Electron transport in carbon nanotube quantum dots in an axial magnetic field

The quantum conductance of the quantum dots (QDs) made of two kinds of primary carbon nanotubes (CNTs), i.e., armchair and zigzag CNTs, threaded by an axial magnetic field, has been studied by using the tight binding approximation and constant interaction model. It is found that under increasing axial magnetic field, each conductance shell of the zigzag CNT-QDs could split into two groups with each group of two peaks moving up or down, respectively. And the up- and down-moving two peaks would re-group with other two peaks, down- and up-moving, in the neighboring shell, forming a new four-peak shell, and then re-splitting, re-grouping again due to the Aharonov-Bohm effect, which is in agreement with those of experiments. But, in contrast, the conductance shells of the armchair CNT-QDs do not split by the magnetic field. Our subsequent theoretical studies show further that the above phenomena, i.e., the conductance shell-splitting, re-grouping, and re-splitting again with increasing the magnetic field exist in all the CNT-QDs except for the armchair one.     

Voltage-controllable spin-polarized transport through parallel-coupled double quantum dots with Rashba spin-orbit interaction

A spin device, consisting of parallel-coupled double quantum dots and three normal metal leads, is proposed to realize spin-polarized current without the help of magnetic field and magnetic material. Based on the Keldysh nonequilibrium Green function technique and equation of motion method, the spin-dependent current formula in each lead is derived. It is shown that not only a fully polarized current but also a tunable pure spin current can be obtained by modulating the structure parameters, strength of Rashba spin-orbit interaction and bias voltages properly. It further demonstrates the dependence of the spin-polarized current on the strength of the Rashba spin-orbit interaction.     

Antiresonance of electron tunneling through a four-quantum-dot ring with two side-coupled quantum dots

Making use of the equation of motion method and Keldysh Green function technique, we obtain the current formula for a two-terminal four-quantum-dot-ring with two side-coupled quantum dots under a DC bias voltage. Antiresonance and resonance of electron tunneling is studied by numerical calculations. Only when the quantum dots in the ring has the same single electron energy level with that of the side-coupled quantum dots, i.e. and both side-coupling are turned on at the same time, the antiresonance appear exactly at ε₀.     

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.     

Spin-polarized current through a lateral double quantum dot with spin–orbit interaction

We study the spin-polarized current through a vertical double quantum dot scheme. Both the Rashba spin–orbit (RSO) interaction inside one of the quantum dots and the strong intradot Coulomb interactions on the two dots are taken into account by using the second-quantized form of the Hamiltonian. Due to the existence of the RSO interaction, spin-up and spin-down electrons couple to the external leads with different strengths, and then a spin polarized current can be driven out of the middle lead by controlling a set of structure parameters and the external bias voltage. Moreover, by properly adjusting the dot levels and the external bias voltages, a pure spin current with no accompanying charge current can be generated in the weak coupling regime. We show that the difference between the intradot Coulomb interactions strongly influences the spin-polarized currents flowing through the middle lead and is undesirable in the generation of the net spin current. Based on the RSO interaction, the structure we propose can efficiently polarize the electron spin without the usage of any magnetic field or ferromagnetic material. This device can be used as a spin-battery and is realizable using the present available technologies.     

ac field-induced Fano resonances in a parallel-coupled double quantum dot system

The effects of an ac electric field on the Fano resonance in a parallel-coupled double quantum dot system are investigated theoretically. The field can induce the photon-assisted Fano resonances for both symmetrical and asymmetrical parallel configurations. The magnitude and position of the photon-assisted Fano peak can be tuned by the ac field strength and frequency, respectively. Furthermore, the Fano resonance can appear with increasing the field frequency for both the symmetrical and asymmetrical configurations. This provides an efficient mechanism to control the Fano resonance. The photon-electron pumping effects for the symmetrical and asymmetrical cases are also studied in the weak- and strong-coupling regime.     

Contact conductance between graphene and quantum wires

The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.     

First-principles electronic transport properties study of small carbon clusters: Cyclic C6

The transport properties of the six-atom carbon ring cluster C₆ sandwiched between Al(100) electrodes have been investigated by first-principles nonequilibrium Green's function technique. Our results demonstrate that the transport properties of monocyclic C₆ with D3h symmetry, with alternating bond angles, the most stable C₆ isomer, show metallic conductance. The charge transfer between the central molecule and the electrodes is very important for its transport properties. We also compare the equilibrium transmission spectra for C₆ in different isomers.     

Equilibrium spin current induced by spin-orbital interaction in a quantum dot system

We report a theoretical study of the equilibrium spin current flowing in a quantum dot system. Two electrodes are the two-dimensional electron gas with Rashba or Dresselhaus spin-orbital interaction. By using the Keldysh Green's function technique, we demonstrated that a nonzero spin current can flow in the system without bias. At the weak coupling between electrodes and the quantum dot, the spin current is approximately proportional to the cross product of two average pseudo-magnetizations in two electrodes, which agrees with the result of the linear response theory; whereas at the opposite case, the strong coupling between the quantum dot and electrodes can lead to a non-sinusoidal behavior of the equilibrium spin current. These behaviors of the equilibrium spin current are similar to the Josephson current.     

Discrete-charge quantum circuits and electrical resistance

From the theory of quantum LC circuits with discrete charge, and semiclassical considerations, we obtain approximate energy eigenvalues, depending on the parameter . Next, we include electrical resistance for the quantum RLC circuit, obtaining a relation that strongly reminds us of the Landauer formula.     

Transport properties of a double quantum dot molecule in the presence of impurity effects

In this Letter, we studied the electronic transport through a parallel-coupled double quantum dot (DQD) molecule including impurity effects at zero temperature. The linear conductance can be calculated by using the Green's function method. An obvious Fano resonance arising from the impurity state in the quantum dot is observed for the symmetric dot-lead coupling structure in the absence of the magnetic flux through the quantum device. When the magnetic flux is presented, two groups of conductance peaks appear in the linear conductance spectra. Each group is decomposed into one Breit-Wigner and one Fano resonances. Tuning the system parameters, we can control effectively the shapes of these conductance peaks. The Aharonov-Bohm (AB) oscillation for the magnetic flux is also studied. The oscillation period of the linear conductance with π, 2π or 4π may be observed by tuning the interdot tunneling coupling or the dot-impurity coupling strengths.     

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.     

Persistent current and transmission probability in the Aharonov-Bohm ring with an embedded quantum dot

Persistent current and transmission probability in the Aharonov-Bohm (AB) ring with an embedded quantum dot (QD) are studied using the technique of the scattering matrix. For the first time, we find that the persistent current can arise in the absence of magnetic flux in the ring with an embedded QD. The persistent current and the transmission probability are sensitive to the lead-ring coupling and the short-range potential barrier. It is shown that increasing the lead-ring coupling or the short-range potential barrier causes the suppression of the persistent current and the increasing resonance width of the transmission probability. The effect of the potential barrier on the number of the transmission peaks is also investigated. The dependence of the persistent current and the transmission probability on the magnetic flux exhibits a periodic property with period of the flux quantum.     

Electron interactions in an antidot in the integer quantum Hall regime

A quantum antidot, a submicron depletion region in a two-dimensional electron system, has been actively studied in the past two decades, providing a powerful tool for understanding quantum Hall systems. In a perpendicular magnetic field, electrons form bound states around the antidot. Aharonov–Bohm resonances through such bound states have been experimentally studied, showing interesting phenomena such as Coulomb charging, h/2e$h/2e$ oscillations, spectator modes, signatures of electron interactions in the line shape, Kondo effect, etc. None of them can be explained by a simple noninteracting electron approach. Theoretical models for the above observations have been developed recently, such as a capacitive-interaction model for explaining the h/2e$h/2e$ oscillations and the Kondo effect, numerical prediction of a hole maximum-density-droplet antidot ground state, and spin-density-functional theory for investigating the compressibility of antidot edges. In this review, we summarize such experimental and theoretical works on electron interactions in antidots.     

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.     

Conductance quantization of an ideal Sharvin contact

Thorough calculations of the conductance of an idealized quantum point contact are presented. The point contact is modelled as a configuration in which two conductive half-spaces are separated by a non-conductive planar screen with a circular window of a given radius a. The screen is considered as opaque for the electrons with the exception of the window. From the viewpoint of the electrical conduction, the half-spaces are interpreted as leads which are perfectly coalesced with one another across the window. We assume that the leads are reservoirs of a strongly degenerate gas of electrons. If the leads are made from an n-type degenerate semiconductor, the Fermi wavelength λ_F = 2π/k_F = 2π/(3π²n)^1/3 may be tens of nanometers. The theory of the conductance Γ_S of such a point contact is reconsidered. Within the framework of the approximation that we use assuming that T = 0, we show that the dependence of Γ_S on the variable k_Fa manifests curved steps terminated by singular spikes. Owing to stochastic influences, the spikes should be seen as maxima in measured spectra. We predict that these maxima should demarcate the edges of the steps in the Γ_S vs. k_Fa plot. This prediction is in agreement with the STM observations reported recently by Nagaoka et al. [K. Nagaoka, S. Yaginuma, T. Nagao, T. Nakayama, Phys. Rev. B. 74 (2006) 033310].     

Fano effect in a T-shaped double quantum dot structure in the presence of Rashba spin-orbit coupling

The influence of Rashba spin-orbit coupling on the Fano lineshape of the conductance spectrum in a T-shaped double quantum dot structure is theoretically studied. By second-quantizing the electron Hamiltonian in this structure, it is found that the Rashba interaction brings about a spin-flip interdot hopping term. With the enhancement of the Rashba interaction, this term separates the two resonant peaks in the conductance spectrum from each other. More importantly, it causes the broadening of the narrow Fano peak, and the narrowing of the broader peak. Finally, the asymmetric Fano lineshape changes into a symmetric profile in the global conductance spectrum.     

Transport Characteristics of Mesoscopic Radio-Frequency Single Electron Transistor

The transport property of a quantum dot under the influence of external time-dependent field is investigated. The mesoscopic device is modelled as semiconductor quantum dot coupled weakly to superconducting leads via asymmetric double tunnel barriers of different heights. An expression for the current is deduced by using the Landauer-Buttiker formula, taking into consideration of both the Coulomb blockade effect and the magnetic field. It is found that the periodic oscillation of the current with the magnetic field is controlled by the ratio of the frequency of the applied ac-field to the electron cyclotron frequency. Our results show that the present device operates as a radio-frequency single electron transistor.     

Quantum RLC circuits: Charge discreteness and resonance

In a recent article [C.A. Utreras-Díaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandía et al. [K. Chandía, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit.     

Flux-dependent transport through an Aharonov-Bohm interferometer with embedded multiple coupled quantum dots

The electron transport through an Aharonov-Bohm (AB) interferometer with embedded four coupled quantum dots (QDs) is studied with the Green's function technique. The QDs are coupled to each other by the hopping integral tc. Two among them connect with the left lead and the other two with the right lead by the tunneling matrix element T which incorporates the effects of the applied magnetic field φ. The linear conductance spectra swap between the molecular levels and the atomic states by adjusting tc and T. Fano effect appears when the electrons tunnel through different channels contributed by different QDs energy levels, and the Fano resonance peaks split for large tc. The Fano factor can be manipulated by tc, T, φ, and the QD energy levels.