We investigate cross-correlations in the tunneling currents through two parallel quantum dots coupled to independent electrodes and gates and interacting via an inter-dot Coulomb interaction. The correlations reveal additional information, beyond what can be learned from the current or conductance, about the dynamics of transport processes of the system. We find qualitatively different scenarios for the dependence of the cross-correlations on the two gate voltages. Reducing the temperature below the inter-dot Coulomb interaction, regions of a given sign change from spherical shapes to angular L-shapes or stripes. Similar shapes have been observed in recent experiments.
In this paper we introduce a simple phenomenological model of the conduction between a couple of serial or parallel quantum dots. This model is extended to arbitrary of number and to a square array of quantum dots. The local potential is computed taking into account the net charge at the quantum dot. Master equation are presented for total current and charge number N taking considering both the local potential and the local current. Interesting results are reported, namely the Negative Differential Resistance for serial quantum dots as well as resonant conductance. A paradoxical asymmetric cur…
We analyze the zero temperature conductance of a parallel T-shaped double quantum dot system. We present an analytical expression for the conductance of the system in terms of the total number of electrons in both quantum dots. Our results confirm that the system's conductance is strongly influenced by the dot which is not directly connected to the leads. We discuss our results in connection with similar results reported in the literature.
It is demonstrated that parallel weakly coupled quantum dots exhibit non-equilibrium blockade regimes caused by a full occupation in the spin triplet state, in analogy to the Pauli spin blockade in serially weakly coupled quantum dots. Charge tends to accumulate in the two-electron triplet for bias voltages that support transitions between the singlet and three-electron states.
We investigated the electron transport properties of parallel-coupled double quantum dot (DQD) devices under magnetic fields. When a low magnetic field was applied, electron tunneling through parallel-coupled DQDs was observed. Under a high magnetic field, we observed both electron tunneling through parallel- and series-coupled DQDs under nonlinear transport conditions. In addition, the Pauli spin blockade was observed, indicating tunneling through the series-coupled DQDs. We attribute these behaviors to the magnetic-field-induced changes in the tunnel-couplings that allow the coexistence of t…
We present quantum transport measurements of interacting parallel quantum dots formed in the strands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominated by one quantum dot, while additional resonances from parallel side dots appear, which exhibit a weak gate coupling. This differential gating effect provides a tunability of the quantum dot system with only one gate electrode and provides control over the carbon nanotube strand that carries the current. By tuning the system to different states we use quantum transport as a spectroscopic tool to investigate th…
We study electron transport through double quantum dots in series. The tunnel coupling of the discrete dot levels to external leads causes a shift of their energy. This energy renormalization affects the transport characteristics even in the limit of weak dot-lead coupling, when sequential transport dominates. We propose an experimental setup which reveals the renormalization effects in either the current-voltage characteristics or in the stability diagram.
We study the transport through evanescent waves in graphene quantum dots of different geometries. The transmission is suppressed when the leads are attached to edges of the same majority sublattice. Otherwise, the transmission depends exponentially on the distance between leads in rectangular dots, and as a power law in circular dots. The transmission through junctions where the transmitted and reflected currents belong to the opposite valley as the incoming one depends on details of the lattice structure at distances comparable to the atomic spacing.
We consider electronic transport through laterally parallel double open quantum dots embedded in a quantum wire in a perpendicular magnetic field. The coupling modes of the dots are tunable by adjusting the strength of a central barrier and the applied magnetic field. Probability density and electron current density are calculated to demonstrate transport effects including magnetic blocking, magnetic turbulence, and a hole-like quasibound state feature. Fano to dip line-shape crossover in the conductance is found by varying the magnetic field.
We derive a complete expression for the interaction correction to the $I-V$ curve of two connected in series metallic quantum dots. For strongly asymmetric dots in a wide range of parameters this interaction correction depends logarithmically on voltage and temperature.
Many electrical applications of quantum dots rely on capacitively coupled gates; therefore, to make reliable devices we need those gate capacitances to be predictable and reproducible. We demonstrate in silicon nanowire quantum dots that gate capacitances are reproducible to within 10% for nominally identical devices. We demonstrate the experimentally that gate capacitances scale with device dimensions. We also demonstrate that a capacitance simulator can be used to predict measured gate capacitances to within 20%. A simple parallel plate capacitor model can be used to predict how the capacita…
Strong spin-orbit interaction characteristic for p-type GaAs systems, makes such systems promising for the realization of spintronic devices. Here we report on transport measurements in nanostructures fabricated on p-type, C-doped GaAs heterostructures by scanning probe oxidation lithography. We observe conductance quantization in a quantum point contact, as well as pronounced Coulomb resonances in two quantum dots with different geometries. Charging energies for both dots, extracted from Coulomb diamond measurements are in agreement with the lithographic dimensions of the dots. The absence of…
We present Coulomb blockade measurements in a graphene double dot system. The coupling of the dots to the leads and between the dots can be tuned by graphene in-plane gates. The coupling is a non-monotonic function of the gate voltage. Using a purely capacitive model, we extract all relevant energy scales of the double dot system.
A large-N diagrammatic approach is used to study coupled quantum dots in a parallel geometry. We show that the Friedel sum rule (FSR) holds at lowest order in a 1/N expansion for this system, thereby suggesting that the ground state is a Fermi liquid. Using the FSR together with the dot occupancy, we compute the dot system's conductance. Our finding that the 1/N expansion indicates the system is a Fermi liquid is in agreement with both prior results based on the Bethe ansatz and slave boson mean field theory.
We argue through a combination of slave boson mean field theory and the Bethe ansatz that the ground state of closely spaced double quantum dots in parallel coupled to a single effective channel are Fermi liquids. We do so by studying the dots' conductance, impurity entropy, and spin correlation. In particularly we find that the zero temperature conductance is characterized by the Friedel sum rule, a hallmark of Fermi liquid physics, and that the impurity entropy vanishes in the limit of zero temperature, indicating the ground state is a singlet. This conclusion is in opposition to a number of…
The symmetry properties of transport beyond the linear regime in chaotic quantum dots are investigated experimentally. A component of differential conductance that is antisymmetric in both applied source-drain bias V and magnetic field B, absent in linear transport, is found to exhibit mesoscopic fluctuations around a zero average. Typical values of this component allow a measurement of the electron interaction strength.
Graphene quantum dots are considered as promising alternatives to quantum dots in III-V semiconductors, e.g., for the use as spin qubits due to their consistency made of light atoms including spin-free nuclei which both imply relatively long spin decoherene times. However, this potential has not been realized in experiments so far, most likely, due to a missing control of the edge configurations of the quantum dots. Thus, a more fundamental investigation of Graphene quantum dots appears to be necessary including a full control of the wave function properties most favorably during transport spe…
Spin-dependent transport through two coupled single-level quantum dots weakly connected to ferromagnetic leads with collinear magnetizations is considered theoretically. Transport characteristics, including the current, linear and nonlinear conductance, and tunnel magnetoresistance are calculated using the real-time diagrammatic technique in the parallel, serial, and intermediate geometries. The effects due to virtual tunneling processes between the two dots via the leads, associated with off-diagonal coupling matrix elements, are also considered. Negative differential conductance and negative…
We study transport through double quantum dots coupled to normal and superconducting leads, where the Andreev reflection plays a key role in determining characteristic transport properties. We shall discuss two typical cases, i.e. double dots with serial or parallel geometry. For the parallel geometry, the interference of electrons via multiple paths is induced, so that the transmission probability has Fano-type dip structures which are symmetric with respect to the Fermi energy. We also investigate the Aharonov-Bohm(AB) effect for the parallel geometry. In some particular situations, we find …
We derive the quantum rate equations for an Aharonov-Bohm interferometer with two vertically coupled quantum dots embedded in each of two arms by means of the nonequilibrium Green's function in the sequential tunneling regime. Basing on these equations, we investigate time-dependent resonant tunneling under a small amplitude irradiation and find that the resonant photon-assisted tunneling peaks in photocurrent demonstrate a combination behavior of Fano and Lorentzian resonances due to the interference effect between the two pathways in this parallel configuration, which is controllable by thre…
We study the spectrum and the transport properties of two identical, vertically coupled quantum dots in a perpendicular magnetic field. We find correlation-induced energy crossings in a magnetic field sweep between states differing only in the vertical degree of freedom. Considering the influence of a slight asymmetry between the dots caused by the applied source-drain voltage in vertical transport experiments these crossings convert to anticrossings accompanied by the build-up of charge polarization which is tunable by the perpendicular magnetic field. The polarization strongly affects the ve…
We theoretically investigate electron transport through an Aharonov-Bohm interferometer containing laterally coupled double quantum dots. We introduce the indirect coupling parameter $α$, which characterizes the strength of the coupling via the reservoirs between two quantum dots. $|α|=1$ indicates the strongest coupling, where only a single mode contributes to the transport in the system. Two conduction modes exist in a system where $|α|\neq 1$. The interference effects such as the Fano resonance and the Aharonov-Bohm oscillation are suppressed as the absolute value of the parameter $α$ decre…
We study the sub-gap spectrum and the transport properties of a double quantum dot coupled to metallic and superconducting leads. The coupling of both quantum dots to the superconducting lead induces a non-local pairing in both quantum dots by the Andreev reflection processes. Additionally, we obtain two channels of Cooper pair tunneling into a superconducting lead. In such a system, the direct tunneling process (by one of two dots) or the crossed tunneling process (by both quantum dots at the same time) is possible. We consider the dependence of the Andreev transmittance on an inter-dot tunne…
We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is two-dimensional with parabolic confinement in the transverse direction. In a broad wire the transport can assume a strong nonadiabatic character and the conductance manifests effects caused by intertwined inter- and intra-dot processes that are identified by analysis of the ``nearfield'' probability distribution of the transported electrons.
We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime the entangled dark state which corresponds to a singlet has a strongly enhanced Fano factor compared to the dark state which corresponds to a mixture of the triplet states. Furthermore we calculate the concurrence of the occupying electrons to show the degree of entanglement in the tra…
Motivated by recent experiments on electric transport through single molecules and quantum dots, we investigate a model for transport that allows for significant coupling between the electrons and a boson mode isolated on the molecule or dot. We focus our attention on the temperature dependent properties of the transport. In the Holstein picture for polaronic transport in molecular crystals the temperature dependence of the conductivity exhibits a crossover from coherent (band) to incoherent (hopping) transport. Here, the temperature dependence of the differential conductance on resonance does…
We report on theoretical studies of transport through graphene quantum dots weakly coupled to external ferromagnetic leads. The calculations are performed by exact diagonalization of a tight-binding Hamiltonian with finite Coulomb correlations for graphene sheet and by using the real-time diagrammatic technique in the sequential and cotunneling regimes. The emphasis is put on the role of graphene flake shape and spontaneous edge magnetization in transport characteristics, such as the differential conductance, tunneling magnetoresistance (TMR) and the shot noise. It is shown that for certain sh…
We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.
We study two double dot systems, one with dots in parallel and one with dots in series, and argue they admit an exact solution via the Bethe ansatz. In the case of parallel dots we exploit the exact solution to extract the behavior of the linear response conductance. The linear response conductance of the parallel dot system possesses multiple Kondo effects, including a Kondo effect enhanced by a nonpertubative antiferromagnetic RKKY interaction, has conductance zeros in the mixed valence regime, and obeys a non-trivial form of the Friedel sum rule.
We consider theoretically the transport through the double quantum dot structure of the recent experiment of C. Payette {\it et al.} [Phys. Rev. Lett. {\bf 102}, 026808 (2009)] and calculate stationary current and shotnoise. Three-level mixing gives rise to a pronounced current suppression effect, the character of which charges markedly with bias direction. We discuss these results in connexion with the dark states of coherent population trapping in quantum dots.
We present a detailed theoretical investigation of the effect of Coulomb interactions on electron transport through quantum dots and double barrier structures connected to a voltage source via an arbitrary linear impedance. Combining real time path integral techniques with the scattering matrix approach we derive the effective action and evaluate the current-voltage characteristics of quantum dots at sufficiently large conductances. Our analysis reveals a reach variety of different regimes which we specify in details for the case of chaotic quantum dots. At sufficiently low energies the intera…
Electronic transport through a triple quantum dot system, with only a single dot coupled directly to external leads, is considered theoretically. The model includes Coulomb correlations in the central dot, while such correlations in the two side-coupled dots are omitted. The infinite-U mean-field slave-boson approach is used to obtain basic transport characteristics in the Kondo regime. When tuning position of the side-coupled dots' levels, transition from subradiant to superradiant like mode (and vice versa) has been found in the spectral function, in analogy to the Dicke effect in atomic phy…
The effects of interplay between spin-orbit coupling and Zeeman splitting on weak localisation and universal conductance fluctuations in lateral semiconductor quantum dots are analysed: All possible symmetry classes of corresponding random matrix theories are listed and crossovers between them achievable by sweeping magnetic field and changing the dot parameters are described. We also suggest experiments to measure the spin-orbit coupling constants.
The role of non-equilibrium effects in the conductance through quantum dots is investigated. Associated with single-electron tunneling are shake-up processes and the formation of excitonic-like resonances. They change qualitatively the low temperature properties of the system. We analyze by quantum Monte Carlo methods the renormalization of the effective capacitance and the gate-voltage dependent conductance. Experimental relevance is discussed.
We systematically investigate electron transport through double quantum dots with particular emphasis on interference induced via multiple paths of electron propagation. By means of the slave-boson mean-field approximation, we calculate the conductance, the local density of states, the transmission probability in the Kondo regime at zero temperature. It is clarified how the Kondo-assisted transport changes its properties when the system is continuously changed among the serial, parallel and T-shaped double dots. The obtained results for the conductance are explained in terms of the Kondo reson…
We calculate the current correlations for the steady-state electron transport through multi-level parallel quantum dots embedded in a short quantum wire, that is placed in a non-perfect photon cavity. We account for the electron-electron Coulomb interaction, and the para- and diamagnetic electron-photon interactions with a stepwise scheme of configuration interactions and truncation of the many-body Fock spaces. In the spectral density of the temporal current-current correlations we identify all the transitions, radiative and non-radiative, active in the system in order to maintain the steady …
We show that the numerical method [M.E. Torio, K. Hallberg, A.H. Ceccatto, and C.R. Proetto, Phys. Rev. B 65, 085302 (2002), cond-mat/0108167v2] does not reproduce correctly the Kondo physics in quantum dot systems with interaction.
A fundamental question in quantum transport is how quantum coherence influences charge transfer through nanostructures. We address this issue for linear triple quantum dots by comparison of a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics for coherent and sequential charge tunneling, respectively. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of lar…
We investigate the Aharonov-Bohm (AB) effect for the double quantum dots in the Kondo regime using the slave-boson mean-field approximation. In contrast to the non-interacting case, where the AB oscillation generally has the period of 4$π$ when the two-subring structure is formed via the interdot tunneling $t_c$, we find that the AB oscillation has the period of 2$π$ in the Kondo regime. Such effects appear for the double quantum dots close to the T-shaped geometry even in the charge-fluctuation regime. These results follow from the fact that the Kondo resonance is always fixed to the Fermi le…
We investigate the Josephson effect in one triple-terminal junction with embedded parallel-coupled double quantum dots. It is found that the inter-superconductor supercurrent has opportunities to oscillate in $4π$ period, with the adjustment of the phase differences among the superconductors. What is notable is that such a result is robust and independent of fermion parities, intradot Coulomb strength, and the dot-superconductor coupling manner. By introducing the concept of spinful many-particle Majorana modes, we present the analytical definition of the Majorana operator via superposing elec…
We study transport through one or two ultrasmall quantum dots with discrete energy levels to which a time-dependent field is applied (e.g., microwaves). The AC field causes photon-assisted tunneling and also transitions between discrete energy levels of the dot. We treat the problem by introducing a generalization of the rotating-wave approximation to arbitrarily many levels. We calculate the dc-current through one dot and find satisfactory agreement with recent experiments by Oosterkamp et al. . In addition, we propose a novel electron pump consisting of two serially coupled single-level quan…
We report transport measurements as a function of bias in open semiconductor quantum dots. These measurements are well described by an effective electron temperature derived from Joule heating at the point contacts and cooling by Wiedemann-Franz out-diffusion of thermal electrons. Using this model, we propose and analyze a quantum dot based sensor which measures absolute magnetic field at micron scales with a noise floor of $\sim 50 μϕ_{0} / \sqrt{Hz}$ at 300 mK.
We study shot noise for generic quantum dots coupled to two leads and allow for an arbitrary strength of diffractive impurity scattering inside the dots. The ballistic quantum dots possess a mixed classical phase space, where regular and chaotic regions coexist. In absence of disorder, the noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. This suppression is due to the deterministic nature of transport through regular regions and along short chaotic trajectories, and disappears by increasing the sca…
We show that two intriguing features of mesoscopic transport, namely the modulation of Coulomb blockade peak-heights and the transmission phase-lapses occurring between subsequent peaks, are closely related. Our analytic arguments are corroborated by numerical simulations for chaotic ballistic quantum dots. The correlations between the two properties are experimentally testable. The statistical distribution of the partial-width amplitude, at the heart of the previous relationship, is determined, and its characteristic parameters are estimated from simple models.
We investigated electron transport through ultra small Si quantum dots. We found that the $B$-dependence of energy levels is dominated by the Zeeman shift, allowing us to measure the spin difference between two successive ground states directly. In some dots the number of electrons N in the dot can be tuned starting from zero, and the total spin of the dot can be mapped as a function of N and B. For one of the dots we deduced that the dot becomes spontaneously polarized at N=6 with a large spin change ΔS=3/2, demonstrating the essential features of spin blockade. Surprisingly, for N>20, the tr…
Strong electron correlations and interference effects are discussed in parallel-coupled single-level and orbitally doubly degenerate quantum dots. The finite-U mean-field slave boson approach is used to study many-body effects. The analysis is carried out in a wide range of parameter space including both atomic-like and molecular-like Kondo regimes and taking into account various perturbations, like interdot tunneling, interdot interaction, mixing of the electrode channels and exchange interaction. We also discuss the influence of singularities of electronic structure and the impact of polariz…
Spin-dependent electronic transport through a quantum dot side-coupled to two quantum dots and attached to ferromagnetic leads with collinear (parallel and antiparallel) magnetizations is analyzed theoretically. The intra-dot Coulomb correlations are taken into account, whereas the inter-dot ones are neglected. Transport characteristics, i.e. conductance and tunnel magnetoresistance associated with the magnetization rotation from parallel to antiparallel configurations, are calculated by the noneqiulibrium Green function technique. The Green functions are derived by the equation of motion meth…
We describe the electronic properties of a double dot for which the lateral coupling between the two vertical dots can be controlled in-situ with a center gate voltage (Vc) and the current flows through the two dots in series. When Vc is large and positive, the two dots merge. As Vc is made less positive, two dots are formed whose coupling is reduced. We measure charging diagrams for positive and negative source-drain voltages in the weak coupling regime and observe current rectification due to the Pauli spin blockade when the hyperfine interaction between the electrons and the nuclei is suppr…
We examine the charge transport through disordered arrays of metallic dots using numerical simulations. We find power law scaling in the current-voltage curves for arrays containing no voids, while for void-filled arrays charge bottlenecks form and a single scaling is absent, in agreement with recent experiments. In the void-free case we also show that the scaling exponent depends on the effective dimensionality of the system. For increasing applied drives we find a transition from 2D disordered filamentary flow near threshold to a 1D smectic flow which can be identified experimentally using c…
We show how the in-plane magnetic field, which breaks time-reversal and rotational symmetries of the orbital motion of electrons in a heterostructure due to the momentum-dependent inter-subband mixing, affects weak localisation correction to conductance of a large-area chaotic lateral quantum dot and parameteric dependences of universal conductance fluctuations in it.
Quantum dots are fabricated in a Ga[Al]As-heterostructure by local oxidation with an atomic force microscope. This technique, in combination with top gate voltages, allows us to generate steep walls at the confining edges and small lateral depletion lengths. The confinement is characterized by low-temperature magnetotransport measurements, from which the dots' energy spectrum is reconstructed. We find that in small dots, the addition spectrum can qualitatively be described within a Fock-Darwin model. For a quantitative analysis, however, a hard-wall confinement has to be considered. In large d…
We investigate electronic transport through parallel double quantum dot(DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying numerical renormalization group(NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin 1 triplet state. The linear conductance will reach the unitary limit ($2e^2/h$) due …
I reply to the new arguments of Muñoz et al. (arXiv:1308.0638) regarding our controversy on non-equilibrium Green functions of the impurity Anderson model, and to new unfounded criticism to my paper Ref. 1 (arXiv:1110.0816). In particular, I show that the lesser self energy given in Ref. 1 does satisfy a Ward identity. References are updated.
The particle transport through a chain of quantum dots coupled to two bosonic reservoirs is studied. For the case of reservoirs of non-interacting bosonic particles, we derive an exact set of stochastic differential equations, whose memory kernels and driving noise are characterised entirely by the properties of the reservoirs. Going to the Markovian limit an analytically solvable case is presented. The effect of interparticle interactions on the transient behaviour of the system, when both reservoirs are instantaneously coupled to an empty chain of quantum dots, is approximated by a semiclass…
In traditional approaches of obtaining quantized acoustoelectric current, a narrow channel is fabricated to form quantum dots, which hold a fixed number of electrons at a certain depth. We propose a natural way of forming quantum dots without the narrow channel, by the interference of two surface acoustic waves (SAWs) propagating across each other. A wide transportation area is defined by the usual (but widely separated) split-gate structure with another independent gate in between. This design can increase the quantized current by one to two orders of magnitude. The three-gate structure also …
We investigate antilocalization due to spin-orbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spin-orbit coupling in dots is demonstrated as a gate-controlled crossover from weak localization to antilocalization.
We study spectral and transport properties of interacting quantum dots with spin. Two particular model systems are investigated: Lateral multilevel and two parallel quantum dots. In both cases different paths through the system can give rise to interference. We demonstrate that this strengthens the multilevel Kondo effect for which a simple two-stage mechanism is proposed. In parallel dots we show under which conditions the peak of an interference-induced orbital Kondo effect can be split.
