Keldysh Green Function Technique Research Articles

Transient dynamics of a single molecular transistor in the presence of local electron-phonon and electron-electron interactions and quantum dissipation.

We consider a single molecular transistor in which a quantum dot with local electron–electron and electron–phonon interactions is coupled to two metallic leads, one of which acts like a source and the other like a drain. The system is modeled by the Anderson-Holstein (AH) model. The quantum dot is mounted on a substrate that acts as a heat bath. Its phonons interact with the quantum dot phonons by the Caldeira–Leggett interaction giving rise to dissipation in the dynamics of the quantum dot system. A simple canonical transformation exactly treats the interaction of the quantum dot phonons with the substrate phonons. The electron–phonon interaction of the quantum dot is eliminated by the celebrated Lang-Firsov transformation. The time-dependent current is finally calculated by the Keldysh Green function technique with various types of bias. The transient-time phase diagram is analysed as a function of the system parameters to explore regions that can be used for fast switching in devices like nanomolecular switches.

Nonlinear interaction effects in a three-mode cavity optomechanical system

We investigate the resonant enhancement of nonlinear interactions in a three-mode cavity optomechanical system with two mechanical oscillators. Using the Keldysh Green's function technique, we find that nonlinear effects on the cavity density of states can be greatly enhanced by the resonant interaction of two phononic polaritons, due to their small effective dissipation. In the large detuning limit and taking into account an upper bound on the achievable dressed coupling, the optimal point for probing the nonlinear effect is obtained, showing that such a three-mode system can exhibit significant nonlinear features also for relatively small values of $g/\ensuremath{\kappa}$.

Quantum transport in a single molecular transistor at finite temperature

We study quantum transport in a single molecular transistor in which the central region consists of a single-level quantum dot and is connected to two metallic leads that act as a source and a drain respectively. The quantum dot is considered to be under the influence of electron–electron and electron–phonon interactions. The central region is placed on an insulating substrate that acts as a heat reservoir that interacts with the quantum dot phonon giving rise to a damping effect to the quantum dot. The electron–phonon interaction is decoupled by applying a canonical transformation and then the spectral density of the quantum dot is calculated from the resultant Hamiltonian by using Keldysh Green function technique. We also calculate the tunneling current density and differential conductance to study the effect of quantum dissipation, electron correlation and the lattice effects on quantum transport in a single molecular transistor at finite temperature.

Nonequilibrium strong-coupling theory for a driven-dissipative ultracold Fermi gas in the BCS-BEC crossover region

We theoretically investigate strong-coupling properties of an ultracold Fermi gas in the BCS-BEC crossover regime in the non-equilibrium steady state, being coupled with two fermion baths. By developing a non-equilibrium strong-coupling theory based on the combined $T$-matrix approximation with the Keldysh Green's function technique, we show that the chemical potential bias applied by the two baths gives rise to the anomalous enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing fluctuations (although the system has no spin imbalance), resulting in the re-entrant behavior of the non-equilibrium superfluid phase transition in the BCS-unitary regime. These pairing fluctuations are also found to anomalously enhance the pseudogap phenomenon. Since various non-equilibrium phenomena have recently been measured in ultracold Fermi gases, our non-equilibrium strong-coupling theory would be useful to catch up this experimental development in this research field.

Nonequilibrium polariton dynamics in a Bose-Einstein condensate coupled to an optical cavity

We study quasiparticle scattering effects on the dynamics of a homogeneous Bose-Einstein condensate of ultracold atoms coupled to a single mode of an optical cavity. The relevant excitations, which are polaritonlike mixed excitations of photonic and atomic density-wave modes, are identified. All the first-order correlation functions are presented by means of the Keldysh Green's function technique. Beyond confirming the existence of the resonant enhancement of Beliaev damping, we find a very structured spectrum of fluctuations. There is a spectral hole burning at half of the recoil frequency reflecting the singularity of the Beliaev scattering process. The effects of the photon-loss dissipation channel and that of the Beliaev damping due to atom-atom collisions can be well separated. We show that the Beliaev process does not influence the properties of the self-organization criticality.

Enhanced nonlinear interaction effects in a four-mode optomechanical ring

With a perturbative treatment based on the Keldysh Green's function technique, we study the resonant enhancement of nonlinear interaction effects in a four-mode optomechanical ring. In such a system, we identify five distinct types of resonant scattering between unperturbed polariton modes, induced by the nonlinear optomechanical interaction. By computing the cavity density of states and optomechanical induced transparency signal, we find that the largest nonlinear effects are induced by a decay process involving the two phonon-like polaritons. In contrast to the conventional two-mode optomechanical system, our proposed system can exhibit prominent nonlinear features even in the regime when the single-photon coupling is much smaller than the cavity damping.

Finite frequency current noise in the Holstein model

We investigate the effects of local vibrational excitations in the nonsymmetrized current noise $S(\omega)$ of a nanojunction. For this purpose, we analyze a simple model - the Holstein model - in which the junction is described by a single electronic level that is coupled to two metallic leads and to a single vibrational mode. Using the Keldysh Green's function technique, we calculate the nonsymmetrized current noise to the leading order in the charge-vibration interaction. For the noise associated to the latter, we identify distinct terms corresponding to the mean-field noise and the vertex correction. The mean-field result can be further divided into an elastic correction to the noise and in an inelastic correction, the second one being related to energy exchange with the vibration. To illustrate the general behavior of the noise induced by the charge-vibration interaction, we consider two limit cases. In the first case, we assume a strong coupling of the dot to the leads with an energy-independent transmission whereas in the second case we assume a weak tunneling coupling between the dot and the leads such that the transport occurs through a sharp resonant level. We find that the noise associated to the vibration-charge interaction shows a complex pattern as a function of the frequency $\omega$ and of the transmission function or of the dot's energy level. Several transitions from enhancement to suppression of the noise occurs in different regions, which are determined, in particular, by the vibrational frequency. Remarkably, in the regime of an energy-independent transmission, the zero order elastic noise vanishes at perfect transmission and at positive frequency whereas the noise related to the charge-vibration interaction remains finite enabling the analysis of the pure vibrational-induced current noise.

Full counting statistics of information content and particle number

We consider a bipartite quantum conductor and discuss the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multi-contour Keldysh Green function technique, we calculate the R\'enyi entropy of a positive integer order $M$ subjected to the particle number constraint, from which we derive the joint probability distribution. For energy-independent transmission, we derive the time dependence of the accessible entanglement entropy, or the conditional entropy. We analyze the joint probability distribution for energy-dependent transmission probability at the steady state under the coherent resonant tunneling and the incoherent sequential tunneling conditions. We also discuss the probability distribution of the efficiency, which measures the information content transfered by a single electron.

Electron transport through a linear tri-quantum-dot molecule Aharonov-Bohm interference

Using the non-equilibrium Keldysh Green's function technique, electron transport properties through a two-terminal linear tri-quantum-dot molecule Aharonov-Bohm (A-B) interference are investigated. The conductance as a function of electron energy is numerically calculated. The influence of magnetic flux and interdot coupling strength on the conductance is researched. Fano resonances emerge in the conductance spectrum, and two bound states in the continuum form simultaneously when the interdot couplings take appropriate values. A conductance dip is observed and evolves into an antiresonance band with increasing magnetic flux. The system can be designed as a quantum switch by adjusting the intramolecular couplings.

Spin Hall effect and spin swapping in diffusive superconductors

We consider the spin-orbit-induced spin Hall effect and spin swapping in diffusive superconductors. By employing the non-equilibrium Keldysh Green's function technique in the quasiclassical approximation, we derive coupled transport equations for the spectral spin and particle distributions and for the energy density in the elastic scattering regime. We compute four contributions to the spin Hall conductivity, namely, skew scattering, side-jump, anomalous velocity, and the Yafet contribution. The reduced density of states in the superconductor causes a renormalization of the spin Hall angle. We demonstrate that all four of these contributions to the spin Hall conductivity are renormalized in the same way in the superconducting state. In its simplest manifestation, spin swapping transforms a primary spin current into a secondary spin current with swapped current and polarization directions. We find that the spin-swapping coefficient is not explicitly but only implicitly affected by superconducting correlations through the renormalized diffusion coefficients. We discuss experimental consequences for measurements of the (inverse) spin Hall effect and spin swapping in four-terminal geometries. In our geometry, below the superconducting transition temperature, the spin-swapping signal is increased an order of magnitude while changes in the (inverse) spin Hall signal are moderate.

Mixed electrical-heat noise spectrum in a quantum dot

Using the Keldysh Green function technique, we calculate the finite-frequency correlator between the electrical current and the heat current flowing through a quantum dot connected to reservoirs. At equilibrium, we find that this quantity, called mixed noise, is linked to the thermoelectric ac-conductance by the fluctuation-dissipation theorem. Out-of-equilibrium, we discuss its spectrum and find evidence of the close relationship between the mixed noise and the thermopower. We study the spectral coherence and identify the conditions to have a strong correlation between the electrical and heat currents. The change in the spectral coherence due to the presence of a temperature gradient between the reservoirs is also highlighted.

Quantum dissipative effects on non-equilibrium transport through a single-molecular transistor: The Anderson-Holstein-Caldeira-Leggett model.

The Anderson-Holstein model with Caldeira-Leggett coupling with environment is considered to describe the damping effect in a single molecular transistor (SMT) which comprises a molecular quantum dot (with electron-phonon interaction) mounted on a substrate (environment) and coupled to metallic electrodes. The electron-phonon interaction is first eliminated using the Lang-Firsov transformation and the spectral density function, charge current and differential conductance are then calculated using the non-equilibrium Keldysh Green function technique. The effects of damping rate, and electron-electron and electron-phonon interactions on the transport properties of SMT are studied at zero temperature.

Continuous third harmonic generation in a terahertz driven modulated nanowire

We consider the possibility of observing continuous third-harmonic generation using a strongly driven, single-band one-dimensional metal. In the absence of scattering, the quantum efficiency of frequency tripling for such a system can be as high as 93%. Combining the Floquet quasi-energy spectrum with the Keldysh Green's function technique, we derive a semiclassical master equation for a one-dimensional band of strongly and rapidly driven electrons in the presence of weak scattering by phonons. The power absorbed from the driving field is continuously dissipated by phonon modes, leading to a quasi-equilibrium in the electron distribution. We use the Kronig-Penney model with varying effective mass to establish the growth parameters of an InAs/InP nanowire near optimal for third harmonic generation at terahertz frequency range.

Heat generated by electrical current in a mesoscopic system perturbed by alternating current fields

To analyze heat generation in a quantum dot coupled to normal leads and subject to an ac field, a formula is derived for the heat generated Q using the nonequilibrium Keldysh Green's function technique. The numerical results show that the external ac field influences significantly the heat generated. The threshold bias decreases to Vt=ω0−nω through photon absorption. Additional steps emerge from photon-assisted tunneling, and the width of the step is equal to the frequency of photon ω and the height increases with the magnitude of the ac field. For large V/ω, the Q/ω curves display many resonant peaks due to multi-photon absorptions and emissions. Moreover, a negative differential heat generation can be observed as ω>ω0.

Phase-dependent heat transport through magnetic Josephson tunnel junctions

We present an exhaustive study of the coherent heat transport through superconductor-ferromagnet(S-F) Josephson junctions including a spin-filter (I$_{sf}$) tunneling barrier. By using the quasiclassical Keldysh Green's function technique we derive a general expression for the heat current flowing through a S/F/I$_{sf}$/F/S junction and analyze the dependence of the thermal conductance on the spin-filter efficiency, the phase difference between the superconductors and the magnetization direction of the ferromagnetic layers. In the case of non-collinear magnetizations we show explicitly the contributions to the heat current stemming from the singlet and triplet components of the superconducting condensate. We also demonstrate that the magnetothermal resistance ratio of a S/F/I$_{sf}$/F/S heat valve can be increased by the spin-filter effect under suitable conditions.

Thermoelectric properties of a chain of coupled quantum dots embedded in a nanowire

The thermoelectric properties of a chain of coupled quantum dots (CCQDs) connected to metallic electrodes are theoretically investigated in the Coulomb blockade regime. An extended Hubbard model is employed to simulate the CCQD system consisted of finite number of quantum dots (QDs). The charge and heat currents are calculated in the framework of Keldysh Green's function technique. The authors obtained a closed-form Landauer expression for the transmission coefficient of the CCQD system with arbitrary number of QDs by using the method beyond mean-field theory. The electrical conductance (Ge), Seebeck coefficient (S), thermal conductance, and figure of merit (ZT) are numerically calculated and analyzed in the linear response regime. In the Coulomb blockade regime thermal conductance is dominated by phonons, the optimization of ZT is determined by the power factor (PF=S2Ge). The authors find that the optimization of ZT value favors the conditions of QD energy levels above the Fermi level of electrodes and QDs with small energy level fluctuations. The optimal ZT values are seriously suppressed by the inelastic scattering of electrons.

Tunneling Current Spectra of a Metal Core/Semiconductor Shell Quantum Dot Molecule

The transport properties of a metal core/semiconductor shell quantum dot molecule (QDM) embedded in a matrix connected to metallic electrodes are theoretically studied in the framework of Keldysh Green function technique. The effects of the electron plasmon interactions (EPIs) on the tunneling current spectra of QDM are examined. The energy levels of the QDs, intradot and interdot Coulomb interactions, electron interdot hopping strengths, and tunneling rates of QDs are renormalized by the EPIs. The differential conductance spectra show peaks arising from the plasmon assisted tunneling process, intradot and interdot Coulomb interactions, and coherent tunneling between the QDs.

Effects of interdot hopping and Coulomb blockade on the thermoelectric properties of serially coupled quantum dots

We have theoretically studied the thermoelectric properties of serially coupled quantum dots (SCQDs) embedded in an insulator connected to metallic electrodes. In the framework of Keldysh Green’s function technique, the Landauer formula of transmission factor is obtained using the equation of motion method. Based on such analytical expressions of charge and heat currents, we calculate the electrical conductance, Seebeck coefficient, electron thermal conductance, and figure of merit (ZT) of SCQDs in the linear response regime. The effects of interdot hopping and electron Coulomb interactions on ZT are analyzed. We demonstrate that ZT is not a monotonic increasing function of interdot electron hopping strength (tc). We also show that in the absence of phonon thermal conductance, SCQD can reach the Carnot efficiency as tcapproaches zero.

Spin polarization in a double-quantum dot interferometer with Rashba spin–orbit interaction

We propose a spin device consisting of three normal metal leads and double quantum dots (QDs) with Rashba spin–orbit (RSO) interaction. On the basis of the nonequilibrium Keldysh Green's function technique, the spin-polarized currents flowing in different leads and spin accumulations in QDs are investigated. It is shown that the spin-polarized currents with opposite direction can be extracted into the left and right leads, respectively, due to the quantum interference between different channels. Moreover, the magnitude and direction of polarization can be modulated electrically by shifting the dots’ levels and tuning the strength of the RSO interaction. The spin-polarized currents exhibit a 2π-periodic function with respect to φR. In addition, the direction of the spin accumulation in two dots is exactly opposite and its magnitude and direction can be easily controlled by tuning the levels.

Fano effect of a parallel-coupled triple Rashba quantum dot system

Using the nonequilibrium Keldysh Green's function technique, the Fano effect of a parallel-coupled triple Rashba quantum dot system is investigated. The conductance as a function of electron energy is numerically calculated. Compared with the case of a parallel-coupled double quantum dot system, two additional Fano resonance peaks occur in the conductance spectrum. By adjusting the structural parameters, the two Fano resonance peaks may change into the resonance peaks. In addition, the influence of Rashba spin-orbit interaction on the conductance is studied.