Tunable supercurrent through a double Aharonov–Bohm interferometer

The supercurrent through a double Aharonov–Bohm interferometer formed by parallel-coupled four quantum dots is investigated theoretically. The possibility of controlling the supercurrent of the system is explored by tuning the interdot coupling, dot energy levels, and magnetic flux treading the ring connecting dots and leads. Whether the supercurrent sign can be changed depends not only on the magnetic flux but also on the quantum dot energy levels. By tuning the quantum dot energy levels, the behavior of the supercurrent shows swap effects, which might be used to design a qubit. It is also found that the oscillation period of the supercurrent with respect to the magnetic flux depends on the ratio of the two parts fluxes.     

Nonlocal Andreev reflection in a three-terminal Aharonov-Bohm interferometer

We theoretically report a nonlocal Andreev reflection in an Aharonov-Bohm interferometer, which is a three-terminal normal metal/superconductor (NS) mesoscopic hybrid system. It is found that this nonlocal Andreev reflection is sensitive to the systematic parameters, such as the bias voltages, the quantum dot levels, and the external magnetic flux. If we set the chemical potential of one normal metal lead equal to zero, the electronic current in the lead results from two competing processes: the quasiparticle transmission and nonlocal Andreev reflection. The appearance of zero electronic current signals unambiguously the existence of this nonlocal Andreev reflection.     

AC field-controlled Andreev tunneling through a serially-coupled double quantum dot system

AC field-controlled Andreev tunneling through two serially-coupled quantum dots are investigated theoretically by using the nonequilibrium Green's function method. The photon-assisted Andreev tunneling is studied in detail. It is found that the average current depends distinctly on the interdot coupling. In the weak interdot coupling case, the average current versus the gate voltage exhibit negative peaks on the left-hand side and positive peaks on the right-hand side of the Fermi level. However, in the strong interdot coupling case, the current exhibit both negative and positive peaks on each side of the Fermi level. Furthermore, the system can function as an electron pump capable of transporting electrons through the resonant photon-assisted Andreev tunneling.     

Reprint of : Single-electron coherence: Finite temperature versus pure dephasing

We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in the presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electron states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electron states to the case of mixed states and clarifies the difference between different types of mixedness.     

Dynamical behavior of electron transport in AlGaAs/GaAs double-barrier structures under a high-frequency radiation field

We investigate the time-dependent dynamical behavior of electron transport in AlGaAs/GaAs double-barrier structures under a high-frequency radiation field. The effects of the radiation field with different amplitude and frequency on the real-time and mean current-voltage curves are taken into account. We find that the amplitude and frequency of the radiation field affect the final stable state current-voltage (I-V) behaviors, which leads to the switching between different current states at a smaller bias than that of the absence of the radiation field, and both current hysteresis and resonant peaks are suppressed by the external radiation field. The high radiation field strength can make the resonant peak of current split and the hysteresis of current disappear. This effect provides the potential to use double-barrier structure as a THz photoelectric switch.     

Tunable supercurrent in a parallel double quantum dot system

The supercurrent through an Aharonov-Bohm interferometer containing two parallel quantum dots connected with two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent is explored by tuning the quantum dot energy levels and the total magnetic flux. By tuning the energy levels, both quantum dots can be in the on-resonance or off-resonance states, and thus the optimal modulation of the supercurrent can be achieved. The supercurrent sign does not change by simply varying the quantum dot energy levels. However, by tuning the magnetic flux, the supercurrent can oscillate from positive to negative, which results in the π-junction transition.     

Interband quantum kinetics with static disorder scattering I: Direct CPA solution for a rectangular-pulse-excited semiconductor

For a two band model semiconductor alloy with the disorder potential concentrated to the conduction band, the photoexcitation by a long rectangular pulse represents a case soluble in the coherent potential approximation. Explicit analytic expressions for the transient electron distribution are derived using the nonequilibrium Green functions. The evanescent coherent component is gradually superseded by the incoherent distribution whose saturation value is obtained using the Ward identity.     

Thermal Rectification Effect of an Interacting Quantum Dot

We investigate the nonlinear thermal transport properties of a single interacting quantum dot with two energy levels tunnel-coupled to two electrodes using nonequilibrium Green function method and Hartree-Fock decoupling approximation. In the case of asymmetric tunnel-couplings to two electrodes, for example, when the upper level of the quantum dot is open for transport, whereas the lower level is blocked, our calculations predict a strong asymmetry for the heat （energy） current, which shows that the quantum dot system may act as a thermal rectifier in this specific situation.     

Entanglement degree of electron pairs out of Andreev reflection

We study the entanglement degree of electron pairs emitted from an s-wave superconductor, which couples to two normal leads via a single-level quantum dot. Within the framework of scattering matrix theory, the concurrence is used to quantify the entanglement. And the result shows that the entanglement degree is generally influenced by the initial separation of the two electrons in a Cooper pair and the normal transmission eigenvalues T₁, T₂. But it is only determined by the eigenvalues in the tunnelling limit, T₁,T₂?1, what is more, it is measurable.     

Cooper-Pair Number-Phase Quantization for a Mesoscopic LC Circuit Including a Josephson Junction

By introducing the entangled state representation and Feynman assumption that ＇electron pairs are bosons, ..., a bound pair acts as a Bose particle ＇, we construct an operator Hamiltonian for a mesoscopic inductance-capacitance （LC） circuit including a Josephson junction, then we use the Heisenberg equation of motion to derive the current equation and the voltage equation across the inductance as well as across the Josephson junction. The result manifestly shows how the junction voltage is affected by the capacitance coupling. In this way the Cooper-pair number-phase quantization for this system is completed.     

Hot electron relaxation in one-dimensional models: exact polaron dynamics versus relaxation in the presence of a Fermi sea

We present the exact solution for the time evolution of the electron and phonon momentum distribution for a one-dimensional polaron model with alinear electronic energy dispersion. The electron momentum distribution is shown to obey aMarkovian quantum kinetic equation. Numerical results for the polaron model are compared to the corresponding exact results, when the negative momentum states are filled in the initial state. The presence of this Fermi sea modifies the dynamics except in the short time regime. The different, long time dynamics might show up in comparison of hot electron relaxation of undoped and doped semiconductors.     

Dephasing of Andreev pairs entering a charge density wave

A Cooper pair from a s-wave superconductor (S) entering a conventional charge density wave (CDW) below the Peierls gap dephases on the Fermi wavelength while one particle states are localized on the CDW coherence length ξ_CDW. It is thus practically impossible to observe a Josephson current through a CDW. The paths following different sequences of impurities interfere destructively, due to the different electron and hole densities in the CDW. The same conclusion holds for averaging over the conduction channels in the ballistic system. We apply two microscopic approaches to this phenomenon: (i) a Blonder, Tinkham, Klapwijk (BTK) approach for a single highly transparent S-CDW interface; and (ii) the Hamiltonian approach for the Josephson effect in a clean CDW and a CDW with non magnetic disorder. The Josephson effect through a spin density wave (SDW) is limited by the coherence length ξ_SDW, not by the Fermi wave-length. A Josephson current through a SDW might be observed in a structure with contacts on a SDW separated by a distance ξ_SDW.     

Modified Josephson Equation for Mesoscopic Parallel LC Circuit Including a Josephson Junction

By introducing the entangled state representation, parallel LC circuit including a 3osephson junction equation associated with the modification of the motion equation. the Cooper-pair number-phase quantization of the mesoscopic is realized. In the Heisenberg picture, the modified Josephson Faraday equation about the inductance is deduced from the     

Electron transport in a double quantum ring: Evidence of an AND gate

We explore AND gate response in a double quantum ring where each ring is threaded by a magnetic flux ?. The double quantum ring is attached symmetrically to two semi-infinite one-dimensional metallic electrodes and two gate voltages, namely, Va and Vb, are applied, respectively, in the lower arms of the two rings which are treated as two inputs of the AND gate. The system is described in the tight-binding framework and the calculations are done using the Green's function formalism. Here we numerically compute the conductance-energy and current-voltage characteristics as functions of the ring-to-electrode coupling strengths, magnetic flux and gate voltages. Our study suggests that, for a typical value of the magnetic flux ?=?₀/2 (?₀=ch/e, the elementary flux-quantum) a high output current (1) (in the logical sense) appears only if both the two inputs to the gate are high (1), while if neither or only one input to the gate is high (1), a low output current (0) results. It clearly demonstrates the AND gate behavior and this aspect may be utilized in designing an electronic logic gate.     

Single-electron coherence: Finite temperature versus pure dephasing

We analyze a coherent injection of single electrons on top of the Fermi sea in two situations, at finite-temperature and in the presence of pure dephasing. Both finite-temperature and pure dephasing change the property of the injected quantum states from pure to mixed. However, we show that the temperature-induced mixedness does not alter the coherence properties of these single-electron states. In particular two such mixed states exhibit perfect antibunching while colliding at an electronic wave splitter. This is in striking difference with the dephasing-induced mixedness which suppresses antibunching. On the contrary, a single-particle shot noise is suppressed at finite temperatures but is not affected by pure dephasing. This work therefore extends the investigation of the coherence properties of single-electron states to the case of mixed states and clarifies the difference between different types of mixedness.     

Tuning of electron transport through a moebius strip: Shot noise

We study electron transport through a moebius strip attached to two metallic electrodes by the use of a Green’s function technique. A parametric approach is used based on the tight-binding model to characterize the electron transport through such a bridge system and it is observed that the transport properties are significantly affected by (a) the transverse hopping strength between the two channels and (b) the strip-to-electrodes coupling strength. In this context we also describe the noise power of the current fluctuations, which provide key information about the electron correlation which is obtained by calculating the Fano factor (F). The knowledge of these current fluctuations gives important ideas for the fabrication of efficient molecular devices.     

Photon-assisted shot noise due to the charging effect in a quantum dot device

We have investigated the spectral density of shot noise for an ultra-small quantum dot(QD) system in the Coulomb blockade regime when irradiated with microwave fields (MWFs) by employing a nonequilibrium Green’s function technique. The shot noise is sensitive to Coulomb interaction, and the photon-assisted Coulomb blockade behaviour strongly modifies the mesoscopic transport. We have calculated the first and second derivatives of shot noise in the strong and weak coupling regimes to compare the theoretical results with existing experimental results. In the strong coupling regime, the first and second derivatives of shot noise display Fano type peak-valley structures around the charging channel 2E _c due to Coulomb interaction. When the magnitudes of the MWFs are sufficiently large, the system displays channel blockade due to photon irradiation. The photon-assisted and Coulomb blockade steps in the noise — as well as the resonant behaviour in the differential noise — are smeared by increasing temperature. The Coulomb interaction suppresses the shot noise, but the ac fields can either suppress the shot noise(balanced case) or enhance the shot noise(unbalanced case). The suppression of shot noise caused by ac fields in the balanced case is greater than that caused by Coulomb interaction in our system. Super-Poissonian shot noise may be induced due to the compound effects of strong Coulomb interaction and photon absorption-emission processes.     

Optimal block-tridiagonalization of matrices for coherent charge transport

Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms require the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrarily complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green’s function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.     

Multi-photon behaviors of shot noise in a quantum dot system under the perturbation of two microwave fields

We have investigated the shot noise affected by the perturbation of two microwave fields (MWFs) with frequencies ω₁ and ω₂, which can be classified as the commensurate and incommensurate external ac fields. The time-dependent current correlation function and the spectral density of shot noise have been obtained. They are very different compared with the single-field applied system in the nonlinear regime of the ac potentials. The different photon absorption and emission processes induce different kinds of noise spectral density. We have performed the numerical calculations for both commensurate balanced and unbalanced photon absorptions and emissions. The multi-photon procedure can be seen clearly from the resonance of shot noise. Different commensurate number q = ω₂/ω₁ contributes to different photon absorption and emission behaviors. It is found that the asymmetric configuration of shot noise is intimately associated with the commensurate number q. The differential conductance appears symmetric and asymmetric behaviors, and the channel blockade exhibits. The shot noise is large enough to surpass its saturated value for the unbalanced photon absorption case. The sensitive behaviors of Fano factor associated with different commensurate numbers and amplitudes of ac fields signify that the shot noise can be controlled by external MWFs significantly.