Equation Of Motion Method Research Articles

Pairing in asymmetrical Fermi systems with intra- and interspecies correlations

We consider inter- and intra-species pairing interactions in an asymmetrical Fermi system. Using equation of motion method, we obtain coupled mean-field equations for superfluid gap functions and population densities. We construct a phase diagram across BCS-BEC regimes. Due to intra-species correlations, the BCS singlet superfluid state can sustain finite polarizations, $P$. For larger $P$, we find phase separations in BCS and BEC regimes. A superfluid phase exists for all $P$ deep in BEC regime. Our results may apply to pairing in ultracold fermions, nuclear and quark matter physics.

Antiferromagnetic and superconducting gaps of some superconductors

A theoretical model is presented to study the antiferromagnetic superconductors in which the effect of the impurity f-electrons and hybridization of the f-electrons with the conduction band are incorporated. The competition between magnetism and superconductivity is investigated in cuprate superconductors of the type R1−xMxCuO4 [R=La, Nd; M=Sr, Ba, Ce]. The antiferromagnetic long range ordering and the superconducting ordering are associated with the same conduction electrons and hence there is strong interplay between the two phenomena. Zubarev’s double time Green’s function technique and equations of motion method is used to evaluate the superconducting gap and antiferromagnetic staggered field. The interplay is studied by varying the coupling parameters, the position of the f-level and the hybridization. It is seen that the antiferromagnetic coupling enhances the superconducting order.

INTERACTING BOSE GAS CONFINED BY AN EXTERNAL POTENTIAL

Interacting Bose gas confined by an external potential is studied using Green functions in spectral representation. The calculation is presented transparently using the equation of motion method. With this, the interplay between the condensed and the non-condensed atoms is inevitably seen. An expression for the condensate number at finite temperature is obtained in the lowest and first orders, from which depletion of bosons from the ground state is qualitatively analyzed. Finally, we discuss the behaviour of the specific heat of a trapped interacting Bose gas in the quasi-continuum limit.

Quantum interference and Coulomb correlation effects in spin-polarized transport through two coupled quantum dots

Spin-dependent transport through two coupled single-level quantum dots attached to ferromagnetic leads with collinear (parallel and antiparallel) magnetizations is analyzed theoretically by the nonequilibrium Green function technique. Transport characteristics, in particular, linear and nonlinear differential conductance and tunnel magnetoresistance associated with the magnetization rotation from antiparallel to parallel alignment, are calculated numerically with intradot Coulomb interaction taken into account. The relevant Green functions are derived by the equation of motion method within the Hartree-Fock decoupling scheme. The dot occupations and Green functions are calculated self-consistently, and the numerical analysis is focused on the interference (Fano antiresonance) and Coulomb interaction effects. It is shown that the presence of Fano antiresonance depends on the sign of the nondiagonal coupling elements.

Multiple Fano resonance in a two-dot system

Interference effects in electron transport across a double quantum dot are studied theoretically within the framework of the Hartree–Fock approach by means of the Green function formalism based on the equation of motion method. An influence of inter–dot Coulomb repulsion of strength U on conductance spectra is analyzed and a limit of U comparable to the tunneling rate between two dots is discussed in detail. A variety of Fano features, including multiple (double or triple) Fano resonances, is found as a result of interferences between four states, molecular bonding and antibonding ones, as well as these states shifted by U. The number and intensity of Fano resonance peaks present in the conductance spectrum strongly depend on the relation between parameters which describe the inter-dot tunneling rate and inter-dot Coulomb interaction between electrons.

Interference effects and Fano resonance in transport across a two dot system in the Kondoregime

Transport across a double dot system of a special geometry with two channels accessible fortunneling electrons is theoretically studied in a region of low temperatures corresponding tothe Kondo regime, and interference effects are analyzed. The spectral functionand the linear conductance are calculated using the Green function formalismbased on the equation of motion method. It is shown that interference processesstrongly influence the spectral function. Moreover, due to interference effectsthe conductance, which is close to zero in a low energy region, shows at highergate voltages a well defined Fano resonance. A development of the Fano peak asthe system undergoes a gradual transition from the serial configuration to thegeometry with two dots partially connected to both electrodes is demonstrated. Theposition and intensity of the Fano resonance strongly depend on the inter-dottunneling rate. The influence of temperature on the resonance is also discussed.

Coherent Transport through Systems of Coupled Quantum Dots

Spin-dependent electronic transport through two coupled single-level quantum dots attached to ferromagnetic leads with parallel and antiparallel magnetizations is analyzed theoretically. The intra-dot Coulomb correlation is taken into account, while the inter-dot Coulomb repulsion is omitted. Conductance and tunnel magnetoresistance associated with magnetization rotation are calculated by the nonequilibrium Green function technique. The relevant Green functions are derived by the equation of motion method in the Hartree{Fock approximation. The dot occupation numbers and the Green functions are calculated self-consistently. The interference efiects in electronic transport through quantum dots are analyzed in two difierent conflgurations. It is shown that the Fano resonance in conductance can be observed even for vanishing inter-dot hopping parameter t. The interplay of the interference efiects and the Coulomb interactions in quantum dots is also analyzed. PACS numbers: 73.23.{b, 73.21.La, 73.23.Hk

Spin‐polarized transport through two coupled quantum dots

AbstractSpin‐dependent transport through two coupled single‐level quantum dots attached to ferromagnetic leads with collinear (parallel and antiparallel) magnetizations is analyzed theoretically. Generally, the intra‐ and inter‐dot Coulomb correlations are taken into account. Transport characteristics, including conductance and tunnel magnetoresistance associated with the magnetization rotation from the parallel to antiparallel configurations, are calculated by the noneqiulibrium Green function technique. The relevant Green functions are derived by the equation of motion method. To close the set of equations we employ the Hartree–Fock decoupling scheme. The dot occupation numbers and the Green functions are calculated self‐consistently. We focus on the interplay of interference (Fano resonance) and Coulomb interaction effects. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron transport through parallel double quantum dots with interdot correlations

AbstractElectron transport through a system of two quantum dots coupled via tunneling processes and attached to external electrodes is studied within the framework of the Green function formalism based on the equation of motion method. Interdot Coulomb interactions are taken into account in a form of a Hubbard‐like term and the interplay between interference and electron correlation effects is investigated. It is shown that Coulomb interactions strongly modify the linear conductance. However, the Fano‐like behaviour can be observed and a dip in the conductance which appears due to interference effects practically is not influenced by interdot correlations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

PAIRING IN ASYMMETRICAL FERMI SYSTEMS

We consider inter- and intra-species pairing interactions in an asymmetrical Fermi system. Using equation of motion method, we obtain coupled mean-field equations for superfluid gap functions and population densities. We construct a phase diagram across BCS-BEC regimes. Due to intra-species correlations, the BCS singlet superfluid state can sustain finite polarizations, P. For larger P, we find phase separations in BCS and BEC regimes. A superfluid phase exists for all P deep in BEC regime. Our results may apply to pairing in ultracold fermions, nuclear and quark matter physics.

CONDENSATE FRACTION IN THE DYNAMIC STRUCTURE FUNCTION OF BOSE FLUIDS

We present results on the behavior of the dynamic structure function in the short wave length limit using the equation of motion method. The one-body continuity equation defines the self-energy, which becomes a functional of the fluctuating two-body correlation function. We evaluate the self-energy in this limit and show that sum rules up to the second moment, which requires the self-energy in the short wave length limit and zero frequency to be proportional to the kinetic energy per particle, are exactly satisfied. We compare our results with the impulse approximation and calculate the condensate fraction. An analytic expression for the momentum distribution is also derived.

The completeness problem in the impurity Anderson model

With the recent development of the nanoscopic technology, the impurity Anderson model (AIM) was experimentally realized in quantum dot devices, and there is renewed interest in the study of the Kondo physics of the AIM. Several Green's functions approximations by the equation of motion method (EOM), that incorporates the Kondo effect through a digamma function, have been presented in the literature as an adequate tool to describe, at least qualitatively, the Kondo effect. However, these approximations present several drawbacks: they are no longer valid as the temperature decreases below the Kondo temperature, because the logarithmic divergence of the digamma function makes the spectral density at the chemical potential to vanish, and the Friedel sum rule and the completeness in the occupation numbers are not fulfilled. In this work we present a critical discussion comparing the results of digamma approximations GF with the atomic approach, recently developed by some of us, that satisfy the completeness and the Friedel sum rule. We present results for the density of states, the Friedel sum rule and the completeness.

Electronic transport through a T-shaped four-quantum dot system

Making use of the equation of motion method and Keldysh Green's function technique, we have developed a calculation method by which an analytical formula for the current under dc bias is obtained and the transmission probabilities are numerically studied for a T-shaped four-quantum dot (QD) system connected to three terminals. The results are explained in terms of the localization properties of the confined states in the system.

Interference effects in a double quantum dot system with inter-dot Coulomb correlations

Electron transport through a double quantum dot system is studied with the use of theGreen function formalism based on the equation of motion method, and an interplaybetween interference and Coulomb blockade effects due to inter-dot correlations isdiscussed. A double structure with two Fano resonances (or antiresonances) isfound in the conductance spectrum. Fano features are weakly influenced by thepresence of Coulomb interaction but the conductance is strongly suppressed in theenergy region with the Fermi level in the leads close to the aligned levels of bothdots. This Coulomb blockade effect takes place when the coupling between thedots is of repulsive character. On the other hand, the conductance of an artificialmolecule with attractive inter-dot coupling is only slightly modified in this energyregion. As a sign of the coupling can be easily changed in a presence of an externalmagnetic field by changes of the magnetic flux there is the possibility to controlvariations of the conductance, which may be important from the application point ofview.

Electron Transport through Double Quantum Dot System with Inter-Dot Coulomb Interaction

A theoretical approach to a problem of electron transport through double quantum dot systems based on non-equilibrium Green function formalism using equation of motion method is presented. I−V characteristics and differential conductance are calculated and discussed in detail in the intermediate regime with tunneling rate between the quantum dots comparable to coupling constants with external electrodes. Effects of inter-dot Coulomb correlations are studied for various values of interaction parameter U . It is shown that the interaction influences transport properties in a pronounced way and apart from the simple Coulomb blockade additional effects can be obtained. When energy levels of two quantum dots are not aligned, the asymmetry in conductance characteristics is closely related to a voltage dependence of population numbers in both quantum dots. For a one bias polarization electrons are well localized in quantum dots in a low voltage region, whereas for the opposite one they are partly delocalized.

Spin dependent transport through a carbon nanotube quantum dot in magnetic field

Spin-polarized transport through a carbon nanotube quantum dot in the Kondo regime is studied by the equation of motion method. Magnetic field perpendicular to the tube axis breaks the spin degeneracy, whereas axial field breaks both the orbital and spin degeneracies. A strong magnetic field anisotropy of conductance and anisotropy of its spin polarization is observed. We propose a new spin filtering mechanism for the nanotubes with the orbitally nondegenerate levels based on the field induced tuning of spin-polarized states from the same shell into orbital degeneracy.

Charge oscillations in two-level system in the presence of time-dependent coupling with electron reservoir

We consider a two-level system coupled with a free-electron reservoir (ER) and exposed to the influence of the electromagnetic field. Applying the equation of motion method for appropriate correlation functions the electron dynamics (the charge oscillations between two levels of a system) has been investigated theoretically for different kinds of coupling with the ER. It is shown, that the damping of charge oscillations depends largely on the time of interaction with the ER. These oscillations depend also on the amplitude and frequency of time-dependent energy levels and form of coupling with the ER.

Quantum criticality of a d-dimensional spin-S XXZ ferromagnetic model with longitudinal infinite-range interactions

A d-dimensional spin-S XXZ ferromagnetic model with uniform long-range interactions in the z-direction is mapped into an effective XY model in a transverse field. Then, using the two-time Green function equation of motion method, the zero-temperature properties for a periodic cubic lattice are exactly obtained close to the quantum critical point signaling the field-induced quantum phase transition from the fully polarized state into a phase with easy-plane spin ordering. We determine the relevant critical exponents which have a mean-field character for any d and S.

Coherent transport through T-shaped electrostatically coupled quantum dots

The Fano–Kondo resonance is studied in a system consisting of a pair of side-coupled double quantum dots attached to quantum wires. The double dots are capacitively coupled. The mean field slave boson approach and the equation of motion method are used. For symmetric dots Kondo effect has two possible sources: spin and charge degeneracies. The conductance as a function of gate voltage is characterized by a Fano asymmetric parameter q. For q=0 a half-reflection is observed. The same value of transmission is expected in the limit q→∞. For intermediate cases transmission line has a general asymmetric Fano-type shape. We show that by tuning the gate voltage or changing magnetic field, the single spin-orbital Kondo channel opens and the system can operate as a spin filter.

Fano effect through parallel-coupled double Coulomb islands

By means of the nonequilibrium Green function and equation of motion method,the electronic transport is theoretically studied through a parallel-coupleddouble quantum dot (DQD) in the presence of on-dot Coulomb interactionU. With focus on the quantum interference in theU-dominant parallel-coupled DQD, we find two types of Fano interferences in theconductance spectra. If the one-particle DQD bonding and antibonding bandsare well separated from their Coulomb blockade counterparts, the main featuresof Fano interference in usual DQD systems are recovered with minor revisions.The most interesting is the hybridization between the antibonding state and theCoulomb counterpart of the bonding state, which gives rises to two new channels forFano resonance. The Fano interference in the Coulomb hybridized systems can becontrolled by the electrostatic and magnetic approaches, and exhibits properties quitedifferent from what are reported in the noninteracting Fano–Anderson model.