Elastic Cotunneling Research Articles

Crossed Andreev reflection on a topological insulator

The nonlocal transport properties of a ferromagnet/superconductor/ferromagnet junction formed on the surface of a three-dimensional topological insulator are investigated. It is found the electron elastic cotunneling and crossed Andreev reflection depend sensitively on the directions of the magnetizations of the two ferromagnets. The basic mechanism behind this effect is that due to the translation invariant along the y-axis, during the tunneling the wave-vector ky of the incident electron must be conserved. The effects of the superconductor length and the bias voltage on the electron elastic cotunneling and crossed Andreev reflection are discussed. If the exchange field is larger than the chemical potential in the ferromagnet leads, a perfect electron elastic cotunneling or crossed Andreev reflection can be obtained in the low-energy regime by varying the magnetization direction in one of the ferromagnet leads.

Thermal Conductance by the Inverse Proximity Effect in a Superconductor

We study heat transport in hybrid lateral normal-metal-superconductor-normal-metal structures. We find the thermal conductance of a short superconducting wire to be strongly enhanced beyond the BCS value due to the inverse proximity effect, resulting from contributions of elastic cotunneling and crossed Andreev reflection of quasiparticles. Our measurements agree with a model based on the quasiclassical theory of inhomogeneous superconductivity in the diffusive limit.

Signatures of exchange correlations in the thermopower of quantum dots

We use a many-body rate-equation approach to calculate the thermopower of a quantum dot in the presence of an exchange interaction. At temperatures much smaller than the single-particle level spacing, the known quantum jumps (discontinuities) in the thermopower are split by the exchange interaction. The origin and nature of the splitting are elucidated with a simple physical argument based on the nature of the intermediate excited state in the sequential tunneling approach. We show that this splitting is sensitive to the number parity of electrons in the dot and the dot's ground-state spin. These effects are suppressed when cotunneling dominates the electrical and thermal conductances. We calculate the thermopower in the presence of elastic cotunneling, and show that some signatures of exchange correlations should still be observed with current experimental methods. In particular, we propose a method to determine the strength of the exchange interaction from measurements of the thermopower.

Local and nonlocal Andreev reflections in double barrier junctions

We study spin dependent charge transport through a junction, consisting of a superconductor connected to two normal or spin-polarized electrodes. Special attention is paid to a process known as a crossed or nonlocal Andreev reflection. The nonlocal reflection occurs when an incident electron (hole) from one electrode, injected with a subgap energy onto o superconducting layer, transforms into an Andreev hole (electron) in the second lead. When two electrons (holes), forming a Cooper pair, come from the same electrode, the process of the Andreev reflection is local. The coherent spin polarized transport in ferromagnet/superconductor/ferromagnet (F/S/F) double barrier junctions is analyzed using the Bogolubov-de Gennes (BdG) equation with appropriate boundary conditions. We calculate and discuss probabilities of the normal, local and crossed Andreev reflections, as well as probability of the elastic co-tunneling. These processes contribute to tunneling current when the distance between the magnetic electrodes is comparable to the superconducting coherence length. The dependence of the tunneling charge transport on the strength of the exchange field in the ferromagnetic electrodes, and on the height of the tunnel barriers are presented. We also discuss the local and nonlocal spin quantum entanglements of quasiparticle pairs induced by the Andreev reflections in the junction.

Nonlocal transport in normal-metal/superconductor hybrid structures: Role of interference and interaction

We have measured local and nonlocal conductance of mesoscopic normal-metal/superconductor hybrid structures fabricated by e-beam lithography and shadow evaporation. The sample geometry consists of a superconducting aluminum bar with two normal-metal wires forming tunnel contacts to the aluminum at distances of the order of the superconducting coherence length. We observe subgap anomalies in both local and nonlocal conductance that quickly decay with magnetic field and temperature. For the nonlocal conductance both positive and negative signs are found as a function of bias conditions, indicating at a competition of crossed Andreev reflection and elastic cotunneling. Our data suggest that the signals are caused by a phase-coherent enhancement of transport rather than dynamical Coulomb blockade.

Superconducting tunneling spectroscopy of a carbon nanotube quantum dot

We report results on superconducting tunneling spectroscopy of a carbon nanotube quantum dot. Using a three-probe technique that includes a superconducting tunnel probe, we map out changes in conductance due to band structure, excited states, and end-to-end bias. The superconducting probe allows us to observe enhanced spectroscopic features, such as robust signals of both elastic and inelastic cotunneling. We also see evidence of inelastic scattering processes inside the quantum dot.

Spin-switch effect from crossed Andreev reflection in superconducting graphene spin valves

We consider the nonlocal quantum transport properties of a graphene superconducting spin valve. It is shown that one may create a spin-switch effect between perfect elastic cotunneling (CT) and perfect crossed Andreev reflection (CAR) for all bias voltages in the low-energy regime by reversing the magnetization direction in one of the ferromagnetic layers. This opportunity arises due to the possibility of tuning the local Fermi level in graphene to values equivalent to a weak magnetic exchange splitting, thus reducing the Fermi surface for minority spins to a single point and rendering graphene to be half metallic. Such an effect is not attainable in a conventional metallic spin valve setup, where the contributions from CT and CAR tend to cancel each other and noise measurements are necessary to distinguish these processes.

Modeling of cotunneling in quantum dot systems

Transport through nanosystems is treated within the second-order von Neumann approach. This approach bridges the gap between rate equations which neglect level broadening and cotunneling, and the transmission formalism, which is essentially based on the single-particle picture thereby treating many-particle interactions on an approximate level. Here we provide an alternative presentation of the method in order to clarify the underlying structure. Furthermore we apply it to the problem of cotunneling. It is shown that both elastic and inelastic cotunneling can be described quantitatively, while the transmission approach with a mean-field treatment of the interaction provides an artificial bistability.

Self-consistent microscopic calculations for nonlocal transport through nanoscale superconductors

We implement self-consistent microscopic calculations in order to describe out-of-equilibrium nonlocal transport in normal-metal-superconductor-normal-metal hybrid structures in the presence of a magnetic field and for arbitrary interface transparencies. A four-terminal setup simulating usual experimental situations is described by means of a tight-binding model. We present results for the self-consistent order-parameter and current profiles within the sample. These profiles illustrate a crossover from a quasiequilibrium to a strong nonequilibrium situation when increasing the interface transparencies and the applied voltages. We analyze in detail the behavior of the nonlocal conductance in these two different regimes. While in quasiequilibrium conditions this can be expressed as the difference between elastic cotunneling and crossed Andreev transmission coefficients, in a general situation additional contributions due to the voltage dependence of the self-consistent order parameter have to be taken into account. The present results provide a first step toward a self-consistent theory of nonlocal transport including nonequilibrium effects and describe qualitatively a recent experiment [P. Cadden-Zimansky and V. Chandrasekhar, Phys. Rev. Lett. 97, 237003 (2006)].

Spin Dependent Electron Tunneling in a Ferromagnet Superconductor Ferromagnet Junction

The coherent spin polarized transport in ferromagnet/superconductor/ferromagnet double barrier junctions is analyzed. Using the Bogolubov–de Gennes equation with appropriate boundary conditions, we calculate probabilities of spin dependent transport processes in the ferromagnet/superconductor/ferromagnet junction. In particular, we discuss the nonlocal processes such as the crossed Andreev reflection and elastic co-tunneling. These processes contribute to tunneling a current when the distance between the two magnetic electrodes is comparable to the superconducting coherence length. The dependences of the tunneling transport processes on the strength of the exchange field in the ferromagnetic electrodes, and on the height of the tunnel barriers are presented.

Introduction to Single-Molecule Transistor

Effects, beyond the Coulomb-blockade model, of a single-molecule transistor are reviewed. The image-charge effect, elastic cotunneling effect (conduction via the Kondo effect), and the inelastic cotunneling effect [non-resonance (vibrational) inelastic electron tunneling spectroscopy] are discussed. Theories on the interaction between the Kondo effect and the molecular vibration are briefly reviewed. Inelastic Kondo effect, switching phenomena and spin-blockade effect are described. Representative experimental results are given.

Virtual electron diffusion through a quantum dot in the presence of electromagnetic fluctuations

We consider a double junction system in the Coulomb blockade regime with an island with discrete energy levels and analyze the effect of electromagnetic fluctuations on elastic cotunneling. We obtain the analytic expression for the elastic cotunneling current at zero temperature, which shows the power-law suppression of cotunneling at low voltages due to circuit impedance $I\ensuremath{\sim}{V}^{1+2\text{ }\text{Re}\text{ }Z(0)/{R}_{K}}$. The results will be useful for calculating the accuracy of single-electron devices used in metrology.

Crossed Andreev Reflection in a Graphene Bipolar Transistor

We investigate the crossed Andreev reflections between two graphene leads connected by a narrow superconductor. When the leads are, respectively, of the n and p type, we find that electron elastic cotunneling and local Andreev reflection are both eliminated even in the absence of any valley-isospin or spin polarizations. We further predict oscillations of both diagonal and cross conductances as a function of the distance between the graphene-superconductor interfaces.

Crossed Andreev reflection in superconducting junctions

In this work crossed Andreev reflection (CAR) and elastic cotunneling (EC) are studied for junctions (N1ISIN2), where N1 and N2 are normal metals, S is a high Tc superconductor and I is an insulator. This study is carried out based on the analytical solutions of Bogoliubov de Gennes equations for anisotropic superconductors. The influence of different pair potential symmetries on the CAR and crossed conductance is analyzed. We show that CAR and EC are higher in dx2-y2 symmetry than in s symmetry. In the case of normal electrodes without magnetization, EC is the predominantly process for dx2-y2 symmetry, while in s symmetry, both processes decay with the same amplitude.

Nonlocal Andreev reflection in a carbon nanotube superconducting quantum interference device

We investigate a superconducting quantum interference device based on carbon nanotubes in a fork geometry [J.-P. Cleuziou et al., Nat. Nanotechnol. 1, 53 (2006)], involving tunneling of evanescent quasiparticles through a superconductor over a distance comparable to the superconducting coherence length, with therefore “nonlocal” processes generalizing nonlocal Andreev reflection and elastic cotunneling. Nonlocal processes induce a reduction of the critical current and modify the current-phase relation. We discuss arbitrary interface transparencies. Such devices in fork geometries are candidates for probing the phase coherence of crossed Andreev reflection.

Electrical Characteristics of Si Single-Electron Transistor Based on Multiple Islands

We investigated the electrical characteristics specifically associated with cotunneling and quantum effects of single-electron transistors (SETs) with three geometrically defined islands. Clear Coulomb oscillation and negative differential conductance were observed. The drain current for the peaks and valleys of the Coulomb oscillation was measured as a function of temperature and drain voltage. Consequently, it was found that the valley current was well described by the inelastic cotunneling theory at temperatures above 40 K in the low-drain-voltage region; on the other hand, elastic cotunneling dominantly contributed to the valley current in the low-temperature and low-drain-voltage region. However, for a high gate voltage, the SET behaved as a single-island device. This is probably because the three islands were electrically enlarged and merged into a single island owing to the high applied gate voltage.

Charge imbalance, crossed Andreev reflection and elastic co-tunnelling in ferromagnet/superconductor/normal-metal structures

We examine here electronic transport in nanoscale systems where normal and ferromagnetic probes are attached to a conventional superconductor. While reviewing the long-studied effects of Andreev reflection and charge imbalance, we concentrate on two recently predicted coherent, nonlocal processes known as crossed Andreev reflection and elastic co-tunnelling. These processes can occur when two spatially separated normal or ferromagnetic probes are separated by a distance comparable to the coherence length of the superconductor. Here we show that normal probes, by avoiding some of the experimental and theoretical complications of ferromagnetic probes, may offer a better opportunity to examine these processes.

Transport properties of semiconducting nanocrystal arrays at low temperatures

We study the electron transport in semiconducting nanocrystal arrays at temperatures $T\ll E_c$, where $E_c$ is the charging energy for a single grain. In this temperature range the electron transport is dominated by co-tunneling processes. We discuss both elastic and inelastic co-tunneling and show that for semiconducting nanocrystal arrays the inelastic contribution is strongly suppressed at low temperatures. We also compare our results with available experimental data.

Crossed Andreev reflection in diffusive contacts: Quasiclassical Keldysh-Usadel formalism

Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal-metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to contribute equally to the nonlocal current, which is of relevance to the use of normal-metal--superconducting heterostructures as sources of entanglement.

Nonlocal Correlations in Normal-Metal Superconducting Systems

We examine nonlocal effects between normal-metal gold probes connected by superconducting aluminum. For highly transparent Au/Al interfaces, we find nonlocal voltages that obey a spatial and temperature evolution distinct from the nonequilibrium charge imbalance signals usually found in such systems. These voltages are consistent with the predicted effects of crossed Andreev reflection and elastic cotunneling, effects that involve coherent correlations between spatially separated electrons.