Single Quantum Dot System Research Articles

Finite‐Frequency Noise and Dynamical Charge Susceptibility in Single and Double Quantum Dot Systems

AbstractThis study reports on finite‐frequency noise and dynamical charge susceptibility in out‐of‐equilibrium quantum dot systems. Both single and double quantum dots connected to one or two reservoirs of electrons are considered, and these quantities are calculated by using the non‐equilibrium Green function technique. The results are discussed in the light of experimental results, particularly in the low‐frequency limit for which an interpretation in terms of an equivalent RC‐circuit is made. Anti‐symmetrized noise is also studied, defined as the difference between absorption and emission noises, and its relationship with the dynamical charge susceptibility in single quantum dots is established. In double quantum dots, the similarities between the dynamical charge susceptibility, the absorption noise, and the dot occupancy, are highlighted by comparing their respective variations with the bias voltage applied between the two reservoirs, and the detuning energy defined as the difference between the lowest level energies in the two dots.

Real-time dynamics in strongly correlated quantum-dot systems

We investigate the real-time dynamical properties of Rabi-type oscillation through strongly correlated quantum-dot systems by means of accurate hierarchical equations of motion. It is an extension of the hierarchical Liouville-space approach for addressing strongly correlated quantum-dot systems. We study two paradigmatic models, the single quantum-dot system, and serial coupling double quantum-dot system. We calculate accurately the time-dependent occupancy of quantum-dot systems subject to a sudden change of gate voltage. The Rabi-type oscillation of the occupancy and distinct relaxation time of the quantum-dot systems with different factors are described. This is helpful to understand dissipation and decoherence in real-time dynamics through nanodevices and provides a theoretical frame to experimental investigation and manipulation of molecular electronic devices.

Thermoelectric transport properties of single quantum dot systems in the presence of Majorana states

We present theoretical results for the thermoelectric transport properties in a single quantum dot system side coupled to a Majorana nanowire. The system’s electrical conductivity G , and the fundamental thermoelectric parameters such as the Seebeck coefficient S and thermal conductivity κ are numerically estimated based on a linear response approximation. Our results prove that the Majorana states in the side nanowire play an important role in the system’s thermoelectric response. In particular, a proper choice of the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M can provide the appropriate physical environment for the experimental detection of Majorana states via thermoelectrical experimental measurements. • We considered the effects of Majorana states on the thermoelectric response of a single quantum dot system. • We present numerical results for the system electrical conductivity, Seebeck coefficient, thermal conductivity, and figure of merit. • The system thermoelectric response is strongly dependent on the quantum dot — Majorana nanowire tunneling rate ξ and of the Majorana states overlap amplitude ɛ M .

Study of quantum speed limit of of transport process of single quantum dot system in dissipative environment

We theoretically study the quantum speed limit (QSL) of the single dot system in dissipative environment based on quantum dot transport theory and Bures angle metric method. The theoretical results show that in the dissipative environment, different tunneling probabilities have different effects. The increase of left tunneling probability has a weak effect on the accelerating capability of the system, due to the Coulomb blocking effect and quantum coherence. On the other hand, the right tunneling probability has a significant influence on the accelerating capability of the system, the accelerating capability is promoted with the increase of right tunneling probability because of the effect of channel blocking and co-tunneling. The increase of energy displacement promotes the accelerating capability of the system and changes the oscillation frequency of the system, owing to its taking longer time for the system to evolve to a target state. The effect of the relaxation rate for the system's accelerating capability is not monotonic, there is an interesting turning point due to the change of electron layout number. When the relaxation rate is less than this point, the accelerating capability of the system will oscillate. When the relaxation rate is higher than this point, the change of accelerating capability is monotonically suppressed by the relaxation rate. In general, the increase of the relaxation rate weakens the acceleration capability of the system. Our results provide theoretical reference for studying the QSL time in a semiconductor device affected by numerous factors.

Heat current rectification in a single quantum dot system with the presence and absence of the magnetic field

Heat current rectification in a single quantum dot system with the presence and absence of the magnetic field

Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model.

We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV,eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μL -μR) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.

Third stable branch and tristability of nuclear spin polarizations in a single quantum dot system

Semiconductor quantum dots provide a spin-coupled system of an electron and nuclei via enhanced hyperfine interaction. We showed that the nuclear spin polarization in single quantum dots can have three stable branches under a longitudinal magnetic field. The states were accompanied by hysteresis loops around the boundaries of each branch with a change in the excitation condition. To explain these findings, we incorporated the electron spin relaxation caused by the nuclear spin fluctuation into the previously-studied dynamic nuclear spin polarization mechanism. The model reproduces the new features of nuclear spin polarization and the associated strong reduction in the observed electron spin polarization, and can refer to the tristability of nuclear spin polarization.

A generalised approach to calculate various transport observables for a linear array of series and parallel quantum dots

A systematic generalised approach to find transport observables for a linear array of different quantum dot (QD) systems has been discussed, using non-equilibrium Green function (NEGF) formalism, in the presence of on-dot Coulomb interaction and inter-dot tunnelling. The equation of motion (EOM) method has been used to derive expressions for Green functions (GFs) within the simplest mean-field approximation to tackle the Coulomb correlation term. Starting from the mathematical structures of GFs for single, double and triple quantum dot systems, the expressions for GFs and transport observables have been generalised for the quantum dot systems containing N number of quantum dots in series as well as parallel linear array of dots. Further, the formulae so obtained have been used for numerical calculations of transmission probability and the I–V characteristics of linear arrays of quantum dots in series as well as parallel configuration containing up to three dots. The results show that, with the increase in number of dots in the scattering region, transmission probability and electron current decrease in series case, while both quantities increase in parallel configuration of dots. The inter-dot tunnelling leads to the splitting of transmission peaks in double QD system in series case whereas, it induces Fano effect in triple QD system in parallel configuration.

Negative Differential Conductance Assisted by Optical Fields in a Single Quantum Dot with Ferromagnetic Electrodes.

In a single quantum dot (QD) system connected with ferromagnetic electrodes, the electron transport properties, assisted by the thermal and Fock state optical fields, are theoretically studied by the Keldysh nonequilibrium Green’s function approach. The results show that the evolution properties of the density of state and tunneling current assisted by the Fock state optical field, are quite different from those of the thermal state. The photon sideband shift decreases monotonously with the increase in the electron–photon coupling strength for the case of the thermal state, while the shift is oscillatory for the case of the Fock state. Negative differential conductance (NDC) appears obviously in a QD system contacted with parallel (P) and antiparallel (AP) magnetization alignment of the ferromagnetic electrode leads, assisted by the Fock state optical field in a wide range of electron–photon interaction parameters. Evident NDC usually only arises in an AP configuration QD system assisted by the thermal state optical field. The results have the potential to introduce a new way to actively manipulate and control the single-electron tunneling transport on a QD system by the quantum states of the optical field.

Full Counting Statistics of Electrons through Interaction of the Single Quantum Dot System with the Optical Field.

In this paper, using the particle-number-resolved master equation, the properties of full counting statistics (FCS) are investigated for a single quantum dot (QD) system interacting with optical fields in the thermal state, Fock state, coherent state, and coherent state with random phase. In these diverse quantum states of optical fields, average tunneling currents have different step shoulder heights at a lower bias voltage with the same light intensity, and a staircase-shaped current can be induced unexpectedly in vacuum state optical field. The characteristics of the Fano factor and skewness in the coherent state differ from those in all of the other cases. For avalanche-like transport at a lower bias voltage, the mechanism is a dynamical channel blockade in a moderate electron–photon interaction regime. There is a pronounced negative differential conductance that results from tuning the phase of the coherent state optical field in a symmetric QD system.

Non-Markovian coherent feedback control of quantum dot systems

In this paper we present a non-Markovian coherent feedback scheme for decoherence suppression in single quantum dot systems. The feedback loop is closed via a quantum tunnelling junction between the natural source and drain baths of the quantum dot. The exact feedback-controlled non-Markovian Langevin equation is derived for describing the dynamics of the quantum dot. To deal with the nonlinear memory function in the Langevin equation, we analyse the Green’s function-based root locus, from which we show that the decoherence of the quantum dot can be suppressed via increasing the feedback coupling strength. The effectiveness of decoherence suppression induced by non-Markovian coherent feedback is demonstrated by a single quantum dot example bathed with Lorentzian noises.

Andreev and Majorana bound states in single and double quantum dot structures

We present a numerical study of the emergence of Majorana and Andreev bound states in a system composed of two quantum dots, one of which is coupled to a conventional superconductor, SC1, and the other connects to a topological superconductor, SC2. By controlling the interdot coupling we can drive the system from two single (uncoupled) quantum dots to double (coupled) dot system configurations. We employ a recursive Green’s function technique that provides us with numerically exact results for the local density of states of the system. We first show that in the uncoupled dot configuration (single dot behavior) the Majorana and the Andreev bound states appear in an individual dot in two completely distinct regimes. Therefore, they cannot coexist in the single quantum dot system. We then study the coexistence of these states in the coupled double dot configuration. In this situation we show that in the trivial phase of SC2, the Andreev states are bound to an individual quantum dot in the atomic regime (weak interdot coupling) or extended over the entire molecule in the molecular regime (strong interdot coupling). More interesting features are actually seen in the topological phase of SC2. In this case, in the atomic limit, the Andreev states appear bound to one of the quantum dots while a Majorana zero mode appears in the other one. In the molecular regime, on the other hand, the Andreev bound states take over the entire molecule while the Majorana state remains always bound to one of the quantum dots.

Full-counting statistics of transient energy current in mesoscopic systems

We investigate the full-counting statistics (FCS) of energy flow carried by electrons in the transient regime. Based on a two-measurement scheme, we formulate a nonequilibrium Keldysh Green's function theory to compute the generating function for FCS of energy transport. Specifically, we express the generating function using the path integral along the Keldysh contour and obtain an exact solution of the generating function using the Grassmann algebra. With this formalism, we calculate the transient energy current and higher-order cumulants for both single- and double-quantum-dot (QD) systems in the transient regime. To examine the finite bandwidth effect of leads to the FCS of energy transport, we have used an exact solvable model with a Lorentizian linewidth where all nonequilibrium Green's functions can be solved exactly in the time domain. It is found that the transient energy current exhibits damped oscillatory behavior. For the single quantum dot system the frequency of oscillation is independent of bandwidth of the leads while the decay rate of the oscillation amplitude is determined by the lifetime of resonant state which increases as the bandwidth decreases. At short times, a universal scaling of maximum amplitude of normalized cumulants is identified for the single-QD system. For the double-QD system, the damped oscillation of energy current is dominated by Rabi oscillation with frequency approximately proportional to the coupling constant between two quantum dots. In general, the transient energy current increases when the coupling between two QDs is stronger. However, when the interdot coupling is larger than half of the external bias the transient energy current is suppressed significantly. All these results can be understood analytically.

Non-Markovian quantum state diffusion for an open quantum system in fermionic environments

Non-Markovian quantum state diffusion (NMQSD) provides a powerful approach to the dynamics of an open quantum system in bosonic environments. Here we develop an NMQSD method to study the open quantum system in fermionic environments. This problem involves anticommutative noise functions (i.e., Grassmann variables) that are intrinsically different from the noise functions of bosonic baths. We obtain the NMQSD equation for quantum states of the system and the non-Markovian master equation. Moreover, we apply this NMQSD method to single and double quantum-dot systems.

Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations; however, its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results. This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.

Phonon-Assisted Spin Current in a Hybrid System with a Single Molecular Quantum Dot System Applied with ac Magnetic Fields

We investigate the spin current through a molecular quantum dot (MQD) ir- radiated with a rotating magnetic field and an oscillating magnetic field by nonequilib- rium Green's function. The rotating magnetic field rotates with the angular frequency ωr around the z-axis with the tilt angle θ, and the time-oscillating magnetic field is lo- cated in the z-axis with the angular frequency ω. Different behaviors have been shown in the presence of electron-phonon interaction(EPI) which plays a significant role in the transport. The spin current displays asymmetric behavior as the source-drain bias eV=0, novel side peaks or shoulders can be found due to the phonon absorption and emission procedure, and the negative spin current becomes stronger as the parameter g increases. However, the spin currents display the same magnitude and the same oscillation behavior in the region m 0B1>3D regardless the parameter g.

Nanometer optomechanical transistor based on nanometer cavity optomechanics with a single quantum dot

A mechanical oscillator coupled to the optical fields of a cavity has emerged as an important new frontier in modern quantum optics and quantum information processing. In the present article, we report on the smallest optomechanical system with a single quantum dot (QD), where the role of the optical cavity is played by an excitonic resonance of the QD, while the role of the mechanical element is played by the lattice vibrations. The coupling between an exciton and phonons via deformation potential serves as the coupling of a mechanical oscillator to the cavity field via radiation pressure. This single quantum dot system provides a realization of the smallest optomechanical system which can act as a quantum optomechanical transistor and is achievable immediately in current experiments.

Statistics property of polarized photon emission driven bya pair of pulses in single quantum dot

We study the properties of the x- and the y-polarized photons of the single quantum dot system driven by a pair of pulses using the generating function approach. Our results show that the quantum interference effects on the line shapes and the Mandels parameter Q of the x- and y-polarized photons and the linear and the nonlinear cross correlations are important.

First-principles investigation of dynamical properties of molecular devices under a steplike pulse

We report a computationally tractable approach to first-principles investigation of time-dependent current of molecular devices under a steplike pulse. For molecular devices, all the resonant states below Fermi level contribute to the time-dependent current. Hence calculation beyond wideband limit must be carried out for a quantitative analysis of transient dynamics of molecules devices. Based on the exact nonequilibrium Green's-function (NEGF) formalism of calculating the transient current [J. Maciejko, J. Wang, and H. Guo, Phys. Rev. B 74, 085324 (2006)], we develop two approximate schemes going beyond the wideband limit, they are all suitable for first-principles calculation using the NEGF combined with density-functional theory. Benchmark test has been done by comparing with the exact solution of a single level quantum dot system. Good agreement has been reached for two approximate schemes. As an application, we calculate the transient current using the first approximated formula with opposite voltage ${V}_{L}(t)=\ensuremath{-}{V}_{R}(t)$ in two molecular structures: ${\text{Al-C}}_{5}\text{-Al}$ and ${\text{Al-C}}_{60}\text{-Al}$. As illustrated in these examples, our formalism can be easily implemented for real molecular devices. Importantly, our new formula has captured the essential physics of dynamical properties of molecular devices and gives the correct steady state current at $t=0$ and $t\ensuremath{\rightarrow}\ensuremath{\infty}$.

Photon emission of single quantum dot driven by continuous external field studied by using the generating function

We studied the properties of the X- and Y- polarized photon emission from the single quantum dot system driven by external cw laser using the generating function approach developed recently. The results demonstrate that the X- and Y- polarized photon show sine or cosine behavior with the field direction in the weak field region. They show, however, stronger nonlinear behavior in the strong field region.