Keldysh Green Function Research Articles

Characteristics of heat generation in a quantum dot

On the basis of the nonequilibrium Keldysh Green's function technique, we study the current-induced heat generation $Q$ in a quantum dot (QD) taking both a bias voltage and a rotating magnetic field into consideration. It is found that under the conditions of small bias voltage, weak dot-lead coupling strength, and low temperature, the generated heat $Q$ is mainly decided by the probability of each electron to scatter off a phonon and shows quantum properties. As a result of this, many interesting phenomena absent in macroscopic devices appear. For example, when the bias voltage energy is slightly larger than one phonon energy but is less than that of two phonons, two peaks appear in the curve of $Q$ versus the QD level, even though only one current peak exists. In particular, the valley between the two peaks in $Q$ is the very site where the single current peak is placed, an ideal condition for device operation. However, if the above conditions are not satisfied, $Q$ behaves as in macroscopic systems, approximately proportionally to the electron current.

Spin Transport in a Rashba Ring-Quantum Dot System Pumped by Microwave Fields

We report a theoretical study on producing electrically spin-polarized current in the Rashba ring with parallel double dots embedded, which are subject to two time-dependent microwave fields. By means of the Keldysh Green's function method, we present an analytic result of the pumped current at adiabatic limit and demonstrate that the interplay between the quantum pumping effect and spin-dependent quantum interference can lead to an arbitrarily controllable spin-polarized current in the device. The magnitude and direction of the charge and spin current can be effectively modulated by system parameters such as the pumping phase difference, Rashba precession phase, and the dynamic phase difference of electron traveling in two arms of ring; moreover, the spin-polarization degree of the charge current can also be tuned in the range [−∞, +∞]. Our findings may shed light on the all-electric way to produce the controllable spin-polarized charge current in the field of spintronics.

Are “Pinholes” the Cause of Excess Current in Superconducting Tunnel Junctions? A Study of Andreev Current in Highly Resistive Junctions

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and is often attributed to microscopic pinholes in the tunnel barrier. We have studied the subgap current in superconductor-insulator-superconductor (SIS) and superconductor-insulator-normal-metal (SIN) junctions. In Al/AlO(x)/Al junctions, we observed a decrease of 2 orders of magnitude in the current upon the transition from the SIS to the SIN regime, where it then matched theory. In Al/AlO(x)/Cu junctions, we also observed generic features of coherent diffusive Andreev transport in a junction with a homogenous barrier. We use the quasiclassical Keldysh-Green function theory to quantify single- and two-particle tunneling and find good agreement with experiment over 2 orders of magnitude in transparency. We argue that our observations rule out pinholes as the origin of the excess current.

Thermoelectric Properties of Double Quantum Dots Embedded in a Nanowire

We theoretically investigate the thermoelectric properties of a serial double quantum dot junction system. A two-level Anderson model including electron hoppings and intradot Coulomb interactions as well as interdot Coulomb interactions is employed to simulate the system. The charge and heat currents in the Coulomb blockade regime are calculated by Keldysh Green's function technique. The electrical conductance, Seebeck coefficient, electronic thermal conductance, and figure of merit (ZT) of the system are calculated in the linear response regime. We find that the figure of merit ZT is markedly reduced by the size fluctuation and Coulomb interactions.

LINEAR CONDUCTANCE AND TUNNEL MAGNETORESISTANCE IN A RASHBA QUANTUM DOT RING COUPLED TO FERROMAGNETIC LEADS

Spin-dependent electronic transport through a quantum ring with a quantum dot (QD) inserted in one of its arms is investigated within the Keldysh Green's function theory. We consider that the ring is connected to external ferromagnetic electrodes and there is Rashba spin-orbit interaction (SOI) in the QD. It is found that the anomalous tunnel magnetoresistance (TMR) peak originated from the electron correlations is split into two by the direct coupling between the two leads, with the two normal Coulomb resonances unchanged. The peak position and the magnitude of the conductance and the TMR can be controlled in terms of the SOI-induced phase factor, which can be adjusted by the gate voltage or the structure parameters. The present device should be realizable within present technology and may have practical usage in spintronics.

Nonequilibrium transport in molecular junctions with strong electron-phonon interactions

We present a combined theoretical approach to study the nonequilibrium transport properties of nanoscale systems coupled to metallic electrodes and exhibiting strong electron-phonon interactions. We use the Keldysh Green function formalism to generalize beyond linear theory in the applied voltage an equation of motion method and an interpolative self-energy approximation previously developed in equilibrium. We analyze the specific characteristics of inelastic transport appearing in the intensity versus voltage curves and in the conductance, providing qualitative criteria for the sign of the step-like features in the conductance. Excellent overall agreement between both approaches is found for a wide range of parameters.

Current noise in molecular junctions: Effects of the electron-phonon interaction

We study inelastic effects on the electronic current noise in molecular junctions, due to the coupling between transport electrons and vibrational degrees of freedom. Using a full counting statistics approach based on the generalized Keldysh Green's function technique, we calculate in an unified manner both the mean current and the zero-frequency current noise. For multilevel junctions with weak electron-phonon coupling, we give analytical formulas for the lowest order inelastic corrections to the noise in terms of universal temperature- and voltage-dependent functions and junction-dependent prefactors, which can be evaluated microscopically, e.g. with ab-initio methodologies. We identify distinct terms corresponding to the mean-field contribution to noise and to the vertex corrections, and we show that the latter contribute substantially to the inelastic noise. Finally, we illustrate our results by a simple model of two electronic levels which are mutually coupled by the electron-phonon interaction and show that the inelastic noise spectroscopy is a sensitive diagnostic tool.

Thermal Rectification Effects of Multiple Semiconductor Quantum Dot Junctions

On the basis of the multiple-energy-level Anderson model, we theoretically study the thermoelectric effects of semiconductor quantum dots (QDs) in the nonlinear response regime. The charge and heat currents in the sequential tunneling process are calculated by Keldysh Green's function technique. The thermal rectification effect can be observed for such a multiple QD junction system, whereas the rectification efficiency is significantly affected by the tunneling rate, size fluctuation, and location distribution of QDs. We also find that the charge current rectification with respect to temperature bias can be observed.

Thermoelectric Effects of Multiple Quantum Dot Junctions in the Nonlinear Response Regime

The thermoelectric effects of semiconductor quantum dots (QDs) embedded into an insulator matrix connected to metallic electrodes are theoretically investigated in the nonlinear response regime. A multilevel Anderson model is used to simulate the multiple QDs junction system. The charge and heat currents in the sequential tunneling process are calculated by the Keldysh Green's function technique. We have demonstrated that thermal rectification and negative differential thermal conductance behaviors can be observed for the multiple QD junction system in the absence of phonon heat current.

Long-range magnetic response of theXYspin chain under far-from-equilibrium conditions

Within the formalism of the Keldysh Green's functions we investigate long-range response of an anisotropic $XY$ chain to the local magnetic field. This field couples to a single spin on a selected lattice site. The system is driven out of equilibrium by a coupling to two semi-infinite $XX$ spin chains. We demonstrate that the long-range response becomes enhanced by a few orders of magnitude upon application of nonequilibrium conditions. This enhancement does not occur in the isotropic $XX$ chain. Our results agree with the recently predicted nonequilibrium-driven long-range magnetic correlations [T. Prosen and I. Pi\ifmmode \check{z}\else \v{z}\fi{}orn, Phys. Rev. Lett. 101, 105701 (2008)]. We argue that this effect may be observed in quasi-one-dimensional triplet superconductors.

Thermoelectric and thermal rectification properties of quantum dot junctions

The electrical conductance, thermal conductance, thermal power and figure of merit (ZT) of semiconductor quantum dots (QDs) embedded into an insulator matrix connected with metallic electrodes are theoretically investigated in the Coulomb blockade regime. The multilevel Anderson model is used to simulate the multiple QDs junction system. The charge and heat currents in the sequential tunneling process are calculated by the Keldysh Green function technique. In the linear response regime the ZT values are still very impressive in the small tunneling rates case, although the effect of electron Coulomb interaction on ZT is significant. In the nonlinear response regime, we have demonstrated that the thermal rectification behavior can be observed for the coupled QDs system, where the very strong asymmetrical coupling between the dots and electrodes, large energy level separation between dots and strong interdot Coulomb interactions are required.

Spin–orbit based coherent spin ratchets

The concept of ratchets, driven asymmetric periodic structures giving rise to directed particle flow, has recently been generalized to a quantum ratchet mechanism for spin currents mediated through spin–orbit interaction. Here we consider such systems in the coherent mesoscopic regime and generalize the proposal of a minimal spin ratchet model based on a non-interacting clean quantum wire with two transverse channels by including disorder and by self-consistently treating the charge redistribution in the nonlinear (adiabatic) ac-driving regime. Our Keldysh–Green function based quantum transport simulations show that the spin ratchet mechanism is robust and prevails for disordered, though non-diffusive, mesoscopic structures. Extending the two-channel to the multi-channel case does not increase the net ratchet spin current efficiency but, remarkably, yields a dc spin transmission increasing linearly with channel number.

Time-dependent quantum transport with superconducting leads

We present results on the microscopic dynamics of electrons in nanoscale systems coupled to superconducting leads. By solving the time-dependent Bogoliubov-deGennes equations for the Nambu-Gorkov Keldysh Green's function we are able to calculate the current and the charge density when the system is perturbed by bias voltages. For scattering of electrons across a normal-superconducting surface we provide a time-dependent picture of the Andreev reflections. When the nanoscale system is contacted to two DC biased superconducting leads the amplitude of the current oscillations at even multiple of the bias can be extracted by Fourier transforming the time-dependent results. In the transient regime the dwelling time is inversely proportional to the bias in agreement with the occurrence of multiple Andreev reflections.

ALL-ELECTRICAL SPIN CONTROL IN A TRIPLE-TERMINAL QUANTUM DOTS RING: EFFECT OF THE INTERDOT COUPLING AND SPIN FLIP

The electron spin polarization in two quantum dots, which are inserted in one arm of a mesoscopic ring, is investigated by means of the non-equilibrium Keldysh Green's function technique. We find that the spin accumulations in the two dots Δni=ni↑-ni↓, where niσ is the spin-σ electron occupation number in dot i, can be efficiently tuned in terms of the applied bias voltage V, the interdot tunneling coupling strength tc and the phase induced by the Rashba spin-orbit interaction. By adjusting these parameters, Δn1 and Δn2 can be generated and manipulated either simultaneously or separately, which may have real usage in spintronics or quantum information devices. We interpret the origin of the spin accumulation in terms of the spin-dependent total effective coupling strengths between the leads and the dots.

Inverse Spin Hall Effect in Two-Terminal Device with Rashba Spin-Orbit Coupling

We report a theoretic study on the inverse spin-Hall effect (ISHE) in a two-terminal nano-device that consists of a two-dimensional electron gas (2DEG) with Rashba spin-orbit coupling (RSOC) and two ideal leads. Based on a two-site toy model and Keldysh Green's function method, we derive an analytic result of ISHE, which shows clearly that a nonzero transverse charge current stems from the combined effect of the RSOC, the spin bias, and its spin polarization direction in spin space. Our further numerical calculations in a larger system other than two-site lattice model demonstrate that the transverse charge current, dependent on the strength of the RSOC, the Fermi energy of the system, as well as the system size, can exhibit oscillating behavior and even reverse its sign due to Rashba spin precession. These properties may be helpful for efficient detection of the spin current (spin bias) by measuring the transverse charge current in a spin-orbital coupling system.

Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions

We investigate the transport properties of a one-dimensional superconductor-normal metal-superconductor (S-N-S) system described within the tight-binding approximation. We compute the equilibrium dc Josephson current and the time-dependent oscillating current generated after the switch-on of a constant bias. In the first case an exact embedding procedure to calculate the Nambu-Gorkov Keldysh Green's function is employed and used to derive the continuum and bound states contributions to the dc current. A general formalism to obtain the Andreev bound states (ABS) of a normal chain connected to superconducting leads is also presented. We identify a regime in which all Josephson current is carried by the ABS and obtain an analytic formula for the current-phase relation in the limit of long chains. In the latter case the condition for perfect Andreev reflections is expressed in terms of the microscopic parameters of the model, showing a limitation of the so called wide-band-limit (WBL) approximation. When a finite bias is applied to the S-N-S junction we compute the exact time-evolution of the system by solving numerically the time-dependent Bogoliubov-deGennes equations. We provide a microscopic description of the electron dynamics not only inside the normal region but also in the superconductors, thus gaining more information with respect to WBL-based approaches. Our scheme allows us to study the ac regime as well as the transient dynamics whose characteristic time-scale is dictated by the velocity of multiple Andreev reflections.

Relativistic many-body XMCD theory including core degenerate effects

A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2.In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.

RPA APPROACH TO NON-LINEAR TRANSPORT IN QUANTUM DOTS

An accurate theoretical treatment of electron-electron interactions in mesoscopic systems is available in very few cases and approximation schemes are developed in most of the applications, especially for many-level quantum dots. Here we present transport calculations within the random-phase approximation for the Coulomb interaction using the Keldysh Green's functions formalism. We describe the quantum dot systems by a tight-binding Hamiltonian. Our method is similar to the one used by Faleev and Stockman [Phys. Rev. B 66 085318 (2002)] in their study of the equilibrium properties of a homogeneous 2D electron gas. The important extension at the formal level is that we combine the RPA and the Keldysh formalism for studying non-linear transport properties of open quantum dots. Within the Keldysh formalism the polarization operator becomes a contour-ordered quantity that should be computed either from the non-interacting Green functions of the coupled quantum dot (the so-called G0W approximation) either self-consistently (GW approximation). We performed both non-selfconsistent and self-consistent calculations and compare the results. In particular we recover the Coulomb diamonds for interacting quantum dots and we discuss the charge sensing effects in parallel quantum dots.

Scanning gate microscopy of quantum rings: effects of an external magnetic field and ofcharged defects

We study scanning gate microscopy (SGM) in open quantum rings obtained from buriedsemiconductor InGaAs/InAlAs heterostructures. By performing a theoretical analysisbased on the Keldysh–Green function approach we interpret the radial fringes observed inexperiments as the effect of randomly distributed charged defects. We associate SGMconductance images with the local density of states (LDOS) of the system. We show thatsuch an association cannot be made with the current density distribution. By varying anexternal magnetic field we are able to reproduce recursive quasi-classical orbits in LDOSand conductance images, which bear the same periodicity as the Aharonov–Bohmeffect.

Electric-current-induced heat generation in a strongly interacting quantum dot in the Coulomb blockade regime

The heat generation by an electric current flowing through a quantum dot with the dot containing both electron-electron interaction and electron-phonon interaction, is studied. Using the non-equilibrium Keldysh Green's function method, the current-induced heat generation is obtained. We find that for a small phonon frequency, heat generation is proportional to the current. However, for a large phonon frequency, heat generation is in general qualitatively different from the current. It is non-monotonic with current and many unique and interesting behaviors emerge. The heat generation could be very large in the Coulomb blockade region, in which the current is very small due to the Coulomb blockade effect. On the other hand, in the resonant tunneling region, the heat generation is very small despite a large current, an ideal condition for device operation. In the curve of heat generation versus the bias, a negative differential of the heat generation is exhibited, although the current is always monotonously increasing with the bias voltage.