Equation Of Motion Method Research Articles

Effect of Interdot Coulomb Repulsion on Charge Transport of Parallel Two Single-Electron Transistors

The charge transport behaviors of two single-electron transistors (SETs) sitting in parallel are investigated using the Anderson model with two impurity levels. Interdot Coulomb interactions as well as intradot Coulomb interactions are included in the model. The nonequilibrium Keldysh–Green's function technique is used to calculate the current–voltage characteristics of this system. Considering the lowest order coupling between dots and electrodes, analytic spectral functions are calculated using the equation of motion method. We found that the interdot Coulomb interactions not only lead to interdot Coulomb blockade effects but also create negative differential conductances. In addition, the hysteretic effects arising from interface traps or defects are also investigated. SETs could be good detectors for determining interface acceptor-type or donor-type traps of quantum dots (QDs).

Applicability of the equations-of-motion technique for quantum dots

The equations-of-motion (EOM) hierarchy satisfied by the Green functions of a quantum dot embedded in an external mesoscopic network is considered within a high-order decoupling approximation scheme. Exact analytic solutions of the resulting coupled integral equations are presented in several limits. In particular, it is found that at the particle-hole symmetric point the EOM Green function is temperature-independent due to a discontinuous change in the imaginary part of the interacting self-energy. However, this imaginary part obeys the Fermi liquid unitarity requirement away from this special point, at zero temperature. Results for the occupation numbers, the density of states and the local spin susceptibility are compared with exact Fermi liquid relations and the Bethe ansatz solution. The approximation is found to be very accurate far from the Kondo regime. In contrast, the description of the Kondo effect is valid on a qualitative level only. In particular, we find that the Friedel sum rule is considerably violated, up to 30%, and the spin susceptibility is underestimated. We show that the widely-used simplified version of the EOM method, which does not account fully for the correlations on the network, fails to produce the Kondo correlations even qualitatively.

Spin dependent tunneling through a quantum dot attached to ferromagnetic electrodes with non-collinear magnetizations

Resonant tunneling through an interacting single-level quantum dot, coupled to ferromagnetic electrodes with non-collinear magnetizations has been analyzed theoretically. The dot is additionally subject to an external magnetic field. The non-equilibrium Green function technique and the equation of motion method have been applied to calculate electric current, tunnel magnetoresistance, and the average spin components in the dot. The relevant Green functions have been calculated in the Hartree-Fock approximation, and the calculations are restricted to the weak coupling regime. Numerical results are presented for a dot which is empty at equilibrium, but can be singly or doubly occupied when a bias voltage is applied.

Kondo effect and spin filtering in coupled quantum dots

The coherent transport through a set of N coupled quantum dots is considered in the limit of infinite intradot and finite or infinite interdot interactions. The mean field slave boson approach and the equation of motion method are used. For the full spin–orbit degenerate case the low energy behavior is characterized by an SU(2N) symmetry with entangled spin and charge correlations. The magnetic field breaks the spin degeneracy, but for the special choices of gate voltages the degeneracy might be recovered in one spin channel allowing the spin filtering.

Double dot Kondo spin filter

Spin-polarized transport through the electrostatically coupled quantum dots in the Kondo regime is studied by the equation of motion method (EOM). We show that by tuning the gate voltages or changing magnetic field, the single spin orbital Kondo channel opens and the system operates as a spin filter.

Spin‐polarized resonant tunneling through two coupled quantum dots

AbstractResonant electronic transport through two coupled non‐interacting single‐level quantum dots attached to ferromagnetic leads with collinear magnetizations is analyzed theoretically. Coupling of the dots to external leads as well as the inter‐dot coupling are assumed to be spin dependent. Basic transport characteristics, including current‐voltage curves, linear and nonlinear conductance, and tunnel magnetoresistance associated with magnetization rotation are calculated using the Green function technique. The relevant Green functions have been calculated by the equation of motion method. Variation of the transport characteristics with such system parameters like energy level position, spin polarization of the leads, and coupling between the dots has been calculated numerically. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of Lattice Vibrations on DOS and Spectral Function in Auger and Tunneling Processes

For the theoretical investigation of the effect of electron-phonon interaction on Auger and tunneling processes, we considered the Anderson-like Hamiltonian, which was developed by P.W. Anderson (1951-1961) to address one of the most challenging problems of 20 th century physics. With suitable modifications, the powerful theoretical machinery which was invented to explain magnetic impurities in metals, could be used to predict the mixing of adsorbate electron on a metal surface. This Hamiltonian can be solved by equation of motion method of Zubarev's double time Green function of the adatoms self energy and DOS (Density of States) can be estimated. It was shown that the 4 th order of the self energy contains the Auger process and can, therefore, contribute to the tunneling process. To calculate these from 1 st principle, we investigated the effect of lattice vibrations following the Anderson model and found that both DOS and spectral function are modified with subsequent modification in the concerned surface parameters.

Orbital Kondo effect and spin polarized transport through quantum dots

AbstractThe coherent spin dependent transport through a set of two capacitively coupled quantum dots placed in a magnetic field is considered within the equation of motion method. The magnetic field breaks the spin degeneracy. For special choices of gate voltages the dot levels are tuned to resonance and the orbital Kondo effect results. For different Zeemann splittings at the dots the Kondo resonance can be formed for only one spin channel. In this case the system operates as an efficient spin filter. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kondo resonance decoherence caused by an external potential

The Kondo problem, for a quantum dot (QD), subjected to an external bias, is analyzed in the limit of infinite Coulomb repulsion by using a consistent equations of motion method based on a slave-boson Hamiltonian. Utilizing a strict perturbative solution in the leads-dot coupling, T, to T^4 and T^6 orders, we calculate the QD spectral density and conductance, as well as the decoherent rate that drive the systemm from the strong to the weak coupling regime. Our results indicate thet the weak coupling regime is reached for voltages larger than a few units of the Kondo temperature.

Quantum transport simulation based on an equation of motion method: An application to current-perpendicular-to-the-plane giant magnetoresistance

A tight-binding equation of motion (EOM) method for the simulation of electronic transport in complex, and inhomogeneous systems is presented. Conductance is calculated in the linear response regime where chemical potentials can mimic electrochemical potentials. The technique is first elucidated by application to several simple systems to clarify important issues. A calculation of current-perpendicular-to-the-plane giant magnetoresistance (GMR) in a $\mathrm{Co}∕\mathrm{Cu}$ multilayer then follows. A 67% GMR is calculated which originates primarily from spin-dependent interface resistances. The advantages of an EOM method are that complicated geometries can be considered, and interactions such as spin-orbit effects or phonons, for example, may be included easily.

Electronic properties of interacting quantum dots

The electronic properties of two interacting dots connected to leads are studied in the Kondo regime. The configuration is such that one dot is inserted into the lead while the other is side-connected to it. The situation, where both dots are in the Kondo regime is investigated. We find that the development of a Kondo state related to the connected dot is mediated by the inserted dot. In this case, an anti-resonance appears in the density of states of the inserted dot, at the Fermi level. The equation of motion method is used to calculate the Green's functions of the system.

Electronic transport through a ring-shaped array of quantum dots

Making use of the equation of motion method and Keldysh Green function technique, we have developed a calculation method for the ring-shaped array of quantum dots with arbitrary dots. A general formula for the current under dc bias is obtained; the transmission probability and the differential conductance are numerically studied.

Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign

Quantum transport in disordered magnetic fields is investigated numerically in two-dimensional systems. In particular, the case where the mean and the fluctuation of disordered magnetic fields are of the same order is considered. It is found that in the limit of weak disorder the conductivity exhibits a qualitatively different behavior from that in the conventional random magnetic fields with zero mean. The conductivity is estimated by the equation of motion method and by the two-terminal Landauer formula. It is demonstrated that the conductance stays on the order of $e^2/h$ even in the weak disorder limit. The present behavior can be interpreted in terms of the Drude formula. The Shubnikov-de Haas oscillation is also observed in the weak disorder regime.

Non-equilibrium Kondo Effect in Electronic Transport through Quantum Dots

Kondo effect in a quantum dot coupled to two metallic leads is studied by the non-equilibrium Green function technique. The quantum dot is described by the Anderson model with electron-electron correlations, and the corresponding Green functions are calculated by the equation of motion method. Nonlinear transport characteristics and the Kondo anomaly in differential conductance are studied in detail.

Electronic correlations in coherent transport through a two quantum dot system

Coherent electronic transport through a double quantum dot (2qd) system connected in a series with electrodes is studied by means of nonequilibrium Green functions and using the equation of motion method, in which all electron correlations in the 2qd are treated exactly. For moderate Coulomb interactions we predict features in a conductance characteristics resulting from transmission through triplet states, which can be strongly activated for larger source-drain voltages. The analysis of the spin-spin correlation functions shows strong antiferromagnetic correlations arising from transport through the singlet state and a reduction of the total magnetic moment. However, when the transmission channel corresponding to the triplet state becomes activated the antiferromagnetic correlations are much weaker, the spins behave as free electrons spins and strongly fluctuate. We speculate that this effect can be seen in wide range of a gate voltage for a double electron occupancy of the 2qd.

Random-phase approximation and its extension for the O(2) anharmonic oscillator

We apply the random phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPA approximations using the equation of motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPA approximations. Then we use a time-dependent approach where the standard RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogoliubov equation. We draw a parallel between the two approaches.

Theoretical Investigation of the Spin‐dependent Exciton Formation Rates in Polymeric Light‐emitting Diodes

AbstractFirst, a brief review is given of recent experimental and theoretical progress in the determination of the spin‐dependent exciton formation rates in electroluminescent π‐conjugated polymers. We then describe our recent development of the coupled‐cluster equation of motion method and present its application to the theoretical study of singlet and triplet exciton formation rates and polymer light‐emitting diode quantum efficiency. It is found that, in general, singlet excitons can be formed with a higher yield than triplet excitons. The underlying mechanism is still a matter of debate. Here, we explore the role of inter‐chain charge‐bond correlation effects.

Magnetotransport in inhomogeneous magnetic fields

Quantum transport in inhomogeneous magnetic fields is investigated numerically in two-dimensional systems using the equation of motion method. In particular, the diffusion of electrons in random magnetic fields in the presence of additional weak uniform magnetic fields is examined. It is found that the conductivity is strongly suppressed by the additional uniform magnetic field and saturates when the uniform magnetic field becomes on the order of the fluctuation of the random magnetic field. The value of the conductivity at this saturation is found to be insensitive to the magnitude of the fluctuation of the random field. The effect of random potential on the magnetoconductance is also discussed.

Electron Transport and Time-Dependent Perturbation in a Two-Dimensional Symplectic System

Electron transport in a two-dimensional symplectic system with time-dependent perturbations is investigated numerically by the equation of motion method. The effect of time-dependent perturbations on the conductivity is examined in the critical regime as well as in the metallic regime. The universal correction to the conductivity, which is consistent with the weak localization theory, is indeed observed in the metallic regime. In the critical regime, it is found that the dependence of the conductivity on the frequency of perturbations can be described by the one-parameter scaling.

Time-Dependent Perturbation in Two-Dimensional Disordered Symplectic Systems: Dephasing and Scaling

The effect of time-dependent perturbations on transport phenomena in disordered systems has been studied in various context, such as the destruction of localization, the suppression of the interference effect, and the effect of temperature. In general, timedependent perturbations destroy the phase coherence. In fact, a numerical study of the dephasing effect by a time-dependent perturbation in two-dimensional disordered systems has been performed by Nakanishi et al. They have investigated the effect of the timedependent on-site potential oscillating with a frequency ω and demonstrated that the ω-dependent correction to the conductivity takes an universal form in the metallic regime. In the present work, we study a different type of time-dependent perturbation, namely the timedependent transfer-integrals. It is expected that this type of perturbation is more representative for the effect of temperature. We consider a two-dimensional disordered system with spin-orbit interaction, which belongs to the symplectic universality class. The system exhibits the Anderson transition even in two dimensions. We numerically evaluate the conductivity as a function of the frequency of the perturbation using the equation of motion method. In the metallic regime, it is examined whether the universal ω-dependent correction to the conductivity can be observed also for the present type of perturbation. For the critical regime, we find that the frequency dependence of the conductivity can be described by the one-parameter scaling. The model we adopt is the Ando model extend to the case where transfer-integrals oscillate with a frequency ω. The Hamiltonian is given by