Transport via coupled states in a C60 peapod quantum dot
Anders Eliasen, Jens Paaske, Karsten Flensberg, Sebastian Smerat, Martin Leijnse, Maarten R. Wegewijs, Henrik I. Jørgensen, Marc Monthioux, Jesper Nygård
We have measured systematic repetitions of avoided crossings in low temperature three-terminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The well-defined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube.
Fullerene peapods, that is carbon nanotubes encapsulating fullerene molecules, can offer enhanced functionality with respect to empty nanotubes. However, the present incomplete understanding of how a nanotube is affected by entrapped fullerenes is an obstacle for peapods to reach their full potential in nanoscale electronic applications. Here, we investigate the effect of C60 fullerenes on electron transport via peapod quantum dots. Compared to empty nanotubes, we find an abnormal temperature dependence of Coulomb blockade oscillations, indicating the presence of a nanoelectromechanical coupli…
We report encapsulated C60 molecules on electron transport in carbon-nanotube peapod quantum dots. We find atomic-like behaviors with doubly degenerate electronic levels, which exist only around ground states, by single electron spectroscopy measured at low back-gate voltages (Vbg's). Correlation with presence of nearly free electrons (NFEs) unique to the peapods is discussed. In contrast, we find that encapsulated C60 molecules do not affect to single charging effect. Moreover, we find anomalously high values of powers observed in power laws in conductance versus energy relationships, which a…
The influence of a fullerene molecule trapped inside a single-wall carbon nanotube on resonant electron transport at low temperatures and strong polaronic coupling is theoretically discussed. Strong peak to peak fluctuations and anomalous temperature behavior of conductance amplitudes are predicted and investigated. The influence of the chiral properties of carbon nanotubes on transport is also studied.
We measure the conductance of carbon nanotube peapods from room temperature down to 250mK. Our devices show both metallic and semiconducting behavior at room temperature. At the lowest temperatures, we observe single electron effects. Our results suggest that the encapsulated C$_{60}$ molecules do not introduce substantial backscattering for electrons near the Fermi level. This is remarkable given that previous tunneling spectroscopy measurements show that encapsulated C$_{60}$ strongly modifies the electronic structure of a nanotube away from the Fermi level.
We present an advanced lateral triple quantum dot made by local anodic oxidation. Three dots are coupled in a starlike geometry with one lead attached to each dot thus allowing for multiple path transport measurements with two dots per path. In addition charge detection is implemented using a quantum point contact. Both in charge measurements as well as in transport we observe clear signatures of states from each dot. Resonances of two dots can be established allowing for serial transport via the corresponding path. Quadruple points with all three dots in resonance are prepared for different e…
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 effect of a dot-lead interaction on transport through a quantum dot hybridized to two semi-infinite Luttinger-liquid leads. A bosonization approach is applied to treat the interaction between charge fluctuations on the dot and the dynamically generated image charge in the leads. The nonequilibrium distribution function of the dot and the tunneling current are computed within a master-equation approach. The presence of the excitonic dot-lead coupling is found to enhance transport in the vicinity of the Coulomb-blockade threshold. This behavior is in contrast to the usual power-law …
The work of the Lublin group on the non-equillibrium transport through the quantum dot coupled to external leads (normal or superconducting) and subject to external time dependent fields has been reviewed.
We investigate a double quantum dot coupled to a transmission line resonator. By driving a current through the double dot, a population inversion between the dot levels can be created, and a lasing state of the radiation field is generated within a sharp resonance window. The transport current correlates with the lasing state. The sharp resonance condition allows for resolving small differences in the dot properties. Dissipative processes in the quantum dots and their effect on the lasing and transport behavior are investigated.
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…
Contents: (1) Model of a lateral quantum dot system (2) Thermally-activated conduction: onset of the Coulomb blockade oscillations and Coulomb blockade peaks at low temperature (3) Activationless transport through a blockaded quantum dot: inelastic and elastic co-tunneling (4) Kondo regime in transport through a quantum dot: effective low-energy Hamiltonian; linear response; weak coupling regime; strong coupling regime; beyond linear response; splitting of the Kondo peak in a magnetic field; Kondo effect in quantum dots with large spin.
In the present work we theoretically study thermoelectric transport and heat transfer in a junction including a $T$-shaped double quantum dot coupled to nonmagnetic electrodes and supplemented with a third dot in a parallel configuration. We focus on the combined effect of Coulomb interactions and quantum interference occurring in the $T$-shaped portion of the considered triple quantum dot on the thermoelectric electron transport. The transport through the system is studied within the Coulomb blockade regime in the limit of strong intra-dot interactions between electrons beyond the linear resp…
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.
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…
We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the interplay between strong electron-phonon coupling and inter-dot tunneling can lead to a negative differential conductance at bias voltages exceeding the phonon frequency. Various transport properties are discussed, and we explain the physics of the occurrence of negative differential conductance in this system.
We investigate sequential tunneling transport through a semiconductor double quantum dot structure by combining a simple microscopic quantum confinement model with a Mott-Hubbard type correlation model. We calculate nonperturbatively the evolution of the Coulomb blockade oscillations as a function of the interdot barrier conductance, obtaining good qualitative agreement with the experimental data over the whole tunneling regime from the weak-coupling individual dot to the strong-coupling coherent double-dot molecular system.
We report the inclusion of phonon scattering to our recently established numerical package QmeQ for transport in quantum dot systems. This enables straightforward calculations for a large variety of devices. As examples we show (i) transport in a double-dot structure, where energy relaxation is crucial to match the energy difference between the levels, and (ii) the generation of electrical power by contacting cold electric contacts with quantum dot states, which are subjected to heated phonons.
Spin-dependent transport through a two-level quantum dot in the sequential tunneling regime is analyzed theoretically by means of a real-time diagrammatic technique. It is shown that the current, tunnel magnetoresistance, and shot noise (Fano factor) strongly depend on the transport regime, providing a detailed information on the electronic structure of quantum dots and their coupling to external leads. When the dot is asymmetrically coupled to the leads, a negative differential conductance may occur in certain bias regions, which is associated with a super-Poissonian shot noise. In the case o…
Studies of electronic charge transport through semiconductor double quantum dots rely on a conventional "hole" model of transport in the three-electron regime. We show that experimental measurements of charge transport through a Si double quantum dot in this regime cannot be fully explained using the conventional picture. Using a Hartree-Fock (HF) formalism and relevant HF energy parameters extracted from transport data in the multiple-electron regime, we identify a novel spin-flip cotunneling process that lifts a singlet blockade.
We investigate theoretically electron transfer in a doble dot in a situation where it is governed by nuclear magnetic field: This has been recently achieved in experiment. We show how to partially compensate the nuclear magnetic field to restore Spin Blockade.
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…
A transport methodology to study the electron transport between quantum dots arrays based in Transfer Hamiltonian approach is presented. The interactions between the quantum dots and between the quantum dots and the electrodes are introduced by transition rates and capacitive couplings. The effects of the local potential are computed within the self-consistent field regime. The model has been developed and expressed in a matrix form in order to make it extendable to larger systems. Transport through several quantum dot configurations have been studied in order to validate the model. Despite th…
We study the transport through side-coupled double quantum dots, connected to normal and superconducting (SC) leads with a T-shape configuration. We find, using the numerical renormalization group, that the Coulomb interaction suppresses SC interference in the side dot, and enhances the conductance substantially in the Kondo regime. This behavior stands in total contrast to a wide Kondo valley seen in the normal transport. The SC proximity penetrating into the interfacial dot pushes the Kondo clouds, which screens the local moment in the side dot, towards the normal lead to make the singlet bo…
We show that the coherence of charge transfer through a weakly coupled double-dot dimer can be determined by analyzing the statistics of the conductance pattern, and does not require large phase coherence length in the host material. We present an experimental study of the charge transport through a small Si nanostructure, which contains two quantum dots. The transport through the dimer is shown to be coherent. At the same time, one of the dots is strongly coupled to the leads, and the overall transport is dominated by inelastic co-tunneling processes.
We report low-temperature transport spectroscopy of a graphene quantum dot fabricated by atomic force microscope nanolithography. The excellent spatial resolution of the atomic force microscope allows us to reliably fabricate quantum dots with short constrictions of less than 15 nm in length. Transport measurements demonstrate that the device is dominated by a single quantum dot over a wide gate range. The electron spin system of the quantum dot is investigated by applying an in-plane magnetic field. The results are consistent with a Lande g-factor of 2 but no regular spin filling sequence is …
We suggest a series of transport experiments on spin precession in quantum dots coupled to one or two ferromagnetic leads. Dot spin states are created by spin injection and analyzed via the linear conductance through the dot, while an applied magnetic field gives rise to the Hanle effect. Such a Hanle experiment can be used to determine the spin lifetime in the quantum dot, to measure the spin injection efficiency into the dot, as well as proving the existence of intrinsic spin precession which is driven by the Coulomb interaction.
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 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 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 report a study of transport blockade features in a quantum dot single-electron transistor, based on an undoped AlGaAs/GaAs heterostructure. We observe suppression of transport through the ground state of the dot, as well as negative differential conductance at finite source-drain bias. The temperature and magnetic field dependence of these features indicate the couplings between the leads and the quantum dot states are suppressed. We attribute this to two possible mechanisms: spin effects which determine whether a particular charge transition is allowed based on the change in total spin, an…
We predict a new zero-bias anomaly in the differential conductance through a quantum dot coupled to two ferromagnetic leads with antiparallel magnetization. The anomaly differs in origin and properties from other anomalies in transport through quantum dots, such as the Kondo effect. It occurs in Coulomb-blockade valleys with an unpaired dot electron. It is a consequence of the interplay of single- and double-barrier cotunneling processes and their effect on the spin accumulation in the dot. The anomaly becomes significantly modified when a magnetic field is applied.
We study the nonequilibrium spin current through a quantum dot consisting of two localized spin-1/2 coupled to two ferromagnetic insulators. The influence of an intra-dot magnetic field and exchange coupling, different dot-reservoir coupling configurations, and the influence of magnon chemical potential differences vs. magnetic field gradients onto the spin current are examined. We discuss various spin switching mechanisms and find that, in contrast to electronic transport, the spin current is very sensitive to the specific coupling configuration and band edges. In particular, we identify 1- a…
We develop a theory of electron transport through quantum dots that are weakly coupled to ferromagnetic leads. The theory covers both the linear and nonlinear transport regime, takes non-collinear magnetization of the leads into account, and allows for an externally-applied magnetic field. We derive generalized rate equations for the dot's occupation and accumulated spin and discuss the influence of the dot's spin on the transmission. A negative differential conductance and a nontrivial dependence of the conductance on the angle between the lead magnetizations is predicted.
We study the effect of an external magnetic field on the transport properties of a quantum dot using a recently developed extension of the functional renormalization group approach to non-equilibrium situations. We discuss in particular the interplay and competition of the different energy scales of the dot and the magnetic field on the stationary non-equilibrium current and conductance. As rather interesting behavior we find a switching behavior of the magnetic field for intermediate correlations and bias voltage.
We present a Green's function based treatment of the effects of electron-phonon coupling on transport through a molecular quantum dot in the quantum limit. Thereby we combine an incomplete variational Lang-Firsov approach with a perturbative calculation of the electron-phonon self energy in the framework of generalised Matsubara Green functions and a Landauer-type transport description. Calculating the ground-state energy, the dot single-particle spectral function and the linear conductance at finite carrier density, we study the low-temperature transport properties of the vibrating quantum do…
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 achie…
The effect of electron-phonon coupling on transport through a pair of strongly correlated quantum dots embedded in the Aharonov-Bohm ring is considered in the mean field slave boson Kotliar-Ruckenstein approach. It is shown that coupling with phonons opens transport gap in the region of double occupancy. Low-bias conductance and thermopower provide information on electron-phonon coupling strength.
We present a detailed study of the surface acoustic wave mediated quantized transport of electrons through a split gate device containing an impurity potential defined quantum dot within the split gate channel. A new regime of quantized transport is observed at low RF powers where the surface acoustic wave amplitude is comparable to the quantum dot charging energy. In this regime resonant transport through the single-electron dot state occurs which we interpret as turnstile-like operation in which the traveling wave amplitude modulates the entrance and exit barriers of the quantum dot in a cyc…
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 study the influence of spin polarization on the degree of coherence of electron transport through interacting quantum dots. To this end, we identify transport regimes in which the degree of coherence can be related to the visibility of the Aharonov-Bohm oscillations in the current through a quantum-dot Aharonov-Bohm interferometer with one normal and one ferromagnetic lead. For these regimes, we calculate the visibility and, thus, the degree of coherence, as a function of the degree of spin polarization of the ferromagnetic lead.
A few electron double electrostatic lateral quantum dot can be transformed into a few electron triple quantum dot by applying a different combination of gate voltages. Quadruple points have been achieved at which all three dots are simultaneously on resonance. At these special points in the stability diagram four occupation configurations are possible. Both charge detection and transport experiments have been performed on this device. In this short paper we present data and confirm that transport is coherent by observing a Pi phase shift in magneto-conductance oscillations as one passes throug…
Correlation effects on electron transport through a system of T-shaped double-dots are investigated, for which only one of the dots is directly connected to the leads. We evaluate the local density of states and the conductance by means of the non-crossing approximation at finite temperatures as well as the slave-boson mean field approximation at zero temperature. It is found that the dot which is not directly connected to the leads considerably influences the conductance, making its behavior quite different from the case of a single-dot system. In particular, we find a novel phenomenon in the…
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.
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 have studied low-temperature single electron transport through ultra-small Si quantum dots. We find that at low temperatures Coulomb blockade is partially lifted at certain gate voltages. Furthermore, we observed an enhancement of differential conductance at zero bias. The magnetic field dependence of this zero bias anomaly is very different from the one reported in GaAs quantum dots, inconsistent with predictions for the Kondo effect.
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 study the coherent transport in multi-terminal mesoscopic Aharonov-Bohm ring with a quantum dot embedded in an arm. Employing the Friedel sum rule for the effective single-particle levels in the quantum dot, we explain some anomalous features which have been observed in the experiment. We attribute these anomalies to the result of nontrivial quantum interference of the quantum dot with the attached ring. Further, we propose a new feature of conductance oscillations which can be a test for the validity of our model.
We report on non-adiabatic transport through a double quantum dot under irradiation of surface acoustic waves generated on-chip. At low excitation powers, absorption and emission of single and multiple phonons is observed. At higher power, sequential phonon assisted tunneling processes excite the double dot in a highly non-equilibrium state. The present system is attractive for studying electron-phonon interaction with piezoelectric coupling.
Nonequilibrium steady states are explicitly constructed for a noninteracting electron model of an Aharonov-Bohm (AB) ring with a quantum dot (QD) with the aid of asymptotic fields. The Fano line shapes and AB oscillations are shown to strongly depend on the bias voltage. Current fluctuations are studied as well.
A strong coupling between an electronic cavity and a quantum dot has been recently demonstrated [Phys. Rev. Lett. 115, 166603 (2015)] and described in a comprehensive theoretical framework [Phys. Rev. B 96, 235431 (2017)]. Here, we focus on the signatures that demonstrate the cavity's impact on inelastic singlet-triplet transport through the dot. We find the same transport signatures in the experiment as predicted by the model that describes the coupled dot--cavity system. Interestingly, a lowest-order treatement of the coupling to the electronic leads on top of an exact diagonalisation of the…
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.
We consider the time-dependent electron transport through a quantum dot coupled to two leads in the presence of the additional over-dot (bridge) tunneling channel. By using the evolution operator method together with the wide-band limit approximation we derived the analytical formulaes for the quantum dot charge and current flowing in the system. The influence of the external microwave field on the time-average quantum dot charge, the current and the derivatives of the average current with respect to the gate and source-drain voltages has been investigated for a wide range of parameters.
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.
Starting with the many-body Schrödinger equation we derive new rate equations for resonant transport in quantum dots linked by ballistic channels with high density of states. The charging and the Pauli exclusion principle effects were taken into account. It is shown that the current in such a system displays quantum coherence effects, even if the dots are away one from another. A comparative analysis of quantum coherence effects in coupled and separated dots is presented. The rate equations are extended for description of coherent and incoherent transport in arbitrary multi-dot systems. It is …
Electron transport properties of few-electron open quantum dots within the spin-restricted Hartree-Fock approximation are studied. The self-consistent numerical calculations were performed for a whole device, including the semi-infinite leads, without employing any phenomenological or adjustable parameters. Inclusion of the non-local Fock potential brings qualitatively new physics in comparison to the Hartree approach: electron screening decreases, resonant energy levels become less pinned to the Fermi energy and clearly correlate with conductance peaks. When coupling between the dot and leads…
Electron transport experiments on two lateral quantum dots coupled in series are reviewed. An introduction to the charge stability diagram is given in terms of the electrochemical potentials of both dots. Resonant tunneling experiments show that the double dot geometry allows for an accurate determination of the intrinsic lifetime of discrete energy states in quantum dots. The evolution of discrete energy levels in magnetic field is studied. The resolution allows to resolve avoided crossings in the spectrum of a quantum dot. With microwave spectroscopy it is possible to probe the transition fr…
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.
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 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 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…
