Interdot Coulomb Repulsion Research Articles

The effect of inter-dot Coulomb interaction on the charge and energy transport properties of a five-terminal system consisting of three Coulomb-coupled quantum dots

We have studied a 5-terminal system consisting of three single level quantum dots (QDs) that are in contact with their respective reservoirs. In addition to the intra-dot Coulomb interaction, the electron in the dot affected by an inter-dot Coulomb repulsion from its adjacent QD. We describe this system by an Anderson type model Hamiltonian and apply the Greens function method to study the transport properties of the system. Since we are interested in temperatures higher than the Kondo temperature, we use the equations of motion technique to calculate Green’s functions. Numerical analysis shows that there is a correlation between the transport characteristics of the lower and upper dot and we can change the conductivity of the lower dot only by varying the parameters of the upper dot and vice versa. We demonstrated that the middle dot play the role of the switch on/off of this correlation. Also, we investigated the effect of thermoelectric properties. We found that the inter-dot Coulomb interaction can improve the thermoelectric performance of the system.

Parallel InAs nanowires for Cooper pair splitters with Coulomb repulsion

Hybrid nanostructures consisting of two parallel InAs nanowires connected by an epitaxially grown superconductor (SC) shell recently became available. Due to the defect-free SC-semiconductor interface and the two quasi-one-dimensional channels being close by, these platforms can be utilized to spatially separate entangled pairs of electrons by using quantum dots (QD) in the so-called Cooper pair splitting (CPS) process. The minimized distance between the QDs overcomes the limitations of single-wire-based geometries and can boost the splitting efficiency. Here we investigate CPS in such a device where strong inter-dot Coulomb repulsion is also present and studied thoroughly. We analyze theoretically the slight reduction of the CPS efficiency imposed by the Coulomb interaction and compare it to the experiments. Despite the competition between crossed Andreev reflection (CAR) and inter-wire capacitance, a significant CPS signal is observed indicating the dominance of the superconducting coupling. Our results demonstrate that the application of parallel InAs nanowires with epitaxial SC is a promising route for the realization of parafermionic states relying on enhanced CAR between the wires.

Spin and charge Kondo effects in capacitively coupled double quantum dots

We investigate low-temperature spin and charge (orbital) Kondo effect of capacitively hierarchical equations of motion. In a charge stability diagram at finite interdot Coulomb repulsion, a line between triple points (LBTP) serves as the degeneracy of charge configuration states. With one electron difference on each dot, these charge configuration states can be regarded as pseudospins. It is shown that charge can also screen its counterpart through the high-order process using tunnelling-coupled reservoirs. In the charge configuration regime , in addition to the spin Kondo effect, the degeneracy and detuning of charge configuration states and may also cause a charge Kondo resonance that agrees with the experiments on triple-peak structures with differential conductance.

Heat current across a capacitively coupled double quantum dot

We study the heat current through two capacitively coupled quantum dots coupled in series with two conducting leads at different temperatures $T_L$ and $T_R$ in the spinless case (valid for a high applied magnetic field). Our results are also valid for the heat current through a single quantum dot with strongly ferromagnetic leads pointing in opposite directions (so that the electrons with given spin at the dot can jump only to one lead) or through a quantum dot with two degenerate levels with destructive quantum interference and high magnetic field. Although the charge current is always zero, the heat current is finite when the interdot Coulomb repulsion $U$ is taken into account due to many-body effects. We study the thermal conductance as a function of temperature and the dependence of the thermal current with the couplings to the leads, $T_L-T_R$, energy levels of the dots and $U$, including conditions for which an orbital Kondo regime takes place. When the energy levels of the dots are different, the device has rectifying properties for the thermal current. We find that the ratio between the thermal current resulting from a thermal bias $T_L>T_R$ and the one from $T_L<T_R$ is maximized for particular values of the energy levels, one above and the other below the Fermi level.

Phase diagram characterized by transmission in a triangular quantum dot**Project supported by the National Natural Science Foundation of China (Grant Nos. 11174228 and 10874132).

We propose a theoretical model to detect the quantum phase transition in a triangular quantum dot molecule with frustration. The boundaries of the phase diagram are accurately determined by the transmission. For small frustration t, as the interdot Coulomb repulsion V increases, the system undergoes a Kosterlitz–Thouless (KT) transition from the Kondo resonance state with a transmission peak at zero energy to the Coulomb blocked state with zero transmission, which is followed by a first transition to the V-induced resonance (VIR) state with unitary transmission. For large frustration t, as V increases, the orbital spin singlet without transmission transits to the VIR state through a KT transition.

Quantum phase transition in a realistic double-quantum-dot system

Observing quantum phase transitions in mesoscopic systems is a daunting task, thwarted by the difficulty of experimentally varying the magnetic interactions, the typical driving force behind these phase transitions. Here we demonstrate that in realistic coupled double-dot systems, the level energy difference between the two dots, which can be easily tuned experimentally, can drive the system through a phase transition, when its value crosses the difference between the intra- and inter-dot Coulomb repulsion. Using the numerical renormalization group and the semi-analytic slave-boson mean-field theory, we study the nature of this phase transition, and demonstrate, by mapping the Hamiltonian into an even-odd basis, that indeed the competition between the dot level energy difference and the difference in repulsion energies governs the sign and magnitude of the effective magnetic interaction. The observational consequences of this transition are discussed.

SU(4) Kondo entanglement in double quantum dot devices

We analyze, from a quantum information theory perspective, the possibility of realizing a SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.

Strongly Correlated Effects in a Triangular Dot System Induced by Inter-Dot Hopping and Coulomb Repulsion

We study the transport property and the phase transition for a triple quantum dot system in a triangular geometry with one centered dot and two side dots by adopting the Wilson’s numerical renormalization group method. When three dots are decoupled with no coupling, the Kondo peak turns to reach the unitary limit, and the spin-1/2 Kondo effect is found. When the hopping between the centered dot and two side dots increases, two side dots form a local spin triplet due to the Ruderman–Kittel–Kasuya–Yosida interaction mediated by the centered dot, and the Kondo peak is suppressed. As the hopping between two side dots increases, a first order quantum phase transition occurs. In this case, two side dots form a spin singlet and the Kondo peak is recovered. When the inter-dot Coulomb repulsion between two side dots is taken into account and the hopping between two side dots is small, the charge on each side dot drops to 0.5 through a first-order quantum phase transition. As a result, one of the side dots is singly occupied, while the other one is empty. The linear conductance is suppressed due to the strong coupling between the centered dot and the singly occupied side dot. When the hopping between two side dots is large enough, the charge on each side dot decreases to 0.5 continuously and a crossover is found, for in this case the symmetry of spin configurations within two side dots is broken.

Screened spin−1 and −1/2 Kondo effect in a triangular quantum dot system with interdot Coulomb repulsion

By means of the numerical renormalization group (NRG) technique, we study the low temperature transport property and the phase transition for a triangular triple quantum dot system, including two centered dots (dot 1 and 2) and one side dot (dot 3). We focus on the effect of interdot repulsion V between two centered dots in a wide range of the interdot hopping tij (i,j = 1,2,3). When the hoppings between the centered dot and the side dot are symmetric, i.e., t13 = t23, and that between two centered dots t12 is small, two centered dots form a spin triplet when V is absent, and a totally screened spin−1 Kondo effect is observed. In this case, one has a spin 1 that is partially screened by the leads as in the usual spin−1 Kondo model, and the remaining spin 1/2 degree of freedom forms a singlet with the side dot. As V is large enough, one of the centered dots is singly occupied, while the other one is empty. The spin−1/2 Kondo effect is found when t13 is small. For large t12, two centered dots form a spin singlet when V = 0, leading to zero conductance. As V is large enough, the spin−1/2 Kondo effect is recovered in the case of small t13. For asymmetric t13≠t23 and small t12, a crossover is found as V increases in comparison with a first order quantum phase transition for the symmetric case. In the regime of large V, the spin−1/2 Kondo effect could also be found when both t13 and t23 are small. We demonstrate the present model is similar to the side-coupled double dot system in some appropriate regimes, and it appears as a possible realization of side-controllable molecular electronics and spintronics devices.

Double quantum dot Cooper-pair splitter at finite couplings

We consider the sub-gap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunnelling between the dots and finite Coulomb intra- and inter-dot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method which easily yields currents, noise and cross-correlators. In particular, for finite inter- and intra-dot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of inter-dot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.

Effect of electronic correlations on magnetotransport through a parallel double quantum dot

We theoretically investigate the effects of electronic correlations (including spin and Coulomb correlations) on the magnetotransport through a parallel double quantum dot (DQD) coupled to ferromagnetic leads. Two dots couple coherently through electron correlations, rather than tunneling directly between two dots, and each dot is coupled to two semi-infinite ferromagnetic leads. We assume that the intradot Coulomb repulsion is much larger than the interdot Coulomb repulsion U. Thus, only the zero, one and two-particle DQD states are relevant to transport. Because of interdot electron correlation, the I-V characteristics of each dot is sensitive to the change in the state of the other dot. This work focuses on the effects of electron spin correlation and electron Coulomb correlation on magnetotransport through this system. In order to determine the transport properties of the system, we use the generalized master equation method. This method is based on the reduced density operator defined by averaging the statistical operator of the total system over the states of all leads. With the framework of the generalized master equation and the sequential tunneling approximation, we calculate the current, differential conductance and tunnel magnetoresistance (TMR) in the dot 1 as a function of bias for different spin correlations and Coulomb correlations. Our results reveal that the magnetotransport through this system is more sensitive to Coulomb correlation than to spin correlation; when Coulomb correlation equals zero, the spin correlation can induce a giant tunnel magnetoresistance, which is further larger than the Jullieres value of TMR; when Coulomb correlation occurs, the giant tunnel magnetoresistance disappears; when Coulomb correlation is equal to or larger than spin correlation, Coulomb correlation can suppress spin correlation; while the coexistence of Coulomb correlation and asymmetry of the DQD system can result in dynamical channel blockade, which can lead to the occurrence of negative tunnel magetoresistance and negative differential conductance. These novel properties lead to the potential applications in nanoelectronics, and relevant underlying physics of this problem is discussed.

Effects of the Antiferromagnetic Spin Coupling and Interdot Coulomb Repulsion on Kondo Effects in Serial Double Quantum Dots

We theoretically study the effects of the antiferromagnetic (AF) spin coupling and the interdot Coulomb repulsion on the Kondo effects in serial double quantum dots by means of the slave-boson mean-field approximation. Our results indicate that in the weak coupling regime, the AF spin coupling strengthens the Kondo resonance, while the interdot Coulomb repulsion suppresses them for the equilibrium case. In the non-equilibrium case, the AF spin coupling strengthens the Kondo resonance only when J > 2.5T0K, while the interdot Coulomb repulsion does not suppress Kondo peaks. In the strong coupling regime, the bias voltage has no effects on the Kondo resonance in this system, and the AF spin coupling increases the height of Kondo peaks only when J < 2.5T0K. However, the inter-dot Coulomb repulsion suppresses the spin Kondo effect, which induces the orbit Kondo effect. Moreover, the relevant underlying physics of these problems are discussed.

Spin filtering in a double quantum dot device: Numerical renormalization group study of the internal structure of the Kondo state

A double quantum dot device, connected to two channels that only interact through interdot Coulomb repulsion, is analyzed using the numerical renormalization group technique. Using a two-impurity Anderson model, and realistic parameter values [S. Amasha, A. J. Keller, I. G. Rau, A. Carmi, J. A. Katine, H. Shtrikman, Y. Oreg, and D. Goldhaber-Gordon, Phys. Rev. Lett. 110, 046604 (2013)], it is shown that, by applying a moderate magnetic field and independently adjusting the gate potential of each quantum dot at half-filling, a spin-orbital SU(2) Kondo state can be achieved where the Kondo resonance originates from spatially separated parts of the device. Our results clearly link this spatial separation effect to currents with opposing spin polarizations in each channel, i.e., the device acts as a spin filter. In addition, an experimental probe of this polarization effect is suggested, pointing to the exciting possibility of experimentally probing the internal structure of an SU(2) Kondo state.

Capacitively coupled double quantum dot system in the Kondo regime

A detailed study of the low-temperature physics of an interacting double quantum dot system in a T-shape configuration is presented. Each quantum dot is modeled by a single Anderson impurity and we include an inter-dot electron-electron interaction to account for capacitive coupling that may arise due to the proximity of the quantum dots. By employing a numerical renormalization group approach to a multi-impurity Anderson model, we study the thermodynamical and transport properties of the system in and out of the Kondo regime. We find that the two-stage-Kondo effect reported in previous works is drastically affected by the inter-dot Coulomb repulsion. In particular, we find that the Kondo temperature for the second stage of the two-stage-Kondo effect increases exponentially with the inter-dot Coulomb repulsion, providing a possible path for its experimental observation.

Analysis of current and shot noise correlations in a double quantum dot interferometer with interdot spin interactions

We examine an electron Aharonov-Bohm (AB) interferometer with individual quantum dots connected in parallel to macroscopic leads. Here, we focus on the effect that both interdot spin-spin exchange interactions and intradot spin flips have on the current- and frequency-dependent current shot noise. By appropriate control of AB magnetic flux, interdot Coulomb repulsion, intradot spin flips, and interdot spin-spin coupling, the probability amplitudes for the different paths of the interferometer can be controlled, leading to broad tunability of both the shape and the contrast of interference fringes in the current. We also show that in the shot noise at finite frequencies corresponding to the spin-spin interaction energies, the noise shows a pronounced super-Poissonian and sub-Poissonian structure. AB flux, which is not an integer multiple of $2\ensuremath{\pi}$, dramatically suppresses the correlations in the shot noise.

Tunnel coupled dangling bond structures on hydrogen terminated silicon surfaces

We study both experimentally and theoretically the electronic behavior of dangling bonds (DBs) at a hydrogen terminated Si(100)-2×1 surface. Dangling bonds behave as quantum dots and, depending on their separation, can be tunnel coupled with each other or completely isolated. On n-type highly doped silicon, the latter have a net charge of -1e, while coupled DBs exhibit altered but predictable filling behavior derived from an interplay between interdot tunneling and Coulomb repulsion. We found good correlation between many scanning tunneling micrographs of dangling bond structures and our theoretical results of a corresponding extended Hubbard model. We also demonstrated chemical methods to prevent tunnel coupling and isolate charge on a single dangling bond.

The effect of the interdot Coulomb interaction on Kondo resonances in series-coupled double quantum dots

We theoretically investigate the effect of the interdot Coulomb repulsion on Kondo resonances in the series-coupled double quantum dot coupled to two ferromagnetic leads. The Hamiltonian of our system is solved by means of the slave-boson mean-field approximation, and the variation of the density of states, the transmission probability, the occupation number, and the Kondo temperature with the interdot Coulomb repulsion are discussed in the Kondo regime. The density of states is calculated for various interdot Coulomb repulsions with both parallel and antiparallel lead-polarization alignments. Our results reveal that the interdot Coulomb repulsion greatly influences the physical property of this system, and relevant underlying physics of this system is discussed.

Kondo and Coulomb Interaction Effects in Spin-Polarized Transport through Double Quantum Dots

By means of the slave-boson mean-field approximation, we theoretically investigate the Kondo and Coulomb interaction effects in spin-polarized transport through two coupled quantum dots coupled to two ferromagnetic leads by the Anderson Hamiltonian. The density of states is calculated in the Kondo regime for the effect of the interdot Coulomb repulsion with both parallel and antiparallel lead-polarization alignments. Our results reveal that the interdot Coulomb interaction between quantum dots greatly influence the density of states of the dots. We then clarify relevant underlying physics of this problem.

Effect of interdot Coulomb repulsion on tunneling current through a double quantum dot system in the weak tunneling limit: Strong electron-phonon coupling

Pronounced effects of the interdot Coulomb repulsion on the tunnel current/gate voltage dependence at the ambient conditions are predicted for the double quantum dot system in the serial configuration immersed in the electrolyte solution in the case of the weak tunneling of electrons both between the dots and between the dots and leads. Electrons at the dots are coupled strongly to the classical phonon modes and Debye screening of the electric field is taken into account. The infinite intradot Coulomb repulsion limit is used. The effects consist of i a very large width of the maximum of the tunnel current/gate voltage dependence of the order of kBT lnk0 /k, where k0 and k are the characteristic rates of the electron tunneling between the dots and between the dots and leads, respectively in the limit k0 /k →0, ii the dependence of the positions of the maxima of the current/gate voltage curve and their widths on the sign of the difference of the electron energy levels of the quantum dots and the energy of the polaron shift, and iii narrow-width Coulomb blockade peaks in the tunnel current/gate voltage curve for k0k. The dependence of the differential conductance on the gate voltage, the energy of the interdot Coulomb repulsion, the Debye screening length, and values of k0 /k and are studied. It is shown that the curves of the differential conductance/bias voltage dependence can be very different for different values of these parameters. These parameters also determine the position of the regions of the negative differential conductance which exist in the general case.

Inter-dot coupling effects on transport through correlated parallel coupled quantum dots

Transport through symmetric parallel coupled quantum dot system has been studied, using non-equilibrium Green function formalism. The inter-dot tunnelling with on-dot and inter-dot Coulomb repulsion is included. The transmission coefficient and Landaur-Buttiker like current formula are shown in terms of internal states of quantum dots. The effect of inter-dot tunnelling on transport properties has been explored. Results, in intermediate inter-dot coupling regime show signatures of merger of two dots to form a single composite dot and in strong coupling regime the behaviour of the system resembles the two decoupled dots.