Elastic Cotunneling Research Articles

Residual Kondo effect in quantum dot coupled to half-metallic ferromagnets

We study the Kondo effect in a quantum dot coupled to half-metallic ferromagneticelectrodes in the regime of strong on-dot correlations. Using the equation of motiontechnique for non-equilibrium Green functions in the slave boson representation, we showthat the Kondo effect is not completely suppressed for anti-parallel magnetization of theleads. In the parallel configuration, there is no Kondo effect but there is an effect associatedwith elastic co-tunnelling which, in turn, leads to similar behaviour of the local (on-dot)density of states (LDOS) as the usual Kondo effect. Namely, the LDOS shows thetemperature-dependent resonance at the Fermi energy, which splits with the bias voltageand the magnetic field. Moreover, unlike for non-magnetic or not fully polarizedferromagnetic leads, only the minority spin electrons can form such resonance in thedensity of states. However, this resonance cannot be observed directly in the transportmeasurements, and we give some clues how to identify the effect in such systems.

Contribution of weak localization to nonlocal transport at normal metal/superconductor double interfaces

In connection with a recent experiment [Russo {\it et al.}, Phys. Rev. Lett. {\bf 95}, 027002 (2005)], we investigate the effect of weak localization on non local transport in normal metal / insulator / superconductor / insulator / normal metal (NISIN) trilayers, with extended interfaces. The negative weak localization contribution to the crossed resistance can exceed in absolute value the positive elastic cotunneling contribution if the normal metal phase coherence length or the energy are large enough.

Antilocalization in Coulomb blockade

We study the effect of spin-orbit scattering on the statistics of the conductance of a quantum dot for Coulomb blockade peaks and valleys. We find the distribution function of the peak heights for strong spin-orbit scattering in the presence and absence of time reversal symmetry. We find that the application of a magnetic field suppresses the average peak height, similar to the antilocalizaion in the bulk systems. For the valleys, we consider the elastic cotunneling contribution to the conductance and calculate its moments at the crossover between ensembles of various symmetries.

Phase Coherence in the Inelastic Cotunneling Regime

Two quantum dots with tunable mutual tunnel coupling have been embedded in a two-terminal Aharonov-Bohm geometry. Aharonov-Bohm oscillations investigated in the cotunneling regime demonstrate coherent tunneling through nonresonant states. Visibilities of more than 0.8 are measured indicating that phase-coherent processes are involved in the elastic and inelastic cotunneling. An oscillation-phase change of pi is detected as a function of bias voltage at the inelastic cotunneling onset.

Coulomb effects and hopping transport in granular metals

We investigate effects of Coulomb interaction and hopping transport in the insulator phase of granular metals and quantum dot arrays. We consider a spatially periodic as well as an irregular array, including disorder in a form of a random on-site electrostatic potential. We study the Mott transition between the insulating and metallic states in the regular system and find the dependence of the Mott gap upon the intergranular coupling. The conductivity of a strictly periodic array has an activation form with the Mott gap as an activation energy. Considering irregular systems we concentrate on the transport properties in the dielectric, low coupling limit and derive the Efros-Shklovskii law for hopping conductivity. In the irregular arrays electrostatic disorder results in the finite density of states on the Fermi level giving rise to the variable range hopping mechanism. We develop a theory of tunneling through a chain of grains and discuss in detail both elastic and inelastic cotunneling mechanisms; the former dominates at very low temperatures and/or very low applied electric fields, while the inelastic mechanism controls tunneling at high temperature/fields. Our results are obtained within the framework of the new technique based on the mapping of quantum electronic problem onto the classical gas of Coulomb charges. The processes of quantum tunnelling of real electrons are represented in this technique as trajectories (world lines) of charged classical particles in $d+1$ dimensions. The Mott gap is related to the dielectric susceptibility of the Coulomb gas in the direction of the imaginary time axis.

Experimental Observation of Bias-Dependent Nonlocal Andreev Reflection

We investigate transport through hybrid structures consisting of two normal metal leads connected via tunnel barriers to one common superconducting electrode. We find clear evidence for the occurrence of nonlocal Andreev reflection and elastic cotunneling through a superconductor when the separation of the tunnel barrier is comparable to the superconducting coherence length. The probability of the two processes is energy dependent, with elastic cotunneling dominating at low energy and nonlocal Andreev reflection at higher energies. The energy scale of the crossover is found to be the Thouless energy of the superconductor, which indicates the phase coherence of the processes. Our results are relevant for the realization of recently proposed entangler devices.

Correlations of spin currents through a quantum dot induced by the Kondo effect

We study correlations of spin currents flowing through a Coulomb blockaded quantum dot. While they vanish for generic parameter values in the regime of elastic cotunneling, these correlations develop as the quantum dot enters the Kondo regime. We analyze this effect for a small effective Kondo coupling such that fluctuations of the spin of the quantum dot can be captured by the perturbative renormalization group. Even in this regime we find that---unlike the mean current---the spin current correlator is not accessible by perturbation theory. It is nonperturbative in the effective coupling of the QD to the leads.

Sign of the crossed conductances at a ferromagnet/superconductor/ferromagnet double interface

Crossed conductance in hybrid Ferromagnet / Superconductor / Ferromagnet (FSF) structures results from the competition between normal transmission and Andreev reflection channels. Crossed Andreev reflection (CAR) and elastic cotunneling (EC) between the ferromagnets are dressed by local Andreev reflections, which play an important role for transparent enough interfaces and intermediate spin polarizations. This modifies the simple result previously obtained at lowest order, and can explain the sign of the crossed resistances in a recent experiment [D. Beckmann {\sl et al.}, cond-mat/0404360]. This holds both in the multiterminal hybrid structure model (where phase averaging over the Fermi oscillations is introduced ``by hand'' within the approximation of a single non local process) and for infinite planar interfaces (where phase averaging naturally results in the microscopic solution with multiple non local processes).

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

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

Transport properties of ferromagnet-d-wave superconductor ferromagnet doublejunctions

We investigate transport properties of a trilayer made of a d-wave superconductorconnected to two ferromagnetic electrodes. Using Keldysh formalism we showthat crossed Andreev reflection and elastic cotunnelling exist also withd-wave superconductors. Their properties are controlled by the existence ofzero-energy states due to the anisotropy of the d-wave pair potential.

Electron dynamics of an artificial atom probed by pulsed microwave spectroscopy

Using picosecond millimetre-wave impulses we probe the electronic structure anddynamics of electrons in a single quantum dot—the artificial atom—which isessential for understanding their applications such as computational elements anddetectors. Although dc transport shows strong elastic cotunnelling in theCoulomb blockade (CB) regime, this effect is suppressed under picosecondimpulses whose energies are commensurate with those of the dot. Undernon-zero bias we find excited-state resonances in the induced complexphotoconductance as well as strong deviations of the dot capacitancecompared to equilibrium values according to the ‘orthodox model’ of CB,a direct signature of the relaxation times of single-electron tunnelling.

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that it can be well represented by averaging out the phase of the electronic wave function. The maximal conductance of a two-channel contact is proportional to $(e^2/h) (a_0/D)^2 \exp{[-D/\xi(\omega^*)]}$, where $D$ is the distance between the contacts, $a_0$ the lattice spacing, $\xi(\omega)$ is the superconducting coherence length, and $\omega^*$ is the cross-over frequency between a perturbative regime ($\omega< \omega^*$) and a non perturbative regime ($\omega^* < \omega < \Delta$). The intercontact Andreev reflection and elastic cotunneling conductances are not equal if the electronic phases take a fixed value. However, these two quantities do coincide if one can average out the electronic phase. The equality between the Andreev and cotunneling conductances is also valid in the presence of at least one extended contact in which the phases take deterministic values.

Electron dynamics of a single quantum dot probed with wideband millimeter-wave spectroscopy

We perform microwave spectroscopy on a single quantum dot using a compact pulsed spectrometer. Although DC transport shows strong elastic cotunneling in the Coulomb blockade regime and inelastic tunneling in the single-electron tunneling (SET) regime, these effects are suppressed under picosecond impulses whose energies are commensurate with those of the dot. Instead, under non-zero bias we find excited-state resonances in the induced complex photoconductance as well as strong deviations of the dot capacitance compared to equilibrium values, a signature of the effective relaxation times of SET.

Noise of a quantum dot system in the cotunneling regime

We study the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum dot systems (QDS) with few-level, nearly degenerate, and continuous electronic spectra. We find that in contrast to sequential tunneling, where the noise is either Poissonian (due to uncorrelated tunneling events) or sub-Poissonian (suppressed by charge conservation on the QDS), the noise in inelastic cotunneling can be super-Poissonian due to switching between QDS states carrying currents of different strengths. In the case of weak cotunneling we prove a nonequilibrium fluctuation-dissipation theorem, which leads to a universal expression for the noise-to-current ratio (Fano factor). In order to investigate strong cotunneling we develop a microscopic theory of cotunneling based on the density-operator formalism and using the projection operator technique. The master equation for the QDS and the expressions for current and noise in cotunneling in terms of the stationary state of the QDS are derived and applied to QDS with a nearly degenerate and continuous spectrum.

Mesoscopic fluctuations of tunneling and cotunneling in quantum dots

Recent measurements of mesoscopic tunneling and cotunneling fluctuations in Coulomb blockaded ballistic quantum dots are presented. The statistics and parametric fluctuations (as a function of magnetic field) of Coulomb blockade peak heights are found to be consistent with random-matrix-theory predictions. Mesoscopic fluctuations of elastic cotunneling, measured in the valleys between blockade peaks, are also presented along with a semiclassical explanation of the observed enhancement of the magnetic field scale of cotunneling fluctuations compared to resonant tunneling fluctuations.

Mesoscopic Fluctuations of Elastic Cotunneling in Coulomb Blockaded Quantum Dots

We report measurements of mesoscopic fluctuations of elastic cotunneling in Coulomb blockaded quantum dots. Unlike resonant tunneling on Coulomb peaks, cotunneling in the valleys is sensitive to charging effects. We observe a larger magnetic field scale for the cotunneling (valley) fluctuations compared to the peaks, as well as an absence of "weak localization" (reduced conductance at B = 0) in valleys. Cotunneling fluctuations remain correlated over several valleys while peak conductance correlations decreases quickly.

Effect of quantum confinement on electron tunneling through a quantum dot

Employing the Anderson impurity model, we study tunneling properties through an ideal quantum dot near the conductance minima. Considering the Coulomb blockade and the quantum confinement on an equal footing, we have obtained current contributions from various types of tunneling processes; inelastic cotunneling, elastic cotunneling, and resonant tunneling of thermally activated electrons. We have found that the inelastic cotunneling is suppressed in the quantum confinement limit, and thus the conductance near its minima is determined by the elastic cotunneling at low temperature ($k_BT \ll \Gamma$, $\Gamma$: dot-reservoir coupling constant), or by the resonant tunneling of single electrons at high temperature ($k_BT \gg \Gamma$).

Mesoscopic Fluctuations of Elastic Cotunneling.

We study mesoscopic fluctuations of the conductance through a quantum dot at the wings of the Coulomb blokade peaks. At low temperatures, the main mechanism of conduction is the elastic cotunneling. The conductance strongly fluctuates with an applied magnetic field. The magnetic correlation field is shown to be controlled by the charging energy, and the correlation function has a universal form. The distribution function for the conductance obtained analytically shows a non-trivial crossover between the orthogonal and unitary ensembles.

Elastic co-tunneling in a 1D quantum hole approach

The influence of the phases of tunneling matrix elements on the rate of the elastic co-tunneling at an ultrasmall normal-conducting double junction is studied in a simple quantum hole approach at zero temperature. The results are compared with experimental data.

Coulomb blockade and off-resonance tunneling in small electronic systems

The minima of the oscillations of the tunnel conductance through a small electronic system present a rich variety of quantum conduction mechanisms when the charging energy E c and the electrochemical potential difference eV between the resevoirs compete with the single particle energy level separation Δ. We emphasize the strong relation between off-resonance tunneling and elastic co-tunneling in the linear conductance regime while, in the non-linear regime, inelastic co-tunneling has no equivalent for the case of resonant tunneling. We also review the recent experimental results which clearly identify this latter regime and we discuss the intermediate regime, valid for few electron systems, where E c ⋍ Δ.