We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave-number set of the incoming plane wave is not conserved during the scattering and many-body bound states appear. By using the scattering state, we study the average nonequilibrium current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account is qualitatively similar to several known results.
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…
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.
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.
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.
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.
We develop an exact non-perturbative framework to compute steady-state properties of quantum-impurities subject to a finite bias. We show that the steady-state physics of these systems is captured by nonequilibrium scattering eigenstates which satisfy an appropriate Lippman-Schwinger equation. Introducing a generalization of the equilibrium Bethe-Ansatz - the Nonequilibrium Bethe-Ansatz (NEBA), we explicitly construct the scattering eigenstates for the Interacting Resonance Level model and derive exact, nonperturbative results for the steady-state properties of the system.
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…
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.
Electron transport through a quantum dot chain with two neighboring dots coupled to both leads is theoretically studied. In such a system, it is found that only for the even-numbered quantum dot structure with the same-number quantum dots coupled to each connecting dot, some eigenstates of the quantum dots decouple from the leads. Namely, all odd eigenstates decouple from the leads in the absence of magnetic flux, but all even eigenstates will decouple from the leads when a magnetic flux is introduced. In addition, by adjusting the magnetic fluxes through any subring, some eigenstates decouple…
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 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 investigate the effects of voltage induced spin-relaxation in a quantum dot in the Kondo regime. Using nonequilibrium perturbation theory, we determine the joint effect of self-energy and vertex corrections to the conduction electron T-matrix in the limit of transport voltage much larger than temperature. The logarithmic divergences, developing near the different chemical potentials of the leads, are found to be cut off by spin-relaxation rates, implying that the nonequilibrium Kondo-problem remains at weak coupling as long as voltage is much larger than the Kondo temperature.
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…
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…
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 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…
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.
The description of quantum transport in a quadruple quantum-dot structure (QQD) is proposed taking into account the Coulomb correlations and nonzero bias voltages. To achieve this goal the combination of nonequilibrium Green's functions and equation-of-motion technique is used. It is shown that the anisotropy of kinetic processes in the QQD leads to negative differential conductance (NDC). The reason of the effect is an interplay of the Fano resonances which are induced by the interdot Coulomb correlations. Different ways to increase the peak-to-valley ratio related to the observed NDC are dis…
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…
We report electronic transport measurements through a silicon hybrid double quantum dot consisting of a donor and a quantum dot. Transport spectra show resonant tunneling peaks involving different valley states, which illustrate the valley splitting in a quantum dot on a Si/SiO2 interface. The detailed gate bias dependence of double dot transport allows a first direct observation of the valley splitting in the quantum dot, which is controllable between 160-240 ueV with an electric field dependence 1.2 +- 0.2 meV/(MV/m). A large valley splitting is an essential requirement to implement a physic…
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 study the nonequlibrium transport through a quantum dot weakly coupled to Luttinger liquids (LL). A general current expression is derived by using nonequilibrium Green function method. Then a special case of the dot with only a single energy level is discussed. As a function of the dot's energy level, we find that the current as well as differential conductance is strongly renormalized by the interaction in the LL leads. In comparison with the system with Fermi liquid (FL) leads, the current is suppressed, consistent with the suppression of the electron tunneling density of states of the LL…
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 use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becom…
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 study low-temperature transport through a Coulomb blockaded quantum dot (QD) contacted by a normal (N), and a superconducting (S) electrode. Within an effective cotunneling model the conduction electron self energy is calculated to leading order in the cotunneling amplitudes and subsequently resummed to obtain the nonequilibrium T-matrix, from which we obtain the nonlinear cotunneling conductance. For even occupied dots the system can be conceived as an effective S/N-cotunnel junction with subgap transport mediated by Andreev reflections. The net spin of an odd occupied dot, however, leads …
We construct a number($n$)-resolved master equation (ME) approach under self-consistent Born approximation (SCBA) for noise spectrum calculation. The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations. We apply this approach to the challenging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum. The proposed $n$-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach, in the sense of being applicable to the shot…
The linear and nonlinear transport through a multi-level lateral quantum dot connected to two leads is investigated using a generalized finite-$U$ slave-boson mean field approach. For a two-level quantum dot, our calculation demonstrates a substantial conductance enhancement near the degeneracy point of the spin singlet and triplet states, a non-monotonic temperature-dependence of conductance and a sharp dip and nonzero bias maximum of the differential conductance. These agree well with recent experiment observations. This two-stage Kondo effect in an out-of-equilibrium situation is attributed…
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…
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 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…
Self-assembled quantum dot (QD) solids are a highly tunable class of materials with a wide range of applications in solid-state electronics and optoelectronic devices. In this perspective, we highlight how the presence of microscopic disorder in these materials can influence their macroscopic optoelectronic properties. Specifically, we consider the dynamics of excitons in energetically disordered QD solids using a theoretical model framework for both localized and delocalized excitonic regimes. In both cases, we emphasize the tendency of energetic disorder to promote nonequilibrium relaxation …
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 study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV-characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried respectively by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Russinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV…
The tight-binding method is employed to investigate the effects of three typical in-plane electric fields on the electronic structure of a triangular zigzag graphene quantum dot. The calculation shows that the single-electron eigenstates evolute independently in two subspaces no matter how the electric fields change. The electric field with fixed-geometry gates chooses several scattered parts of the zero-energy eigenspace as the new zero-energy eigenstates, regardless of the field strength. Moreover, the new zero-energy eigenstates remain unchanged and the associated levels are linear as the f…
The theory of quantum transport through a dot under a finite bias voltage is developed using perturbation theory in the Keldysh formalism. It is found that the Kondo resonance splits into double peaks when the voltage exceeds the Kondo temperature, $eV>k_B T_K $, which leads to the appearance of a second peak in conductance, in addition to the zero-bias peak. The possible relevance of the new peak to the 0.7 conductance anomaly observed in quantum point contact is discussed.
We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. We show that the master equation in the occupation-state basis…
Quantum thermal transport in two-quantum-dot system with Dzyaloshinskii-Moriya interaction (DM interaction) has been studied. The sign of thermal rectification can be controlled through changing the energy splitting or the DM interaction strength. The anisotropic term in the system can also affect the sign of rectification. Compared with other proposals [Phys. Rev. B 80, 172301 (2009)], our model can offer larger rectification efficiency and show the potential application in designing the polarity-controllable thermal diode with a small size system (N=2). Moreover, quantum correlations of two-…
We investigate the effect of many-body interactions on the optical absorption spectrum of a charge-tunable quantum dot coupled to a degenerate electron gas. A constructive Fano interference between an indirect path, associated with an intra dot exciton generation followed by tunneling, and a direct path, associated with the ionization of a valence-band quantum dot electron, ensures the visibility of the ensuing Fermi-edge singularity despite weak absorption strength. We find good agreement between experiment and renormalization group theory, but only when we generalize the Anderson impurity mo…
Electron transport through a strongly correlated quantum dot (QD) embedded in an Aharonov-Bohm (AB) ring is investigated with the aid of the finite-U slave-boson mean-field (SBMF) approach extended to nonequilibrium regime. A nonequilibrium steady state (NESS) of the mean-field Hamiltonian is constructed with the aid of the C*-algebraic approach for studying infinitely extended systems. In the linear response regime, the Fano-Kondo resonances and AB oscillations of the conductance obtained from the SBMF approach are in good agreement with those from the numerical renormalization group techniqu…
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…
Using the modified perturbation theory, we theoretically study the nonequilibrium Andreev transport through a quantum dot coupled to normal and superconducting leads (N-QD-S), which is strongly influenced by the Kondo and superconducting correlations. From the numerical calculation, we find that the renormalized couplings between the leads and the dot in the equilibrium states characterize the peak formation in the nonequilibrium differential conductance. In particular, in the Kondo regime, the enhancement of the Andreev transport via a Kondo resonance occurs in the differential conductance at…
We examine the recently proposed imaginary-time formulation for strongly correlated steady-state nonequilibrium for its range of validity and discuss significant improvements in the analytic continuation of the Matsubara voltage as well as the fermionic Matsubara frequency. The discretization error in the conventional Hirsch-Fye algorithm has been compensated in the Fourier transformation with reliable small frequency behavior of self-energy. Here we give detailed discussions for generalized spectral representation ansatz by including high order vertex corrections and its numerical analytic co…
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…
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 demonstrate that nonequilibrium nanoscopic systems with Majorana zero modes admit special kind of universality which cannot be classified as of strictly transport or strictly thermodynamic nature. To reveal such kind of Majorana universality we explore purely thermal nonequilibrium states of a quantum dot whose low-energy degrees of freedom are governed by Majorana zero modes. Specifically, the quantum dot is coupled to a topological superconductor, supporting Majorana zero modes, as well as to two normal metallic contacts with the same chemical potentials but different temperatures. It is …
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 a steady state non-equilibrium transport between two interacting helical edge states of a two dimensional topological insulator, described by helical Luttinger liquids, through a quantum dot. For non-interacting dot the current is obtained analytically by including the self-energy correction to the dot Green's function. For interacting dot we use equation of motion method to study the influence of weak on-site Coulomb interaction on the transport. We find the metal-to-insulator quantum phase transition for attractive or repulsive interactions in the leads when the magnitude of the int…
We present a phenomenological model to consider the effect of shape symmetry breaking on the optical properties of self-assembled quantum dots. We compare between quantum dots with two-fold rotational and two reflections ($C_{2v}$) symmetry and quantum dots in which this symmetry is reduced by perturbation to one reflection only ($C_{s}$). We show that this symmetry reduction drastically affects the optical activity of the dark exciton. In symmetric quantum dots, one of the dark exciton eigenstate is totally dark and the other, due to heavy- and light-hole mixing, has a small dipole moment pol…
The nonequilibrium dynamics of a quantum dot with electron-phonon interactions described by a generalized Holstein model is presented. A combination of methodologies including the reduced density matrix formalism, the multilayer multiconfiguration time-dependent Hartree method, and a time-dependent nonequilibrium Green function approach, is used to explore the transient behavior on multiple timescales as the system approaches steady-state. The dot population dynamics on short to intermediate times is governed by the dot-lead hybridization parameter ($Γ$) and by the typical phonon frequency ($ω…
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 analyze universal transport properties of a strongly interacting quantum dot in the Kondo regime when the quantum dot is placed in an external magnetic field. The quantum dot is described by the asymmetric Anderson model with the spin degeneracy removed by the magnetic field resulting in the Zeeman splitting. Using an analytical expression for the tunneling density of states found from a Keldysh effective field theory, we obtain in the whole energy range the universal differential conductance and analytically demonstrate its Fermi-liquid and logarithmic behavior at low- and high-energies, r…
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…
