Elastic Cotunneling Research Articles

Crossed Andreev reflection in topological insulator F/d-wave SC/F junction

We investigate theoretically the nonlocal conductance arising from the crossed Andreev reflection and electron elastic cotunneling processes in a topological insulator ferromagnet/d-wave superconductor/ferromagnet (F/d-wave SC/F) junction with in-plane magnetization. We find that these nonlocal conductances depend strongly on the d-wave superconducting orientation angular α. The effect of the bias voltage on the crossed Andreev reflection and electron elastic cotunneling is also investigated. Except for α=π/4 case, where crossed Andreev reflection conductance is negligibly small, a perfect crossed Andreev reflection can be obtained in the anti-parallel magnetization configuration by proper tuning of the bias voltage.

Thermally induced subgap features in the cotunneling spectroscopy of a carbon nanotube

We report on the nonlinear cotunneling spectroscopy of a carbon nanotube quantum dot coupled to Nb superconducting contacts. Our measurements show rich subgap features in the stability diagram which become more pronounced as the temperature is increased. Applying a transport theory based on the Liouville–von Neumann equation for the density matrix, we show that the transport properties can be attributed to processes involving sequential as well as elastic and inelastic cotunneling of quasiparticles thermally excited across the gap. In particular, we predict thermal replicas of the elastic and inelastic cotunneling peaks, in agreement with our experimental results.

Valley- and spin-switch effects in molybdenum disulfide superconducting spin valve

We propose a hole-doped molybdenum disulfide (MoS$_2$) superconducting spin valve (F/S/F) hybrid structure in which the Andreev reflection process is suppressed for all incoming waves with a determined range of the chemical potential in ferromagnetic (F) region and the cross-conductance in the right F region depends crucially on the configuration of magnetizations in the two F regions. Using the scattering formalism, we find that the transport is mediated purely by elastic electron cotunneling (CT) process in a parallel configuration and changes to the pure crossed Andreev reflection (CAR) process in the low-energy regime, without fixing of a unique parameter, by reversing the direction of magnetization in the right F region. This suggests both valley- and spin-switch effects between the perfect elastic CT and perfect CAR processes and makes the nonlocal charge current to be fully valley- and spin-polarized inside the right F region where the type of the polarizations can be changed by reversing the magnetization direction in the right F region. We further demonstrate that the presence of the strong spin-orbit interaction $\lambda$ and an additional topological term ($\beta$) in the Hamiltonian of MoS$_2$ result in an enhancement of the charge conductance of the CT and CAR processes and make them to be present for long lengths of the superconducting region. Besides, we find that the thermal conductance of the structure with a small length of the highly doped superconducting region exhibits linear dependence on the temperature at low temperatures whereas it enhances exponentially at higher temperatures. In particular, we demonstrate that the thermal conductance versus the strength of the exchange field ($h$) in F region displays a maximum value at $h<\lambda$, which moves towards larger exchange fields by increasing the temperature.

Experimental determination of the elastic cotunneling rate in a hybrid single-electron box

We report measurements of charge configurations and charge transfer dynamics in a hybrid single-electron box composed of aluminum and copper. We used two single-electron transistors (SETs) to simultaneously read out different parts of the box, enabling us to map out stability diagrams of the box and identify various charge transfer processes in the box. We further characterized the elastic cotunneling in the box, which is an important source of error in electron turnstiles consisting of hybrid SETs, and found that the rate was as low as 1 Hz at degeneracy and compatible with theoretical estimates for electron tunneling via virtual states in the central superconducting island of the box.

Coherent conductance and magnetoresistance in a topological insulator ferromagnet/superconductor/ferromagnet junction

We investigate theoretically the coherent conductance and magnetoresistance in a topological insulator ferromagnet/superconductor/ferromagnet (F/SC/F) junction with perpendicular magnetization. It is shown that there exists a large difference between the coherent conductance of the parallel and antiparallel magnetization configurations, which leads to a large magnetoresistance. The superconductor layer thickness dependence of the magnetoresistance is discussed in terms of the contributions of the local Andreev reflection, electron elastic cotunneling and crossed Andreev reflection to the parallel and antiparallel conductances.

Nonlocal spectroscopy of Andreev bound states

We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes $u$ and $v$.

Superconducting proximity effect in silicene: Spin-valley-polarized Andreev reflection, nonlocal transport, and supercurrent

We theoretically study the superconducting proximity effect in silicene, which features massive Dirac fermions with a tunable mass (band gap), and compute the conductance across a normal-superconductor (N-S) silicene junction, the nonlocal conductance of an N-S-N junction, and the supercurrent flowing in an S-N-S junction. It is demonstrated that the transport processes consisting of local and nonlocal Andreev reflection may be efficiently controlled via an external electric field owing to the buckled structure of silicene. In particular, we demonstrate that it is possible to obtain a fully spin-valley-polarized crossed Andreev reflection process without any contamination of elastic cotunneling or local Andreev reflection, in stark contrast to ordinary metals. It is also shown that the supercurrent flowing in the S-N-S junction can be fully spin-valley polarized and that it is controllable by an external electric field.

Localized Many-Particle Majorana Modes with Vanishing Time-Reversal Symmetry Breaking in Double Quantum Dots

We introduce the concept of spinful many-particle Majorana modes with local odd operator products, thereby preserving their local statistics. We consider a superconductor-double-quantum-dot system where these modes can arise with negligible Zeeman splitting when Coulomb interactions are present. We find a reverse Mott-insulator transition, where the even- and odd-parity bands become degenerate. Above this transition, Majorana operators move the system between the odd-parity ground state, associated with elastic cotunneling, and the even-parity ground state, associated with crossed Andreev reflection. These Majorana modes are described in terms of one, three, and five operator products. Parity conservation results in a 4π periodic supercurrent in the even state and no supercurrent in the odd state.

Nonlocal spin correlations mediated by a superconductor

Nonlocal charge correlations induced in two normal metals contacted separately to a superconductor have been studied intensively in the past few years. Here we investigate nonlocal correlations induced by the transfer of pure spin currents through a superconductor on a scale comparable to the superconducting coherence length. As with charge currents, two processes contribute to the nonlocal spin signal: crossed Andreev reflection (CAR), where an electron with spin-up injected from one normal metal into the superconductor results in a hole with spin-down being injected into the second normal metal, and elastic cotunneling (EC), where the electron with spin-up injected from the first normal metal results in an electron with spin-up being injected into the second normal metal. Unlike charge currents, however, the spin currents associated with CAR and EC add due to the fact that the bulk superconductor cannot sustain a net spin current.

Charge frustration in a triangular triple quantum dot.

We experimentally investigate the charge (isospin) frustration induced by a geometrical symmetry in a triangular triple quantum dot. We observe the ground-state charge configurations of sixfold degeneracy, the manifestation of the frustration. The frustration results in omnidirectional charge transport, and it is accompanied by nearby nontrivial triple degenerate states in the charge stability diagram. The findings agree with a capacitive interaction model. We also observe unusual transport by the frustration, which might be related to elastic cotunneling and the interference of trajectories through the dot. This work demonstrates a unique way of studying geometrical frustration in a controllable way.

Shot noise spectroscopy on a semiconductor quantum dot in the elastic and inelastic cotunneling regimes

We report shot noise spectroscopy on a semiconductor quantum dot in a cotunneling regime. The DC conductance measurements show clear signatures of both elastic and inelastic cotunneling transport inside a Coulomb diamond. We observed Poissonian shot noise with the Fano factor $F\approx 1$ in the elastic cotunneling regime, and super-Poissonian Fano factor $1<F<3$ in the inelastic cotunneling regime. The differences in the value of the Fano factor between elastic and inelastic processes reveal the microscopic mechanisms involved in the cotunneling transport.

Majorana Single-Charge Transistor

We study transport through a Coulomb blockaded topologically nontrivial superconducting wire (with Majorana end states) contacted by metallic leads. An exact formula for the current through this interacting Majorana single-charge transistor is derived in terms of wire spectral functions. A comprehensive picture follows from three different approaches. We find Coulomb oscillations with universal halving of the finite-temperature peak conductance under strong blockade conditions, where the valley conductance mainly comes from elastic cotunneling. The nonlinear conductance exhibits finite-voltage sidebands due to anomalous tunneling involving Cooper pair splitting.

Numerical model of crossed Andreev reflection and charge imbalance

We present a numerical model of local and nonlocal transport properties in a lateral spin valve structure consisting of two magnetic electrodes in contact with a third perpendicular superconducting electrode. By considering the transport paths for a single electron incident at the local F/S interface---in terms of probabilities of crossed or local Andreev reflection, elastic cotunneling, or quasiparticle transport---we show that this leads to nonlocal charge imbalance. We compare this model with experimental data from an aluminum-permalloy (Al/Py) lateral spin valve geometry device and demonstrate the effectiveness of this simple approach in replicating experimental behavior.

Coherent nonlocal correlations in Andreev interferometers

Andreev interferometers, hybrid normal–superconducting loops, are well suited for studying phase-coherent effects, as they combine the robust quantum phase of a superconductor with a finite resistance normal section where phase-dependent transport properties can be easily measured. While they have previously been used to demonstrate local, phase-coherent properties, they may also be integrated into structures where nonlocal phase coherence occurs. In this paper, we use Andreev interferometer devices to experimentally establish the existence of nonlocal phase coherence between two normal metals linked by a superconductor. The generation of phase-coherent nonlocal signals is brought about by producing a nonequilibrium quasiparticle distribution in the normal section of the interferometer and tuning the phase with an external magnetic flux through the loop. Quasiclassical modeling of our experiment shows that the nonequilibrium distribution, coupled with the flux, leads to an induced supercurrent that is not constant along the length of the interferometer's normal section. The supercurrent–quasiparticle current conversion that occurs in this section is manifested in the production of flux-dependent nonlocal voltages through the mechanisms of crossed Andreev reflection and elastic cotunneling.

Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizable CAR is achieved. When one of the ribbon leads is magnetized not only is the CAR exclusive, but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.

Finite-Bias Cooper Pair Splitting

In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the nonlocal electrical transport through the device can be tuned by electrical means and that the energy dependence of the effective density of states in the QDs is relevant for the rates of Cooper pair splitting (CPS) and elastic cotunneling. Such experimental tools are necessary to understand and develop CPS-based sources of entangled electrons in solid-state devices.

Density of states spectra in ferromagnet/superconductor/ferromagnet heterostructures

We investigate density of states (DOS) spectra of a ferromagnet/superconductor/ferromagnet structure by including the interface spin-flip scattering potential into the existing mean-field Hamiltonian. We show that the spin-flip scattering can lead to electron spin mixing in the vicinity of an FS interface, enabling s-wave singlet and odd-frequency triplet pairs conversion and the existence of Andreev bound states with subgap energy ($\ifmmode\pm\else\textpm\fi{}{\ensuremath{\varepsilon}}_{b}$) via the intra- and interband Andreev reflections. This adds spin-resolved subgap peaks to the DOS spectrum. The relevant elastic co-tunneling at $\ifmmode\pm\else\textpm\fi{}{\ensuremath{\varepsilon}}_{b}$ enhances the local conductance, while its competition with the crossed Andreev reflection will lead to a sign change in the nonlocal differential conductance with the bias energy.

Current and noise correlations in a double-dot Cooper-pair beam splitter

We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branching current and the noise crossed correlations in terms of single and two-particle Green's function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunneling, the antisymmetric case (the two levels have opposite energies with respect to the superconducting chemical potential) optimizes the Crossed Andreev Reflection (CAR) process while the symmetric case (the two levels have the same energies) favors the Elastic Cotunneling (EC) process. Switching on the direct tunneling tends to suppress the CAR process, leading to negative noise crossed correlations over the whole voltage range for large enough direct tunneling.

Crossed Andreev reflection in graphene normal–superconductor–normal structures with pseudo-diffusive interfaces

In this Letter graphene normal–superconductor–normal heterostructures are modeled for studying the crossed Andreev reflection. A thin layer of undoped graphene with Fermi energy at the Dirac point at is assumed the interface between superconductor layer and each normal lead. The resulting contribution of the crossed Andreev reflection to the nonlocal conductance equals that of the electron elastic cotunneling. We explain this as another figure of merit for pseudodiffusive conduction at the Dirac point of the undoped layers. Also structures with only one undoped layer at the interface between the superconductor and one of the normal leads, as well as structures in which one of the leads is ferromagnetic, show pseudodiffusive conduction at the Dirac points.

Variable-range-hopping conductivity in polygrain samples of icosahedral Al–Re–Pd

We further develop a model, based on an analogy with granular electronic conductors, which explains the nature of the variable-range-hopping conductivity in polygrain samples of icosahedral Al–Re–Pd with resistivity ratios of in an excess of ∼13. The electrical conductivity of the model is determined by intergranular tunnelling and electrostatic energy. In polygrain icosahedral Al–Re–Pd, pores and precipitates of secondary phases create the barriers. Depending on the barrier height and electrostatic disorder, either an insulating variable-range-hopping regime of an Efros–Shklovskii or Mott type with elastic co-tunnelling or a metallic regime typical of homogeneously disordered conductors is possible.