-quantum-dot case.
Large-scale simulations of the spin dynamics in quantum dots subjected to trains of periodic laser pulses enable us to describe and understand related experiments. By comparing the data for different models to experimental results, we gain an improved understanding of the relevant physical mechanisms. Using sophisticated numerical approaches and an efficient implementation combined with extrapolation arguments, nonequilibrium stationary states are reached for parameter ranges close to the ones in real experiments. With the help of high performance computing, we can tune the experimental parame…
Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split…
We develop a non-equilibrium theory to describe weak Coulomb blockade effects in open quantum dots. Working within the bosonized description of electrons in the point contacts, we expose deficiencies in earlier applications of this method, and address them using a 1/N expansion in the inverse number of channels. At leading order this yields the self-consistent potential for the charging interaction. Coulomb blockade effects arise as quantum corrections to transport at the next order. Our approach unifies the phase functional and bosonization approaches to the problem, as well as providing a si…
We present a microscopic theory for both equilibrium and nonequilibrium transport properties of coupled double quantum dots (DQD). A general formula for current tunneling through the DQD is derived by the nonequilibrium Green's function method. Using a Hartree-Fock approach, effects of multi-level coupling and nonequilibrium electron distributions in resonant tunneling are considered. We find that the peak in the resonant tunneling current through two symmetric dots will split only when the inter-dot coupling is stronger than dot-lead coupling. We predict that population inversion can be achie…
Orbital Kondo effect in a system of two single-level quantum dots attached to external electron reservoirs is considered theoretically. The dots are coupled via direct hoping term and Coulomb interaction. The Kondo temperature is evaluated from the scaling approach and slave boson technique. The later method is also used to calculate linear conductance of the system. Nonlinear conductance, in turn, is calculated in terms of the nonequilibrium Green function formalism.
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a cutoff-independent formalism. We present quantitatively reliable results for the nonlinear conductance in the mixed-valence and empty-orbital regime of the nonequilibrium Anderson impurity model with finite on-site Coulomb repulsion.
Via projection operator technology, we restrict our discussion of Double Quantum Dots system in subspaces of fixed electron population. When an incident electron tries to pass through the dots, we find transmission peaks occur, if the system energy scans through eigen-levels in one-more-electron higher subspace of the dots. Also, we find some selection rules for this resonant transmission. We attribute some of these rules to the differences between many-electron bonding states and anti-bonding states.
We investigate entanglement between electrons in serially coupled double quantum dots attached to non interacting leads. In addition to local repulsion we consider the influence of capacitive inter-dot interaction. We show how the competition between extended Kondo and local singlet phases determines the ground state and thereby the entanglement.
Quantum tunneling dominates coherent transport at low temperatures in many systems of great interest. In this work we report a many--body tunneling (MBT), by nonperturbatively solving the Anderson multi-impurity model, and identify it a fundamental tunneling process on top of the well--acknowledged sequential tunneling and cotunneling. We show that the MBT involves the dynamics of doublons in strongly correlated systems. Proportional to the numbers of dynamical doublons, the MBT can dominate the off--resonant transport in the strongly correlated regime. A $T^{3/2}$--dependence of the MBT curre…
We analyze the interactions between two Kondo Quantum Dots connected to a Rashba-active Quantum Wire. We find that the Kondo-doublet interaction, at an inter-dot distance of the order of the wire Fermi length, is over an order of magnitude greater than the RKKY interaction. The effects induced on the Kondo-doublet interaction by the wire spin-orbit coupling can be used to control the Quantum Dots spin-spin correlation. These results imply that the widely used assumption that the RKKY is the dominant interaction between Anderson impurities must be revised.
We analyze the quantum interference effects appearing in the charge current through the double quantum dots coupled in T-shape configuration to an isotropic superconductor and metallic lead. Owing to proximity effect the quantum dots inherit a pairing which has the profound influence on nonequilibrium charge transport, especially in the subgap regime |eV| < Delta. We discuss under what conditions the Fano-type lineshapes might appear in such Andreev conductance and consider a possible interplay with the strong correlation effects.
The electrostatic interaction between two capacitively-coupled metal double-dots is studied at low temperatures. Experiments show that when the Coulomb blockade is lifted by applying appropriate gate biases to both double-dots, the conductance through each double-dot becomes significantly lower than when only one double-dot is conducting. A master equation is derived for the system and the results obtained agree well with the experimental data. The model suggests that the conductance lowering in each double-dot is caused by a single-electron tunneling in the other double-dot. Here, each double…
The interplay between interference effects and electron-electron interactions in electron transport through an interacting double quantum dot system is investigated using a hierarchical quantum master equation approach which becomes exact if carried to infinite order and converges well if the temperature is not too low. Decoherence due to electron-electron interactions is found to give rise to pronounced negative differential resistance, enhanced broadening of structures in current-voltage characteristics and an inversion of the electronic population. Dependence on gate voltage is shown to be …
We employ density functional calculated eigenstates as a basis for exact diagonalization studies of semiconductor double quantum dots, with two electrons, through the transition from the symmetric bias regime to the regime where both electrons occupy the same dot. We calculate the singlet-triplet splitting $J(ε)$ as a function of bias detuning $ε$ and explain its functional shape with a simple, double anti-crossing model. A voltage noise suppression "sweet spot," where $dJ(ε)/dε=0$ with nonzero $J(ε)$, is predicted and shown to be tunable with a magnetic field $B$.
A two quantum-dot device is coupled in parallel for studying the competition between the pseudo-spin Kondo effect and strongly hybridized molecular states. Cryogenic measurements are performed in the regime of weak coupling of the two dots to lead states under linear transport conditions. Detailed simulations verify the finding of the transition between the two different regimes.
We study a $3$-level quantum dot in the singly occupied cotunneling regime coupled via a generic tunneling matrix to several multi-channel leads in equilibrium or nonequilibrium. We derive an effective model where also each reservoir has three channels labelled by the quark flavors $u$, $d$ and $s$ with an effective d.o.s. polarized w.r.t. an eight-dimensional $F$-spin corresponding to the eight generators of $SU(3)$. In equilibrium we perform a standard poor man scaling analysis and show that tunneling via virtual intermediate states induces flavor fluctuations on the dot which become $SU(3)$…
We study theoretically the current-voltage characteristics, shot noise, and full counting statistics of a quantum wire double barrier structure. We model each wire segment by a spinless Luttinger liquid. Within the sequential tunneling approach, we describe the system's dynamics using a master equation. We show that at finite bias the non-equilibrium distribution of plasmons in the central wire segment leads to increased average current, enhanced shot noise, and full counting statistics corresponding to a super-Poissonian process. These effects are particularly pronounced in the strong interac…
In a recent paper [Physica E 39 (2007) 214, arXiv:0708.1842v1] Crisan, Grosu and Tifrea revisited the problem of the conductance through a double quantum dot molecule connected to electrodes in a T-shape configuration. The authors obtained an expression for the conductance that disagrees with previous results in the literature. We point out an error in their derivation of the conductance formula and show that it gives unphysical results even for non-interacting quantum dots.
We investigate a symmetrical double quantum dot system serially attached to the leads. The emphasis is on the numerical analysis of finite inter-dot tunneling in the presence of inter-dot repulsive capacitive coupling. The results reveal the competition between extended Kondo phases and local singlet phases in spin and charge degrees of freedom. The corresponding phase diagram is determined quantitatively.
We review recent progresses in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots, and quantum wires. A variety of physical phenomena is addressed, relating to co-tunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, nonequilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.
We present exact results on the non-equilibrium current fluctuations for 2 quantum dots in series throughout a crossover from non-Fermi liquid to Fermi liquid behavior described by the 2 impurity Kondo model. The result corresponds to resonant tunneling of carriers of charge $2e$ for a critical inter-impurity coupling. At low energy scales, the result can be understood from a Fermi liquid approach that we develop and use to also study non-equilibrium transport in an alternative double dot realization of the 2 impurity Kondo model under current experimental study.
The spin noise in singly charged self-assembled quantum dots is studied theoretically and experimentally under the influence of a perturbation, provided by additional photoexcited charge carriers. The theoretical description takes into account generation and relaxation of charge carriers in the quantum dot system. The spin noise is measured under application of above barrier excitation for which the data are well reproduced by the developed model. Our analysis demonstrates a strong difference of the recharging dynamics for holes and electrons in quantum dots.
Numerical results are presented for transport properties of two coupled double-level quantum dots. The results strongly suggest that under appropriate circumstances the dots can develop a novel ferromagnetic (FM) correlation at quarter-filling (one electron per dot). In the strong coupling regime (Coulomb repulsion larger than electron hopping) and with the inter-dot tunneling larger than the tunneling to the leads, an S=1 Kondo resonance develops in the density of states, leading to a peak in the conductance. A qualitative 'phase diagram', incorporating the new FM phase, is presented. It is a…
We demonstrate delicate control over the Kondo effect and its interplay with quantum interference in an Aharonov-Bohm interferometer containing one Kondo dot and one noninteracting dot. It is shown that the Kondo resonance undergoes a dramatic evolution as the interdot tunnel coupling progressively increases. A novel triple Kondo splitting occurs from the interference between constant and Lorentzian conduction bands that cooperate in forming the Kondo singlet. The device also manifests a highly controllable Fano-Kondo effect in coherent electronic transport, and can be tuned to a regime where …
Double quantum dots offer unique possibilities for the study of many-body correlations. A system containing one Kondo dot and one effectively noninteracting dot maps onto a single-impurity Anderson model with a structured (nonconstant) density of states. Numerical renormalization-group calculations show that while band filtering through the resonant dot splits the Kondo resonance, the singlet ground state is robust. The system can also be continuously tuned to create a pseudogapped density of states and access a quantum critical point separating Kondo and non-Kondo phases.
Scaling laws and universality are often associated with systems exhibiting emergent phenomena possessing a characteristic energy scale. We report nonequilibrium transport measurements on two different types of single-molecule transistor (SMT) devices in the Kondo regime. The conductance at low bias and temperature adheres to a scaling function characterized by two parameters. This result, analogous to that reported recently in semiconductor dots with Kondo temperatures two orders of magnitude lower, demonstrates the universality of this scaling form. We compare the extracted values of the scal…
We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid `charge-ordered' phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormal…
We show that through an interdot off-site electron correlation in a double quantum-dot (DQD) device, Kondo resonances emerge in the local density of states without the electron spin-degree of freedom. We identify the physical mechanism behind this phenomenon: rather than forming a spin singlet in the device as required in the conventional Kondo physics, we found that exchange of electron position between the two quantum dots, together with the off-site Coulomb interaction, are sufficient to induce the Kondo resonance. Due to peculiar co-tunneling events, the Kondo resonance in one dot may be p…
Electron transport through parallel double quantum dot system with interdot tunneling and strong on-site Coulomb interaction is studied in the Kondo regime by using the finite-$U$ slave boson technique. For a system of quantum dots with degenerate energy levels, the linear conductance reaches the unitary limit ($2e^2/h$) due to the Kondo effect at low temperature when the interdot tunneling is absent. As the interdot tunneling amplitude increases, the conductance decreases in the singly occupied regime and a conductance plateau structure appears. In the crossover to the doubly occupied regime,…
Strong electron and spin correlations are studied in parallel-coupled double quantum dots with interdot spin superexchange $J$. In the Kondo regime with {\it}{degenerate} dot energy levels, a coherent transport occurs at zero temperature, where two entangled (bonding and antibonding) resonances are formed near the Fermi energy. When increasing $J$ or the dot-lead parallel-coupling \QTR{it}{asymmetry} ratio $Γ_{2}/Γ_{1}$, a swap between two entangled resonances occurs and the line shapes of the linear conductance are interchanged. The zero-bias differential conductance shows a peak at the criti…
In moderately strong magnetic fields, the difference in Lande g-factors in each of the dots of a coupled double quantum dot device may induce oscillations between singlet and triplet states of the entangled electron pair and lead to a nonequilibrium electron spin polarization. We will show that this polarization may partially survive the rapid inhomogeneous decoherence due to random nuclear magnetic fields.
Absorption of energy quanta generated by quantum point contact results in the inelastic current through the double quantum dot placed nearby. In contrast to a single quantum dot, the inelastic current through the double quantum dot is sensitive to the energy dependence of the quantum point contact transmission, which can explain the experimentally observed features. We calculate the inelastic current as a function of microscopic parameters of the circuit.
We study theoretically nonequilibrium Landau-Zener-Stückelberg (LZS) dynamics in a driven double quantum dot (DQD) including dephasing and, importantly, energy relaxation due to environmental fluctuations. We derive effective nonequilibrium Bloch equations. These allow us to identify clear signatures for LZS oscilations observed but not recognized as such in experiments [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010] and to identify the full environmental fluctuation spectra acting on a DQD given experimental data as in [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010]. Herein we f…
We investigate the competition between pair entanglement of two spin qubits in double quantum dots attached to leads with various topologies and the separate entanglement of each spin with nearby electrodes. Universal behavior of entanglement is demonstrated in dependence on the mutual interactions between the spin qubits, the coupling to their environment, temperature and magnetic field. As a consequence of quantum phase transition an abrupt switch between fully entangled and unentangled states takes place when the dots are coupled in parallel.
We report the computer-automated tuning of gate-defined semiconductor double quantum dots in GaAs heterostructures. We benchmark the algorithm by creating three double quantum dots inside a linear array of four quantum dots. The algorithm sets the correct gate voltages for all the gates to tune the double quantum dots into the single-electron regime. The algorithm only requires (1) prior knowledge of the gate design and (2) the pinch-off value of the single gate $T$ that is shared by all the quantum dots. This work significantly alleviates the user effort required to tune multiple quantum dot …
