Parallel Double Quantum Dot System Research Articles

Thermoelectric enhancement of a parallel double quantum dot system connecting to Luttinger liquid leads

In this work, we study the thermoelectric properties of the parallel-coupled double quantum dot connected to Luttinger liquid (LL) leads. By applying nonequilibrium Green's function methods, the expressions of the electron current, heat currents, and transport coefficients are derived. We mainly focus on the effect of intralead Coulomb interaction and the spatial asymmetry of the system. Various causes for the enhancement of the thermoelectric efficiency are investigated. We find that Coulomb interactions in the LL not only enhance quantum interference but also considerably enhance thermoelectric effects. For moderately strong intralead interaction, the figure of merit can be considerably high and reach over 60 in the case of weakly coupled to LL leads and detuning of the energy levels, while in the case of strongly coupled to LL leads and the two aligned levels, the figure of merit approaches 8. The quantum interference induced by the Coulomb interaction yields a very high thermoelectric efficiency when the intralead interaction is very strong. These results may provide a design rule for the development of high-efficiency thermoelectric devices and facilitate optimization of device performance.

On the competition between the Kondo effect and the exchange interaction in a parallel double quantum dot system

We study the competition between the Kondo effect and the exchange interaction in the parallel double quantum dot (DQD) system within an effective action field theory. The strong on-site Coulomb interactions in DQDs are treated by using the Hubbard–Stratonovich transformation and the introduction of scalar potential fields. We show that a self-consistent perturbation approach, which takes into account the statistical properties of the potential fields acting on electrons in DQDs, describes well the crossover from the Kondo regime to the spin-singlet state in this system. The linear conductance and the intradot/interdot spin excitation spectra of this system are obtained.

Time-dependent thermoelectric transport in nanosystems: Reflectionless Luttinger field approach

Recently the Luttinger field approach was proposed by Eich et al. in Phys. Rev. B 90, 115116 (2014). as a way to simulate switching on a temperature gradient across a nanoscale device initially in thermal equilibrium. The time-dependent particle and heat currents can then be calculated by propagating the initial equilibrium state of the system in time. Unfortunately, applying a uniform Luttinger field in the whole of a lead causes a discrepancy between steady-state currents in the long time limit and those predicted by the Landauer-B\uttiker formulas as well as artifacts at short times. Here we propose a modified approach where the Luttinger field gradually reaches its final value across a transition region. If the length of the transition region is sufficient, the electrons move through without reflecting. In this way the correct energy distribution of electrons originating from such a lead, corresponding to the new temperature, is established in the scattering region. Our approach is tested on a single quantum dot and a parallel double quantum dot system.

Cavity‐photon contribution to the effective interaction of electrons in parallel quantum dots

A single cavity photon mode is expected to modify the Coulomb interaction of an electron system in the cavity. Here we investigate this phenomena in a parallel double quantum dot system. We explore properties of the closed system and the system after it has been opened up for electron transport. We show how results for both cases support the idea that the effective electron‐electron interaction becomes more repulsive in the presence of a cavity photon field. This can be understood in terms of the cavity photons dressing the polarization terms in the effective mutual electron interaction leading to nontrivial delocalization or polarization of the charge in the double parallel dot potential. In addition, we find that the effective repulsion of the electrons can be reduced by quadrupolar collective oscillations excited by an external classical dipole electric field.

Ground State Properties and Electron Transport in Parallel Double Quantum Dot System with Charge Number N tot ≤ 2

We study the ground state properties and the electron transport in a double quantum dot system with the numerical renormalization group method for a wide range of the charge energy 𝜖. When 𝜖 is chosen in the Kondo regime, we find a quantum phase transition of first order between local spin triplet and singlet with increasing interdot hopping t. For small t, the Kondo resonance is observed, while for large t, it is strongly suppressed. When 𝜖 is in the mixed-valence regime, the system transits from a magnetic frustration phase to the singlet continuously, and the potential scattering peak is suppressed. For 𝜖 in the frozen impurity regime, the system transits to the spin singlet through a crossover, and the linear conductance is merely determined by the charge density of the bonding state. Our results is consistent with the perturbation theory.

Influences of electron-phonon interaction on the thermoelectric effect in a parallel double quantum dot system

A quantum-dot system is a typical low-dimensional system, and previous researches showed that its thermoelectric conversion efficiency can be markedy improved due to its unique physical properties. In this poper, we choose the parallel double-quantum-dot structure and discuss the influence of the electron-phonon interaction on the thermoelectric-related parameters, i.e., the electric conductance, thermopower, the figure of merit, and thermal conductance, by using the nonequilibrium Green's function method. Our theoretical calculation results show that under the condition of low temperature, the occurrence of the Fano interference can assist to enhance the thermoelectric effect. When the electron-phonon interaction is taken into account, it can suppress the electric and thermal conductances to a certain extent because of its negative effect on the Fano interterence. However, we readily find that apparently the strengthening of the electron-phonon interaction cannot suppress the maximum of the thermopower. Instead, in some regions, the thermopower has an opportunity to enhance due to the appearance of a new channel caused by the electron-phonon interaction. Meanwhile, the figure of merit is found to cause similar effects to the thermopower. Therefore, in the case of low temperature, the electron-phonon interaction contributes little to the destruction of the thermoelectric effect, namely, it is not the necessary condition for the suppression of the thermoelectric effect. With the increase of temperature, the negative effect of the electron-phonon interaction on the Fano interference becomes relatively distinct, which inevitably weakens the thermoelectric effect. Results of this paper will help to clarify the influence of electron-phonon interaction on the thermoelectric effect.

Magnetic flux tuning of Fano-Kondo interplay in a parallel double quantum dot system

We investigate the Fano-Kondo interplay in an Aharonov-Bohm ring with an embedded non-interacting quantum dot and a Coulomb interacting quantum dot. Using a slave-boson mean-field approximation we diagonalize the Hamiltonian via scattering matrix theory, and derive the conductance in the form of a Fano expression, which depends on the mean field parameters. We predict that in the Kondo regime the magnetic field leads to a gapped energy level spectrum due to hybridisation of the non-interacting QD state and the Kondo state, and can quantum-mechanically alter the electron's path preference. We demonstrate that an abrupt symmetry change in the Fano resonance, as seen experimentally, could be a consequence of an underlying Kondo channel.

Ground State of the Parallel Double Quantum Dot System

We resolve the controversy regarding the ground state of the parallel double quantum dot system near half filling. The numerical renormalization group predicts an underscreened Kondo state with residual spin-1/2 magnetic moment, ln2 residual impurity entropy, and unitary conductance, while the Bethe ansatz solution predicts a fully screened impurity, regular Fermi-liquid ground state, and zero conductance. We calculate the impurity entropy of the system as a function of the temperature using the hybridization-expansion continuous-time quantum Monte Carlo technique, which is a numerically exact stochastic method, and find excellent agreement with the numerical renormalization group results. We show that the origin of the unconventional behavior in this model is the odd-symmetry "dark state" on the dots.

Electron-photon interaction associated with uncertainty-based tunneling in a parallel double quantum dot

The electron-photon interaction associated with the uncertainty based tunneling (EPAUT) in the parallel double quantum dot system is studied. In the considered system, the electron interacts with the single mode detuning quantum photon field, i.e., ${\ensuremath{\omega}}_{\mathit{ph}}+\ensuremath{\Delta}={\ensuremath{\epsilon}}_{2}\ensuremath{-}{\ensuremath{\epsilon}}_{1}$, and transits between the quantum dots (QDs). The corresponding characteristic temperature is calculated and compared with the Kondo temperature to recognize the role of the related quantities. There are two energy uncertainties in the considered system. One is the energy difference between the energy of electron-photon interacting quasiparticle and the Fermi energy of the lead. The other is the detuning factor $\ensuremath{\Delta}$. Besides, $\ensuremath{\mid}\ensuremath{\Delta}∕\ensuremath{\pi}\ensuremath{\mid}$ is the bandwidth of the intermediate state of EPAUT. The peak of the density of state corresponding to the EPAUT rises when the temperature is in the order of or below the characteristic temperature. The EPAUT peak can be modified via tuning the Fermi energy of the lead connected to the adjoined QD. Hence, the conductance between the connected leads is varied via tuning the Fermi energy of the lead connected to the adjoined QD.

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.

Fano resonance in electron transport through parallel double quantum dots in the Kondo regime

Electron transport through parallel double quantum dot system with interdot tunneling and strong on-site Coulomb interaction is studied in the Kondo regime by using the finite-$U$ slave boson technique. For a system of quantum dots with degenerate energy levels, the linear conductance reaches the unitary limit $(2{e}^{2}∕h)$ due to the Kondo effect at low temperature when interdot tunneling is absent. As the interdot tunneling amplitude increases, the conductance decreases in the singly occupied regime and a conductance plateau structure appears. In the crossover to the doubly occupied regime, the conductance increases to reach a maximum value of $G=2{e}^{2}∕h$. For parallel double dots with different energy levels, we show that the interference effect plays an important role in electron transport. The linear conductance is shown to have an asymmetric line shape of the Fano resonance as a function of gate voltage.