Dot-lead Coupling Research Articles

Tunable Fano effect in parallel-coupled double quantum dot system

With the help of the Green function technique and the equation of motion approach, the electronic transport through a parallel-coupled double quantum dot(DQD) is theoretically studied. Owing to the inter-dot coupling, the bonding and antibonding states of the artificial quantum-dot-molecule may constitute an appropriate basis set. Based on this picture, the Fano interference in the conductance spectra of the DQD system is readily explained. The possibility of manipulating the Fano lineshape in the tunnelling spectra of the DQD system is explored by tuning the dot-lead coupling, the inter-dot coupling, the magnetic flux threading the ring connecting dots and leads, and the flux difference between two sub-rings. It has been found that by making use of various tuning, the direction of the asymmetric tail of Fano lineshape may be flipped by external fields, and the continuous conductance spectra may be magnetically manipulated with lineshape retained. More importantly, by adjusting the magnetic flux, the function of two molecular states can be exchanged, giving rise to a swap effect, which might play a role as a qubit in the quantum computation.

Analytical results on coherent conductance in a general periodic quantum dot: Transfer matrix method

In this work, we study the conductance of a general periodic quantum dot (QD) attached to ideal semi-infinite uniform metallic leads (nanocrystals), fully analytically. We propose a new general formula which relates conductance to transfer matrix (TM) for an isolated cell in the periodic dot. The equation describes exactly the dependence of the transmission coefficient (TC) on Fermi energy, dot-size, dot–lead coupling, and gate voltage for an arbitrary periodic dot. Then, we derive a nonlinear equation which gives the resonance, bound, and surface state energies. Finally, the TC has been calculated for gapless, single, and double gap models exactly. Moreover, we have also calculated the effects of the cross-section of the leads, which were separated by a polymer chain on the conductance. Our calculations can be generalized to any type of QD and quantum wire (QW) within the one-electron approximation, and, can be applied to, e.g., molecular, polymer, and nanocrystal junctions, where these results may be useful in designing future molecular electronic devices.

Phonon effects in molecular transistors: Quantal and classical treatment

We present a comprehensive theoretical treatment of the effect of electron-phonon interactions in molecular transistors, including both quantal and classical limits and we study both equilibrated and out of equilibrium phonons. We present detailed results for conductance, noise and phonon distribution in two regimes. One involves temperatures large as compared to the rate of electronic transitions on and off the dot; in this limit our approach yields classical rate equations, which are solved numerically for a wide range of parameters. The other regime is that of low temperatures and weak electron-phonon coupling where a perturbative approximation in the Keldysh formulation can be applied. The interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented. We also discuss the nature of the low-T to high-T crossover.

Mesoscopic Fluctuations of Co-Tunneling and Kondo Effect in Quantum Dots

Conductance of a quantum dot in the Coulomb blockade regime is discussed. At moderately low temperatures, the thermally-assisted transport of electrons through the dot gives way to elastic co-tunneling [1]. The amplitude of the elastic co-tunneling is sensitive to the specific structure of electron wave functions in a given sample. The conductance exhibits strong mesoscopic fluctuations [2]. Statistical properties of these fluctuations are reviewed in this lecture. At lower temperatures, conductance through a dot is altered by the Kondo effect, if the number of electrons on the dot is odd. We describe the universal features of the Kondo conductance [3, 4], and briefly discuss the manifestations of this effect in the limiting cases of weak and strong [5] dot-lead coupling.

Interaction-driven spin precession in quantum-dot spin valves.

We analyze spin-dependent transport through spin valves composed of an interacting quantum dot coupled to two ferromagnetic leads. The spin on the quantum dot and the linear conductance as a function of the relative angle theta of the leads' magnetization directions is derived to lowest order in the dot-lead coupling strength. Because of the applied bias voltage spin accumulates on the quantum dot, which for finite charging energy experiences a torque, resulting in spin precession. The latter leads to a nontrivial, interaction-dependent, theta dependence of the conductance. In particular, we find that the spin-valve effect is reduced for all theta not equal pi.

Adiabatic spin pumping through a quantum dot with a single orbital level

We investigate an adiabatic spin pumping through a quantum dot with a single orbital energy level under the Zeeman effect. Electron pumping is produced by two periodic time dependent parameters, a magnetic field, and a difference of the dot-lead coupling between the left and right barriers of the dot. The maximum charge transfer per cycle is found to be e, the unit charge in the absence of a localized moment in the dot. Pumping rates for charge and spin are different, so that spin pumping is possible without charge pumping in a certain situation. They are tunable by changing the minimum and maximum value of the magnetic field.

Tristability in a non-equilibrium double-quantum-dot in the Kondo regime

Electron tunneling through a non-equilibrium double quantum dot in the Kondo regime is studied. In the region of negative differential resistance, it is shown that this system possesses a complex response to the applied potential characterized by a tristable solution for the current. Increasing the applied potential or reducing the inter-dot coupling, the system goes through a transition from a coherent inter-dot regime to an incoherent one. The different nature of the solutions is characterized and it is shown that the effects of the asymmetry in the dot-lead coupling can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution of the problem.

Signs of quantum dot–lead matrix elements: The effect on transport versus spectral properties

A small quantum dot coupled to two external leads is considered. Different signs of the dot-lead coupling matrix elements give rise to qualitatively different behavior of physical observables such as the conductance, the phase of the transmission amplitude, and the differential capacitance of the dot. For certain relative signs the conductance may vanish at values of the gate potential, where the spectral density is maximal. Zeroes of the conductance are robust against increasing the dot-lead coupling. They are associated with abrupt phase lapses in the transmission phase whose width vanishes as the square of the temperature. We carefully distinguish between phase lapses of $\ensuremath{-}\ensuremath{\pi}$ and phase antilapses of $\ensuremath{\pi}.$

Asymmetric line shape and Fano interference in the transport of electrons through a multilevel quantum dot in the Coulomb blockade regime

We investigate the resonant transmission of electrons through a multilevel quantum in the Coulomb blockade regime. We show that the quantum interference between the path through the resonant level and the paths via other (nonresonant) levels results in the Fano asymmetry of the transmission peaks. The Fano parameter q is expressed in terms of the level spacing and the dot-lead coupling. The Coulomb blockade provides another origin of asymmetry for the resonances of the conductance due to the asymmetric occupation about a resonant point. Physical ingredients that influence these two mechanisms of the asymmetry are discussed.

Effect of spectral fluctuations on conductance-peak height statistics in quantum dots

Within random matrix theory for quantum dots, both the dot's one-particle eigenlevels and the dot-lead couplings are statistically distributed. While the effect of the latter on the conductance is obvious and has been taken into account in the literature, the statistical distribution of the one-particle eigenlevels is generally replaced by a picket-fence spectrum. Here we take the random matrix theory eigenlevel distribution explicitly into account, and observe significant deviations in the conductance distribution and magnetoconductance of closed quantum dots at experimentally relevant temperatures.

Kondo effect and antiferromagnetic correlation in transport through tunneling-coupled double quantum dots

We propose to study the transport through tunneling-coupled double quantum dots (DQDs) connected in series to leads, using the finite-$U$ slave-boson mean field approach developed initially by Kotliar and Ruckenstein [Phys. Rev. Lett. {\bf 57}, 1362 (1986)]. This approach treats the dot-lead coupling and the inter-dot tunnelling $t$ nonperturbatively at arbitrary Coulomb correlation $U$, thus allows the anti-ferromagnetic exchange coupling parameter $J=4t^2/U$ to appear naturally. We find that, with increasing the inter-dot hopping, the DQDs manifest three distinct physical scenarios: the Kondo singlet state of each dot with its adjacent lead, the spin singlet state consisting of local spins on each dot and the doubly occupied bonding orbital of the coupled dots. The three states exhibit remarkably distinct behavior in transmission spectrum, linear and differential conductance and their magnetic-field dependence. Theoretical predictions agree with numerical renormalization group and Lanczos calculations, and some of them have been observed in recent experiments.

Fano resonances and Aharonov-Bohm effects in transport through a square quantum dot molecule

We study the Aharonov-Bohm effect in a coupled 2$\times$2 quantum dot array with two-terminals. A striking conductance dip arising from the Fano interference is found as the energy levels of the intermediate dots are mismatched, which is lifted in the presence of a magnetic flux. A novel five peak structure is observed in the conductance for large mismatch. The Aharonov-Bohm evolution of the linear conductance strongly depends on the configuration of dot levels and interdot and dot-lead coupling strengths. In addition, the magnetic flux and asymmetry between dot-lead couplings can induce the splitting and combination of the conductance peak(s).

The Kondo effect in a one- and two-electron quantum dot

We study the Kondo effect in a vertical quantum dot holding only one- or two-electrons. We observe clear Kondo features in the temperature and bias voltage dependence of the conductance when there is only one electron in the dot (spin S=1/2). The estimated Kondo temperature is much higher than in previous reports due to large dot-lead tunnel coupling on the order of 800 μeV . We also observe a Kondo enhancement of the conductance when the two-electron ground state makes a transition from a spin singlet ( S=0) to a triplet ( S=1) at a magnetic field of 3.2 T . The bias voltage dependence of the differential conductance at this transition field shows weak features that may be related to the Zeeman splitting of the triplet state.

Kondo effect in coupled quantum dots under magnetic fields

The Kondo effect in coupled quantum dots is investigated theoretically under magnetic fields. We show that the magnetoconductance (MC) illustrates peak structures of the Kondo resonant spectra. When the dot-dot tunneling coupling $V_C$ is smaller than the dot-lead coupling $\Delta$ (level broadening), the Kondo resonant levels appear at the Fermi level ($E_F$). The Zeeman splitting of the levels weakens the Kondo effect, which results in a negative MC. When $V_{C}$ is larger than $\Delta$, the Kondo resonances form bonding and anti-bonding levels, located below and above $E_F$, respectively. We observe a positive MC since the Zeeman splitting increases the overlap between the levels at $E_F$. In the presence of the antiferromagnetic spin coupling between the dots, the sign of MC can change as a function of the gate voltage.

Kondo resonant spectra in coupled quantum dots

The Kondo effect in coupled quantum dots is investigated from the viewpoint of transmission spectroscopy using the slave-boson formalism of the Anderson model. The antiferromagnetic spin-spin coupling $J$ between the dots is taken into account. Conductance $G$ through the dots connected in a series is characterized by the competition between the dot-dot tunneling coupling $V_{C}$ and the level broadening $\Delta$ in the dots (dot-lead coupling). When $V_{C}/\Delta < 1$, the Kondo resonance is formed between each dot and lead, which is replaced by a spin-singlet state in the dots at low gate voltages. The gate voltage dependence of $G$ has a sharp peak of $2 e^2/h$ in height in the crossover region between the Kondo and spin-singlet states. The sharp peak of $G$ survives when the energy levels are different between the dots. When $V_{C} / \Delta > 1$, the "molecular levels" between the Kondo resonant states appear; the Kondo resonant peaks are located below and above the Fermi level in the leads at low gate voltages. The gate voltage dependence of $G$ has a broad peak, which is robust against $J$. The broad peak splits into two peaks when the energy levels are different, reflecting the formation of the asymmetric molecular levels between the Kondo resonant states.

Coulomb effects on the transport properties of quantum dots in a strong magnetic field

We investigate the transport properties of quantum dots placed in a strong magnetic field using a quantum-mechanical approach based on the two-dimensional tight-binding Hamiltonian with direct Coulomb interaction and the Landauer-B\"uttiker formalism. The electronic transmittance and the Hall resistance show Coulomb oscillations and also prove multiple addition processes. We identify this feature as the ``bunching'' of electrons observed in recent experiments and give an elementary explanation in terms of spectral characteristics of the dot. The spatial distribution of the added electrons may distinguish between the edge and bulk states and it has specific features for bunched electrons. The dependence of the charging energy on the number of electrons is discussed for a strong magnetic field. The crossover from the tunneling to quantum Hall regime is analyzed in terms of dot-lead coupling.

Electron Transport Through Coupled Quantum Dots Below the Kondo Temperature

Conductance G, through coupled quantum dots in series isinvestigated below the Kondo temperature, based on the slaveboson formalism of the Anderson model with theantiferromagnetic spin–spin coupling J. Electron transport ischaracterized by the ratio of the dot–dot tunneling couplingV C to the level broadening in the dots Δ(dot-lead coupling). When V C /Δ 1, the Kondo levelsare split below and above the Fermi level in the leads for lowgate voltages. The gate voltage dependence of G has a broadpeak, which is fairly robust against J. This broad peak isdivided into two peaks when the energy levels are differentbetween the dots.

Quantum phase transition in coupled quantum dots

We study two quantum dots in the limit of strong dot-lead coupling and weak dot-dot tunneling. The model maps on Ising-coupled Kondo impurities. We argue that a new quantum critical fixed point exists at an intermediate value of the mutual capacitance, supporting non-Fermi-liquid behavior. We construct the total conductance across the double dot structure. It exhibits a strongly peaked behavior as a function of the mutual capacitance, gate voltage, and temperature.

Nonequilibrium Transport and Population Inversion in Double Quantum Dot Systems

We present a microscopic theory for both equilibrium and nonequilibrium transport properties of coupled double quantum dots (DQD). A general formula for current tunneling through the DQD is derived by the nonequilibrium Green's function method. Using a Hartree–Fock approach, effects of multi-level coupling and nonequilibrium electron distributions in resonant tunneling are considered. We find that the peak in the resonant tunneling current through two symmetric dots will split only when the inter-dot coupling is stronger than dot-lead coupling. We predict that population inversion can be achieved in one dot in the nonequilibrium regime.

Nonequilibrium-Green's-function theory of transport in interacting quantum dots.

We present an approach for modeling nonequilibrium steady-state transport in quantum dots with interacting electrons, which employs real-time many-body Green's functions on a tight-binding basis and accounts for dot-lead coupling exactly. This real-time Green's-function description of transport is used to investigate the steady-state charge-density and current-voltage characteristics of one- and two-dimensional quantum dots having interacting electrons. The quantum dots are composed of a rectangular lattice of tight-binding sites, allowing for multiple degrees of freedom and a spatially varying external electric field. We investigate the effects of both the dot-lead coupling strength and finite current flowing in the dot. Our results indicate that as dot-lead coupling is increased, the Coulomb blockade disappears smoothly; furthermore, the Coulomb blockade may persist even in dots which have tunnel-junction resistances less than h/${\mathit{e}}^{2}$. We also find that in the Coulomb-blockade regime under conditions of current flow, the assumption of integer steady-state charge on the dot does not necessarily hold true, although the effect of single-electron tunneling does.