Multiple Andreev Reflections Research Articles

Full counting statistics of superconductor hybrid structures involving a time-dependent field

Here we discuss the charge transfer statistics of superconductor-quantum dot-superconductor contacts in nonequilibrium and involving a time-dependent field via the applied voltage. In this case, the effects of multiple Andreev reflections and the Josephson effect exhibit distinctive features. In addition to the effects observable in the conductance, we will also discuss the effects observable in the noise.

Doping Evolution of the Superconducting Order Parameter of Na(Fe, Co)As Alkali-Metal Pnictides

Using incoherent multiple Andreev reflection effect spectroscopy, we have studied the multiple-gap superconducting state of underdoped and overdoped Na(Fe, Co)As single crystals. We directly determined the magnitudes of the microscopic superconducting order parameters, their temperature dependences, and characteristic ratios \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\Delta (0){\ ext{/}}{{k}_{B}}{{T}_{c}}$$\\end{document}. The obtained large data statistics unambiguously proves a significant decrease in the degree of the large superconducting gap possible anisotropy in the overdoped compositions away from the antiferromagnetic and nematic regions of the doping phase diagram.

Superconducting Field-Effect Transistors with PdxTe-Te Intimate Contacts.

Superconducting-based electronic devices have shown great potential for future quantum computing applications. One key building block device is a superconducting field-effect transistor based on a superconductor-semiconductor-superconductor Josephson-junction (JJ) with a gate-tunable semiconducting channel. However, the performance of such devices is highly dependent on the quality of the superconductor to semiconductor interface. In this study, we present an alternative method to obtain a high-quality interface by using intimate contact. We investigate the proximity-induced superconductivity in chiral crystal tellurium (Te) and fabricate a PdxTe-Te-PdxTe JJ with an ambipolar supercurrent that is gate-tunable and exhibits multiple Andreev reflections. The semiconducting two-dimensional Te single crystal is grown hydrothermally and partially converted to superconducting PdxTe by controlled annealing. Our work demonstrates a promising path for realizing controllable superconducting electronic devices with high-quality superconducting interfaces; thus, we can continue to advance the field of quantum computing and other interface-based technologies.

Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices.

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.

Interplay of Andreev Reflection and Coulomb Blockade in Hybrid Superconducting Single-Electron Transistors.

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.

Comparison of the Gap Structure of Underdoped and Overdoped Superconducting Pnictides BaFe2 – xNixAs2

We compare the structure of the superconducting order parameter of overdoped BaFe1.88Ni0.12As2and underdoped BaFe1.92Ni0.08As2pnictides with similarTc≈18.0−18.3K. Using incoherent multiple Andreev reflection effect spectroscopy, we directly determined the magnitudes of the two microscopic superconducting order parameters: the small superconducting gap and probably anisotropic large gap, their characteristic ratios and temperature dependences. We discuss similarity and difference in the gap structure, as well as possible influence of antiferromagnetic phase to superconducting properties.

Upper Critical Field and Tunneling Spectroscopy of Underdoped Na(Fe,Co)As Single Crystals.

A comprehensive study of superconducting properties of underdoped NaFe0.979Co0.021As single crystals by a combination of upper critical field measurements and incoherent multiple Andreev reflection effect (IMARE) spectroscopy is presented. The Hc2(T) temperature dependences are measured at magnetic fields up to 16 T with in-plane and out-of-plane field directions and considered within single-band and two-band models in order to estimate the Hc2(0) value. In IMARE spectroscopy probes, the magnitude, characteristic ratio, and temperature dependence of the superconducting order parameters (ΔL,S(T)) are determined locally and directly. A possible k-space anisotropy of the large superconducting gap is demonstrated. We show that usage of a quadruple of λij0 coupling constants obtained in the IMARE experiment can significantly reduce the number of free parameters required to fit the Hc2(T) dependence within a two-band approach (from six to two).

Multiple Andreev reflections in diffusive SINIS and SIFIS junctions

We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)-superconductor junctions with low-transparency interfaces. Assuming strong thermalization in the weak link, we calculate the current-voltage dependence I(V)I(V). At intermediate temperatures, \varepsilon_\mathrm{Th}\ll T\ll\DeltaεTh≪T≪Δ, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferromagnetic junction. We find that the exchange field produces a non-trivial splitting of the subharmonic gap structure. This effect relies on thermalization and vanishes in SFS junctions with no energy relaxation in the weak link.

Supercurrent, Multiple Andreev Reflections and Shapiro Steps in InAs Nanosheet Josephson Junctions.

We report an experimental study of proximity induced superconductivity in planar Josephson junction devices made from free-standing InAs nanosheets. The nanosheets are grown by molecular beam epitaxy, and the Josephson junction devices are fabricated by directly contacting the nanosheets with superconductor Al electrodes. The fabricated devices are explored by low-temperature carrier transport measurements. The measurements show that the devices exhibit a gate-tunable supercurrent, multiple Andreev reflections, and a good quality superconductor-semiconductor interface. The superconducting characteristics of the Josephson junctions are investigated at different magnetic fields and temperatures and are analyzed based on the Bardeen-Cooper-Schrieffer (BCS) theory. The measurements of the ac Josephson effect are also conducted under microwave radiations with different radiation powers and frequencies, and integer Shapiro steps are observed. Our work demonstrates that InAs nanosheet based hybrid devices are desired systems for investigating the forefront of physics, such as two-dimensional topological superconductivity.

Phase-tunable multiple Andreev reflections in a quantum spin Hall strip

A quantum spin Hall strip where different edges are contacted by s-wave superconductors with a phase difference φ supports Majorana bound states protected by time-reversal symmetry. We study signatures of these states in a four-terminal setup where two Josephson junctions are built on opposite edges of the strip and the phase difference between superconductors can be controlled by an external flux. Applying a voltage bias across the quantum spin Hall strip results in a sequence of conductance peaks from multiple Andreev reflections (MARs). We find that this so-called subharmonic gap structure is very sensitive to the phase difference and displays a phase-controlled even–odd effect, where all odd spikes disappear when the Majorana states are formed for . Moreover, the remaining even spikes split when the superconductors forming the junction have different gap size. We explain these features by showing that any midgap bound states enhance the transmission of the even order MARs, while the reduced density of states at the gap edges suppresses the odd order ones.

Suppression of Nonequilibrium Quasiparticle Transport in Flat-Band Superconductors.

We study nonequilibrium transport through a superconducting flat-band lattice in a two-terminal setup with the Schwinger-Keldysh method. We find that quasiparticle transport is suppressed and coherent pair transport dominates. For superconducting leads, the ac supercurrent overcomes the dc current, which relies on multiple Andreev reflections. With normal-normal and normal-superconducting leads, the Andreev reflection and normal currents vanish. Flat-band superconductivity is, thus, promising not only for high critical temperatures, but also for suppressing unwanted quasiparticle processes.

Superfluid Signatures in a Dissipative Quantum Point Contact.

We measure superfluid transport of strongly interacting fermionic lithium atoms through a quantum point contact with local, spin-dependent particle loss. We observe that the characteristic non-Ohmic superfluid transport enabled by high-order multiple Andreev reflections transitions into an excess Ohmic current as the dissipation strength exceeds the superfluid gap. We develop a model with mean-field reservoirs connected via tunneling to a dissipative site. Our calculations in the Keldysh formalism reproduce the observed nonequilibrium particle current, yet do not fully explain the observed loss rate or spin current.

Multiple Andreev reflections in topological Josephson junctions with chiral Majorana modes

Andreev bound states (ABS) occur in Josephson junctions when the total phase of the Andreev and normal reflections is a multiple of $2\pi$. In ballistic junctions with an applied voltage bias, a quasi-particle undergoes multiple Andreev reflections before entering the leads, resulting in peaks in the current-voltage $I(V)$ curve. Here we present a general model for Josephson junctions with spin-active interlayers i.e., magnetic or topological materials with broken time-reversal symmetry. We investigate how ABS change the peak positions and shape of $I(V)$, which becomes asymmetric for a single incident angle. We show how the angle-resolved $I(V)$ curve becomes a spectroscopic tool for the chirality and degeneracy of ABS.

Quantum interferometer for quartets in superconducting three-terminal Josephson junctions

An interferometric device is proposed in order to analyze the quartet mode in biased three-terminal Josephson junctions (TTJs), and to provide experimental evidence for emergence of a single stationary phase, the so-called quartet phase. In such a quartet-Superconducting Quantum Interference Device (quartet-SQUID), the flux sensitivity exhibits period ${hc}/{4e}$, which is the fingerprint of a transient intermediate state involving two entangled Cooper pairs. The quartet-SQUID provides two informations: an amplitude that measures a total ``quartet critical current'', and a phase lapse coming from the superposition of the following two current components: the quartet supercurrent that is odd in the quartet phase, and the phase-sensitive multiple Andreev reflection (phase-MAR) quasiparticle current, that is even in the quartet phase. This makes a TTJ a generically "$\theta$-junction". Evidence for phase-MARs plays against conservative scenarii involving synchronization of AC Josephson currents, based on ``adiabatic'' phase dynamics and RSJ-like models.

Driven Andreev molecule

We study the voltage-biased S-QD-S-QD-S Josephson junction, composed of three superconductors (S) and two quantum dots (QDs). In the absence of an applied voltage, the Andreev bound states on each quantum dot hybridize, forming an ``Andreev molecule.'' However, understanding of this system in a nonequilibrium setup is lacking. Applying commensurate dc voltages on the bijunction makes the system time periodic, and the equilibrium Andreev bound states evolve into a ladder of resonances with a finite lifetime due to multiple Andreev reflections (MARs). Starting from the time-periodic Bogoliubov--de Gennes equations we map the problem to a tight-binding chain in Floquet space. The resolvent of this non-Hermitian block matrix is obtained via a continued fraction method. We numerically calculate the Floquet-Andreev spectra which could be probed by local tunneling spectroscopy on the dots. We also consider the subgap current, and show that the Floquet resonances determine the position of the MAR steps. Proximity of the two dots causes splitting of the steps, while at large distances we observe interference effects which cause oscillations in the current-voltage curves. The latter effect should persist at very long distances.

Anomalous critical supercurrent and half-integer Shapiro steps based on Josephson junction of topological insulator nanowires

Topological insulator-based Josephson junction, as a candidate device for searching for Majorana zero energy modes, has attracted much attention. One of the key issues along this direction is to fabricate Josephson junctions with high-quality interfaces, hoping to searching for 4π-period current-phase relation in topologically non-trivial Josephson junction. In this work, the Josephson junctions based on three-dimensional topological insulator nanowires Bi<sub>2</sub>Te<sub>3</sub> and Bi<sub>2</sub>(Se<sub><i>x</i></sub>Te<sub>1–<i>x</i></sub>)<sub>3</sub> are fabricated to study their superconducting proximity effects, multiple Andreev reflections, and current-phase relations. A number of interesting phenomena are observed, including the anomalous enhancement in junctions’ critical supercurrent with magnetic field, and the appearance of half-integer Shapiro steps in the ac Josephson effect. And, we discuss the possible origins of the observed anomalous behaviors in general, and their relation with the ferromagnetic layer of TiTe alloy formed at the interface between the topological insulator nanowires and the Ti buffer layer of the metallic electrodes, in particular. We provide the experimental evidence for the formation of a ferromagnetic TiTe alloy layer at the interface of our device. And, we believe that the formation of such a layer in our Josephson device breaks the time reversal symmetry, leading to the observed anomalous enhancement of the critical supercurrent with magnetic field, as well as the appearance of half-integer Shapiro steps. Our results suggest that to study the topologically non-trivial behaviors such as 4π-period current-phase relation, one still needs to improve the interface quality of the superconductor-normal metal-superconductor type of Josephson junction devices.

Anomalous temperature dependence of multiple Andreev reflections in a topological insulator Josephson junction

As a promising platform for unconventional superconductivity, Josephson junctions (JJs) of tetradymite topological insulators (TIs) and s-wave superconductors have been investigated in recent years. This family of TI materials, however, often suffers from spurious bulk transport, which hampers the observation of the exotic physics of their topological surface states. Thus, disentangling the transport mechanism of bulk and surface contributions in TI JJs is of high importance when investigating proximity induced superconductivity in those crystals. In this work, we add to the insights regarding these contributions by studying the temperature-dependent behaviour of a Bi2Te3-based JJ with transparent interfaces. In electrical transport measurements, we investigate differential conductance spectra of multiple Andreev reflections (MARs) and find a qualitative temperature-dependent change from peak features at low temperatures to dip features at higher ones. The observation of both kind of MAR patterns in a single JJ suggests contributions of diffusive bulk and ballistic surface states and links to a similar finding in the temperature dependence of the critical current. Our work advances the research of induced superconductivity in TIs and offers new avenues to study the induced superconductivity in the topological surface states of these materials.

Near-surface InAs two-dimensional electron gas on a GaAs substrate: Characterization and superconducting proximity effect

We have studied a near-surface two-dimensional electron gas based on an InAs quantum well on a GaAs substrate. In devices without a dielectric layer we estimated large electron mobilities on the order of ${10}^{5}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{Vs}$. We have observed quantized conductance in a quantum point contact, and determined the $g$ factor. Using samples with an epitaxial Al layer, we defined multiple Josephson junctions and found the critical current to be gate tunable. Based on multiple Andreev reflections the semiconductor-superconductor interface is transparent, with an induced gap of $125\phantom{\rule{0.28em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{eV}$. Our results suggest that this InAs system is a viable platform for use in hybrid topological superconductor devices.

InAs/MoRe Hybrid Semiconductor/Superconductor Nanowire Devices

Implementing superconductors capable of proximity-inducing a large energy gap in semiconductors in the presence of strong magnetic fields is a major goal toward applications of semiconductor/superconductor hybrid materials in future quantum information technologies. Here, we study the performance of devices consisting of InAs nanowires in electrical contact with molybdenum-rhenium (MoRe) superconducting alloys. The MoRe thin films exhibit transition temperatures of ∼10 K and critical fields exceeding 6 T. Normal/superconductor devices enabled tunnel spectroscopy of the corresponding induced superconductivity, which was maintained up to ∼10 K, and MoRe-based Josephson devices exhibited supercurrents and multiple Andreev reflections. We determine an induced superconducting gap lower than expected from the transition temperature and observe gap softening at finite magnetic field. These may be common features for hybrids based on large-gap, type II superconductors. The results encourage further development of MoRe-based hybrids.

Determination of the Superconducting Order Parameter of BaFe1.92Ni0.08As2 Weakly Underdoped Pnictides by Two Complementary Techniques

The structure of the superconducting order parameter of weakly underdoped BaFe1.92Ni0.08As2 pnictides with the critical temperature Tc ≈ 18.2 K has been determined. Two microscopic superconducting order parameters—the small superconducting gap ΔS(0) and, supposedly, the edges of the large gap with anisotropy in the ab plane Delta _{{text{L}}}^{{{text{out}}}}(0) and Delta _{{text{L}}}^{{{text{in}}}}(0)—have been determined at T ≪ Tc, together with their temperature dependences, using incoherent multiple Andreev reflection spectroscopy. It has been shown that the determined temperature dependence of the lower critical field Hc1(T) can be described in the two-band approximation both within the so-called alpha model (using experimental ΔS(0), Delta _{{text{L}}}^{{{text{out}}}}(0), and Delta _{{text{L}}}^{{{text{in}}}}(0) values) and using the temperature dependences ΔS(T) and Delta _{{text{L}}}^{{{text{out}}{text{,in}}}}(T) obtained by multiple Andreev reflection spectroscopy under the assumption of a fairly strong anisotropy of the small superconducting gap, where the experimental ΔS(0) value is taken as the outer edge of its angular distribution.