Multiple Andreev Reflections Research Articles

Supercurrent and multiple Andreev reflections in micrometer-long ballistic graphene Josephson junctions.

Ballistic Josephson junctions are predicted to support a number of exotic physics processess, providing an ideal system to inject the supercurrent in the quantum Hall regime. Herein, we demonstrate electrical transport measurements on ballistic superconductor-graphene-superconductor junctions by contacting graphene to niobium with a junction length up to 1.5 μm. Hexagonal boron nitride encapsulation and one-dimensional edge contacts guarantee high-quality graphene Josephson junctions with a mean free path of several micrometers and record-low contact resistance. Transports in normal states including the observation of Fabry-Pérot oscillations and Sharvin resistance conclusively witness the ballistic propagation in the junctions. The critical current density JC is over one order of magnitude larger than that of the previously reported junctions. Away from the charge neutrality point, the ICRN product (IC is the critical current and RN the normal state resistance of junction) is nearly a constant, independent of carrier density n, which agrees well with the theory for ballistic Josephson junctions. Multiple Andreev reflections up to the third order are observed for the first time by measuring the differential resistance in the micrometer-long ballistic graphene Josephson junctions.

Structure and Anisotropy of the Superconducting Order Parameter in Ba0.65K0.35Fe2As2 Probed by Andreev Spectroscopy

The superconducting order parameters in optimally doped Ba0.65K0.35Fe2As2 single crystals have been directly measured using multiple Andreev reflection effect spectroscopy of superconductor–normal metal–superconductor break-junctions. We determine two superconducting gaps, which are nodeless in the k x k y -plane of the momentum space, and resolve a substantial in-plane anisotropy of the large gap. The temperature dependences of the gaps indicate a strong coupling within the bands where ΔL develops, a weak coupling in the condensate with the small gap ΔS, and a moderate interband interaction between the two condensates. The own critical temperatures of both condensates have been estimated (under the hypotherical assumption of zero interband interaction).

Coulomb Blockade and Multiple Andreev Reflection in a Superconducting Single-Electron Transistor

In superconducting quantum point contacts, multiple Andreev reflection (MAR), which describes the coherent transport of m quasiparticles each carrying an electron charge with $$m\ge 3$$ , sets in at voltage thresholds $$eV = 2\Delta /m$$ . In single-electron transistors, Coulomb blockade, however, suppresses the current at low voltage. The required voltage for charge transport increases with the square of the effective charge $$eV\propto \left( me\right) ^2$$ . Thus, studying the charge transport in all-superconducting single-electron transistors (SSETs) sets these two phenomena into competition. In this article, we present the fabrication as well as a measurement scheme and transport data for a SSET with one junction in which the transmission and thereby the MAR contributions can be continuously tuned. All regimes from weak to strong coupling are addressed. We extend the Orthodox theory by incorporating MAR processes to describe the observed data qualitatively. We detect a new transport process the nature of which is unclear at present. Furthermore, we observe a renormalization of the charging energy when approaching the strong coupling regime.

Observation of Electron Coherence and Fabry–Perot Standing Waves at a Graphene Edge

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

Quench dynamics in superconducting nanojunctions: Metastability and dynamical Yang-Lee zeros

We study the charge transfer dynamics following the formation of a phase or voltage biased su- perconducting nano-junction using a full counting statistics analysis. We demonstrate that the evolution of the zeros of the generating function allows one to identify the population of different many body states much in the same way as the accumulation of Yang-Lee zeros of the partition function in equilibrium statistical mechanics is connected to phase transitions. We give an exact expression connecting the dynamical zeros to the charge transfer cumulants and discuss when an approximation based on "dominant" zeros is valid. We show that, for generic values of the parameters, the system gets trapped into a metastable state characterized by a non-equilibrium population of the many body states which is dependent on the initial conditions. We study in particular the effect of the switching rates in the dynamics showing that, in contrast to intuition, the deviation from thermal equilibrium increases for the slower rates. In the voltage biased case the steady state is reached independently of the initial conditions. Our method allows us to obtain accurate results for the steady state current and noise in quantitative agreement with steady state methods developed to describe the multiple Andreev reflections regime. Finally, we discuss the system dynamics after a sudden voltage drop showing the possibility of tuning the many body states population by an appropriate choice of the initial voltage, providing a feasible experimental way to access the quench dynamics and control the state of the system.

Magnetic, superconducting and electron-boson properties of GdO(F)FeAs oxypnictides

We performed comprehensive studies of nearly optimal fluorine-substituted GdO1−xFx FeAs oxypnictide superconductors with TC=48−53K. Specific heat measurements revealed a sharp peak at T=3.5K that shifts to lower temperatures with magnetic field increase. This peak corresponds to an antiferromagnetic ordering in Gd3+ ion sublattice and may indicate coexistence between superconducting and magnetic orderings. Andreev transport through artificially made constriction demonstrated two channels for the carriers from the band(s) with the large superconducting gap as well as from those with the small gap. As expected, the presence of a transport channel with the bands mixing (ΔL+ΔS) was not detected. Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we determined two superconducting gaps, ΔS≈2.7meV, and ΔL≈11.6meV. The reproducible fine structure in the dI(V)/dV spectra of the Andreev contacts (satellites of the main subharmonic gap structure for ΔL) was interpreted as caused by a resonant emission of bosons with the energy ε0=12−15meV≈ΔL+ΔS during the process of multiple Andreev reflections (MAR) for normal carriers in ΔL-band(s) transport channel.

Strong Proximity Josephson Coupling in Vertically Stacked NbSe2-Graphene-NbSe2 van der Waals Junctions.

A layered two-dimensional superconducting material 2H-NbSe2 is used to build a van der Waals heterostructure, where a proximity-coupled superconducting order can be induced in the interfacing materials. Vertically stacked NbSe2-graphene-NbSe2 is fabricated using van der Waals interlayer coupling, producing defect-free contacts with a high interfacial transparency. The atomically thin graphene layer allows the formation of a highly coherent proximity Josephson coupling between the two NbSe2 flakes. The temperature dependence of the junction critical current (Ic) reveals short and ballistic Josephson coupling characteristics that agree with theoretical prediction. The strong Josephson coupling is confirmed by a large junction critical current density of 1.6 × 104 A/cm2, multiple Andreev reflections in the subgap structure of the differential conductance, and a magnetic-field modulation of Ic. This is the first demonstration of strongly proximity-coupled Josephson junctions with extremely clean interfaces in a dry-transfer-stacked van der Waals heterostructure.

Evidence of a multiple boson emission in Sm1−xThxOFeAs

We studied a reproducible fine structure observed in dynamic conductance spectra of Andreev arrays in Sm1−xThxOFeAs superconductors with various thorium concentrations and critical temperatures . This structure is unambiguously caused by a multiple boson emission (of the same energy) during the process of multiple Andreev reflections. The directly determined energy of the bosonic mode reaches for optimal compounds. Within the studied range of Tc, this energy as well as the large and the small superconducting gaps, nearly scale with critical temperature with the characteristic ratio (and , respectively) resembling the expected energy of spin resonance and spectral density enhancement in and states, respectively.

Shot Noise in NbN/AlN/NbN Superconducting Tunneling Junctions

With sensitivity approaching the quantum limit, superconductor-insulator-superconductor (SIS) mixers play an important role in radio astronomy and atmospheric science at millimeter and submillimeter wavelengths. As one of the intrinsic noise sources in superconducting tunneling junctions, shot noise is still not well understood, particularly for those of relatively high energy gap (e.g., NbN/AlN/NbN). In this paper, we mainly study the multiple Andreev reflection (MAR) enhanced shot noise of two different NbN SIS junctions (i.e., junction array and long junction) as well as their temperature dependence. Barrier strength Z is taken into consideration for theoretical analysis of effective charge of the MAR effect based on the Blonder-Tinkham-Klapwijk (BTK) theory with the Andreev clusters method. It has been found that the effective charge of the MAR effect is inversely proportional to temperature, the barrier strength Z and transparency T are proportional to temperature. Detailed measurement results and analysis will be presented.

High-Transparency Al/Bi2Te3Double-Barrier Heterostructures

We have fabricated highly transparent Al/Bi2Te3/Al superconductor/normal metal/superconductor double-barrier heterostructures. Transport measurements reveal the presence of multiple Andreev reflections related to two distinct energy gaps that we identify as the induced superconducting gap in the two electrodes. The realization of high-transparency Josephson junctions with topological insulators is an important step towards the study of topological superconductivity and Majorana fermions.

Tunable pseudogaps due to nonlocal coherent transport in voltage-biased three-terminal Josephson junctions

We investigate the proximity effect in junctions between $N=3$ superconductors under commensurate voltage bias. The bias is chosen to highlight the role of transport processes that exchange multiple Cooper pairs coherently between more than two superconductors. Such non-local processes can be studied in the dc response, where local transport processes do not contribute. We focus on the proximity-induced normal density of states that we investigate in a wide parameter space. We reveal the presence of deep and highly tunable pseudogaps and other rich structures. These are due to a static proximity effect that is absent for $N=2$ and is sensitive to an emergent superconducting phase associated to non-local coherent transport. In comparison with results for $N=2$, we find similarities in the signature peaks of multiple Andreev reflections. We discuss the effect of electron-hole decoherence and of various types of junction asymmetries. Our predictions can be investigated experimentally using tunneling spectroscopy.

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

We theoretically study transport properties of voltage-biased one-dimensional superconductor--normal metal--superconductor tunnel junctions with arbitrary junction transparency where the superconductors can have trivial or nontrivial topology. Motivated by recent experimental efforts on Majorana properties of superconductor-semiconductor hybrid systems, we consider two explicit models for topological superconductors: (i) spinful p-wave, and (ii) spin-split spin-orbit-coupled s-wave. We provide a comprehensive analysis of the zero-temperature dc current $I$ and differential conductance $dI/dV$ of voltage-biased junctions with or without Majorana zero modes (MZMs). The presence of an MZM necessarily gives rise to two tunneling conductance peaks at voltages $eV = \pm \Delta_{\mathrm{lead}}$, i.e., the voltage at which the superconducting gap edge of the lead aligns with the MZM. We find that the MZM conductance peak probed by a superconducting lead $without$ a BCS singularity has a non-universal value which decreases with decreasing junction transparency. This is in contrast to the MZM tunneling conductance measured by a superconducting lead $with$ a BCS singularity, where the conductance peak in the tunneling limit takes the quantized value $G_M = (4-\pi)2e^2/h$ independent of the junction transparency. We also discuss the "subharmonic gap structure", a consequence of multiple Andreev reflections, in the presence and absence of MZMs. Finally, we show that for finite-energy Andreev bound states (ABSs), the conductance peaks shift away from the gap bias voltage $eV = \pm \Delta_{\mathrm{lead}}$ to a larger value set by the ABSs energy. Our work should have important implications for the extensive current experimental efforts toward creating topological superconductivity and MZMs in semiconductor nanowires proximity coupled to ordinary s-wave superconductors.

Observation of bosonic resonances in GdO1−x F x FeAs by intrinsic multiple Andreev reflection effect spectroscopy

The current–voltage characteristics and dynamic conductance spectra of Andreev arrays in nearly optimal GdO1 − x F x FeAs superconductors with the critical temperature T c = 46–50 K have been studied. A reproducible fine structure that accompanies large gap features and caused by boson emission during the process of multiple Andreev reflections has been observed. At T = 4.2 K, the bosonic mode energy e0 = (12 ± 2) meV has been obtained.

Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction

Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductor-superconductor interface, indicating near-unity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 {\mu}eV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, revealing the subband structure of the semiconductor quantum well, consistent with magnetotransport experiment of the bare InAs performed on the same wafer.

Evolution of superconducting gaps in Th-substituted Sm1−xThxOFeAs studied by multiple Andreev reflection spectroscopy

Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we studied SnS contacts in the layered oxypnictide superconductors Sm$_{1-x}$Th$_x$OFeAs with various thorium doping and critical temperatures $T_C = 21-54$ K. We observe a scaling between both superconducting gaps and $T_C$. The determined BCS-ratio for the large gap $2\Delta_L/k_BT_C = 5.0-5.7$ and its eigen BCS-ratio (in a hypothetical case of zero interband coupling) $2\Delta_L/k_BT_C^L = 4.1-4.6$ both exceeding the weak-coupling limit 3.52, and for the small gap $2\Delta_S/k_BT_C = 1.2-1.6$ remain nearly constant within all the $T_C$ range studied. The temperature dependences $\Delta_{L,S}(T)$ agree well with a two-band BCS-like Moskalenko and Suhl model. We prove intraband coupling to be stronger than interband coupling, whereas and Coulomb repulsion constants $\mu^{\ast}$ are finite in Sm-based oxypnictides.

Critical analysis of soft point contact Andreev reflection spectra between superconducting films and pressed In

We present a critical analysis of an alternative technique of point contact Andreev reflection (PCAR) spectroscopy used to extract energy resolved information of superconductors which is based on making ‘soft-contacts’ between superconductors and indium. This technique is not sensitive to mechanical vibrations and hence can be used in a cryogen free platform increasing its accessibility to users having no access to cryogenic liquids. Through our experiments on large number of superconducting films we show that the PCAR spectra below the Tc of In show sub-harmonic gap structures consistent with the theory of multiple Andreev reflection (MAR) and a zero bias conductance (ZBC) anomaly associated with the Josephson supercurrent. Furthermore, we demonstrate that large contact resistance with low transparency ballistic contacts in the PCAR regime are required to obtain reliable spectroscopic data. One limitation of the technique arises for low contact resistance junctions where the superconducting proximity effect (SPE) reduces the value of the superconducting energy gap.

Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction

A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction $({S}_{a},{S}_{b},{S}_{c})$ biased with voltages $(V,\ensuremath{-}V,0)$ is considered, but the conclusions hold more generally for resonant semiconducting quantum wire setups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for $V=0$) evolve into nonequilibrium Floquet-Wannier-Stark-Andreev (FWS-Andreev) ladders of resonances (for $V\ensuremath{\ne}0$). These resonances acquire a finite width due to multiple Andreev reflection (MAR) processes. We also consider the effect of an extrinsic linewidth broadening on the quantum dot, introduced through a Dynes phenomenological parameter. The dc-quartet current manifests a crossover between the extrinsic relaxation dominated regime at low voltage to an intrinsic relaxation due to MAR processes at higher voltage. Finally, we study the coupling between the two FWS-Andreev ladders due to Landau-Zener-St\"uckelberg transitions, and its effect on the crossover in the relaxation mechanism. Three important low-energy scales are identified, and a perspective is to relate those low-energy scales to a recent noise cross-correlation experiment (Y. Cohen et al., arXiv:1606.08436).

Resonant subgap current transport in Josephson field effect transistor

We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal metal region (N), which is controlled by the gate induced potential barrier (I). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose length significantly exceeds the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the difference $\delta_m$ between the static Andreev levels, $eV_n = n\delta_m$. Moreover, the averaged IVC follows the power rather than exponential behavior, and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions whose length is comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the Andreev interlevel distance, $eV_n = \delta_m/n$ rather than the gap subharmonics $2\Delta/n$.

Conductance spectroscopy of nontopological-topological superconductor junctions

We calculate the zero-temperature differential conductance $dI/dV$ of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful $p$-wave and (ii) $s$-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap $\Delta_s$ is zero and there are two symmetric conductance peaks appearing at $eV = \pm \Delta_s$ with the quantized value $(4-\pi)2e^2/h$ due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for $e|V| < \Delta_s$ arising from multiple Andreev reflections. The conductance at $eV = \pm \Delta_s$ in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.

Direct evidence of two superconducting gaps in FeSe0.5Te0.5: SnS-Andreev spectroscopy and the lower critical field

We present direct measurements of the superconducting order parameter in nearly optimal FeSe$_{0.5}$Te$_{0.5}$ single crystals with critical temperature $T_C \approx 14$ K. Using intrinsic multiple Andreev reflection effect (IMARE) spectroscopy and measurements of lower critical field, we directly determined two superconducting gaps, $\Delta_L \approx 3.3 - 3.4$ meV and $\Delta_S \approx 1$ meV, and their temperature dependences. We show that a two-band model fits well the experimental data. The estimated electron-boson coupling constants indicate a strong intraband and a moderate interband interaction.