Sinusoidal Current-phase Relation Research Articles

Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes

We used the asymmetric superconducting quantum interference device (SQUID) technique to extract the current phase relation (CPR) of a Josephson junction with a 3D-topological insulator (3D-TI) Bi2Se3 nanobelt as the barrier. The obtained CPR shows deviations from the standard sinusoidal CPR with a pronounced forward skewness. At temperatures below 200 mK, the junction skewness values are above the zero temperature limit for short diffusive junctions. Fitting of the extracted CPR shows that most of the supercurrent is carried by ballistic topological surface states (TSSs), with a small contribution of diffusive channels primarily due to the bulk. These findings are instrumental in engineering devices that can fully exploit the properties of the topologically protected surface states of 3D TIs.

Asymmetric higher-harmonic SQUID as a Josephson diode

We theoretically investigate asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics. Our main focus is on the "minimal model" with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. The current-voltage characteristic (CVC) turns out to be asymmetric, $I(-V) \neq -I(V)$. The asymmetry is due to the presence of the second harmonic and depends on the magnetic flux through the interferometer loop, vanishing only at special values of the flux such as integer or half-integer in the units of the flux quantum. The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the simplest manifestations of which is the direction dependence of the critical current. We analyze asymmetry of the overall $I(V)$ shape both in the absence and in the presence of external ac irradiation. In the voltage-source case of external signal, the CVC demonstrates the Shapiro spikes. The integer spikes are asymmetric (manifestation of the JDE) while the half-integer spikes remain symmetric. In the current-source case, the CVC demonstrates the Shapiro steps. The JDE manifests itself in asymmetry of the overall CVC shape, including integer and half-integer steps.

Nb/Au/NbSe2 hybrid Josephson junctions

We fabricated thin film Nb/Au/NbSe2 hybrid Josephson junctions by a dry transfer technique with only a single lithography step in the process. A thin Au layer is deposited on Nb to prevent oxidation during the fabrication process. The superconducting van der Waals (vdW) material NbSe2 is placed on top of the Nb/Au layer. Electrical transport properties are studied in detail and are compared to numerical simulations. The current–voltage characteristics we observe are typical for superconductor-normal metal-superconductor junctions and we do not observe an effect of a potential insulating barrier between NbSe2 and Au. The modulation of the critical current in magnetic fields indicates an inhomogeneous distribution of supercurrent density, presumably caused by the roughness of the Nb/Au interface to NbSe2. Nevertheless, we observe clear integer Shapiro steps, indicating a sinusoidal current phase relation of junctions. We do not see an impact of the anisotropic s-wave and the charge density wave in NbSe2 on the Josephson effects. Our method presents a viable and simple way to fabricate hybrid Josephson junctions between superconducting films and two-dimensional (2D) vdW superconducting materials, which might offer a chance for widespread applications.

Josephson detection of time-reversal symmetry broken superconductivity in SnTe nanowires

A Josephson junction (JJ) couples the supercurrent flowing between two weakly linked superconductors to the phase difference between them via a current-phase relation (CPR). While a sinusoidal CPR is expected for conventional junctions with insulating weak links, devices made from some exotic materials may give rise to unconventional CPRs and unusual Josephson effects. In this work, we present such a case: we investigate the proximity-induced superconductivity in SnTe nanowires by incorporating them as weak links in JJs and observe a deviation from the standard CPR. We report on indications of an unexpected breaking of time-reversal symmetry in these devices, detailing the unconventional characteristics that reveal this behavior. These include an asymmetric critical current in the DC Josephson effect, a prominent second harmonic in the AC Josephson effect, and a magnetic diffraction pattern with a minimum in critical current at zero magnetic field. The analysis examines how multiband effects and the experimentally visualized ferroelectric domain walls give rise to this behavior, giving insight into the Josephson effect in materials that possess ferroelectricity and/or multiband superconductivity.

Voltage Fluctuations in ac Biased Superconducting Transition-Edge Sensors.

We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the "excess" noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation.

Fully in situ Nb/InAs-nanowire Josephson junctions by selective-area growth and shadow evaporation.

Josephson junctions based on InAs semiconducting nanowires and Nb superconducting electrodes are fabricated in situ by a special shadow evaporation scheme for the superconductor electrode. Compared to other metallic superconductors such as Al, Nb has the advantage of a larger superconducting gap which allows operation at higher temperatures and magnetic fields. Our junctions are fabricated by shadow evaporation of Nb on pairs of InAs nanowires grown selectively on two adjacent tilted Si (111) facets and crossing each other at a small distance. The upper wire relative to the deposition source acts as a shadow mask determining the gap of the superconducting electrodes on the lower nanowire. Electron microscopy measurements show that the fully in situ fabrication method gives a clean InAs/Nb interface. A clear Josephson supercurrent is observed in the current–voltage characteristics, which can be controlled by a bottom gate. The large excess current indicates a high junction transparency. Under microwave radiation, pronounced integer Shapiro steps are observed suggesting a sinusoidal current–phase relation. Owing to the large critical field of Nb, the Josephson supercurrent can be maintained to magnetic fields exceeding 1 T. Our results show that in situ prepared Nb/InAs nanowire contacts are very interesting candidates for superconducting quantum circuits requiring large magnetic fields.

An ideal Josephson junction in an ultracold two-dimensional Fermi gas.

The role of reduced dimensionality in high-temperature superconductors is still under debate. Recently, ultracold atoms have emerged as an ideal model system to study such strongly correlated two-dimensional (2D) systems. Here, we report on the realization of a Josephson junction in an ultracold 2D Fermi gas. We measure the frequency of Josephson oscillations as a function of the phase difference across the junction and find excellent agreement with the sinusoidal current phase relation of an ideal Josephson junction. Furthermore, we determine the critical current of our junction in the crossover from tightly bound molecules to weakly bound Cooper pairs. Our measurements clearly demonstrate phase coherence and provide strong evidence for superfluidity in a strongly interacting 2D Fermi gas.

Strongly correlated superfluid order parameters from dc Josephson supercurrents.

The direct-current (dc) Josephson effect provides a phase-sensitive tool for investigating superfluid order parameters. We report on the observation of dc Josephson supercurrents in strongly interacting fermionic superfluids across a tunneling barrier in the absence of any applied potential difference. For sufficiently strong barriers, we observed a sinusoidal current-phase relation, in agreement with Josephson's seminal prediction. We mapped out the zero-resistance state and its breakdown as a function of junction parameters, extracting the Josephson critical current behavior. By comparing our results with an analytic model, we determined the pair condensate fraction throughout the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation crossover. Our work suggests that coherent Josephson transport may be used to pin down superfluid order parameters in diverse atomic systems, even in the presence of strong correlations.

Anomalous Josephson effect in noncentrosymmetric superconductors

We reveal the underlying physics of the anomalous Josephson effect in a magnetic Josephson junction between two noncentrosymmetric superconductors. The key point is that the two effective superconducting gaps provide two sets of Andreev bound states which carry two supercurrents with different amplitudes. When the magnetization direction of the ferromagnet is suitably chosen, the two supercurrents experience opposite phase shifts from the conventional sinusoidal current-phase relation. Then the total Josephson current results in a continuously tunable ground-state phase difference by adjusting the ferromagnet parameters and the triplet-singlet ratio of noncentrosymmetric superconductors. The emergence of anomalous Josephson current can definitely confirm the existence of triplet pairing and the ground-state phase difference serves as a tool to determine the triplet-singlet ratio of noncentrosymmetric superconductors.

Spin-triplet superconducting current in metal-oxide heterostructures with composite ferromagnetic interlayer

Superconducting heterostructures fabricated from oxide superconductor $\text{YBa}_{2}\text{Cu}_{2}\text{O}_{7-\delta}$ and a composite ferromagnet La0.7Sr0.3MnO3/SrRuO3 interlayer and Au/Nb counter electrode were studied experimentally. Superconducting current was observed at magnetic field $H$ raised up to 2000 Oe, which is greater than saturation magnetic field of manganite La0.7Sr0.3MnO3 (of order 100 Oe) and greater by a few orders than the value of magnetic field corresponding to penetration of one magnetic flux quantum. Microwave measurements of integer and half-integer Shapiro steps in conditions when relatively low external magnetic field $H was applied showed that the second harmonic in the current-phase relation of superconducting current becomes as big as the first harmonic. Fourier analysis of $I_{C}(H)$ dependence allows extracting the components of fractional periods in $I_{C}(H)$ function that also confirms a deviation from the sinusoidal current-phase relation. The obtained experimental data are explained by theoretical models that predict a huge enhancement of the second harmonic of the spin-triplet component in the superconducting current. The current-phase relation could be controlled by an external magnetic field, changing the directions of magnetization in the composite bilayer ferromagnet, which is inserted between two spin-singlet superconductors.

Evidence for an anomalous current-phase relation in topological insulator Josephson junctions.

Josephson junctions with topological insulator weak links can host low-energy Andreev-bound states giving rise to a current-phase relation that deviates from sinusoidal behaviour. Of particular interest are zero-energy Majorana-bound states that form at a phase difference of π. Here we report on interferometry studies of Josephson junctions and superconducting quantum interference devices (SQUIDs) incorporating topological insulator weak links. We find that the nodes in single-junction diffraction patterns and SQUID oscillations are lifted and independent of chemical potential. At high temperatures, the SQUID oscillations revert to conventional behaviour, ruling out asymmetry. The node-lifting of the SQUID oscillations is consistent with low-energy Andreev-bound states exhibiting a nonsinusoidal current-phase relation, co-existing with states possessing a conventional sinusoidal current-phase relation. However, the finite nodal currents in the single-junction diffraction pattern suggest an anomalous contribution to the supercurrent possibly carried by Majorana-bound states, although we also consider the possibility of inhomogeneity.

Experimental Realization of Josephson Junctions for an Atom SQUID

We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.

Triplet superconducting correlations in oxide heterostructures with a composite ferromagnetic interlayer

The superconducting current induced by the penetration of the long-range triplet component of superconducting correlations into a composite ferromagnetic interlayer has been detected in mesa-heterostructures based on oxide cuprate superconductors YBa2Cu3O7 - delta and Au/Nb bilayer films with the composite oxide interlayer that is made of ferromagnetic films of manganite La0.7Sr0.3MnO3 and ruthenate SrRuO3 and has a thickness much larger than the length of correlations determined by the exchange field. The deviation of the superconducting current in the mesa-heterostructure with the fraction of the second harmonic of 13% from a sinusoidal current-phase relation has been detected; this deviation can also be due to the generation of the triplet component of superconducting correlations in the ferromagnet.

Microwave reflection measurement of critical currents in a nanotube Josephson transistorwith a resistive environment

A scheme for measuring small intrinsic critical currentsIc in nanoscale devices is described. Changes in Josephson inductanceLJ are converted to frequency variations that are recorded via microwave reflection measurementsat 700–800 MHz. The critical current is determined from the frequency shift of the reflectionmagnitude at zero phase bias assuming a sinusoidal current–phase relation. The method isused to study a multiwalled carbon nanotube transistor with Pd/Nb contacts inside aresistive on-chip environment. We observe gate-tunable critical currents up toIc ∼ 8 nA correspondingto LJ > 40 nH. The method presented is also applicable to devices shunted by closed superconductingloops.

Current-Phase Relation of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7-X</sub>/Nb Unconventional Superconductor Junctions

The knowledge of the current-phase relation (CPR) in superconducting junctions is essential in many applications like low-dissipative superconducting electronics or superconducting qubits for quantum computation. Theory predicts that unconventional superconductivity induces a significant second harmonic J2 in the CPR. Consequently, anomalies such as half-integer Shapiro steps should be observed in the microwave assisted current-voltage characteristics of the junctions. We performed electric transport measurements in YBa2Cu3O7-x/Nb unconventional superconductor junctions for 72 different tunneling directions in the ab plane and found no trace of such anomalies. This suggest that J2 is insignificantly small so that YBa2Cu3O7-x/Nb junctions have a purely sinusoidal CPR.

Josephson coupling in untwinned YBa2Cu3O7-x/Nb d-wave junctions

Theory predicts that d-wave superconductivity induces a significant second harmonic J2 in the Josephson current, as a result of zero-energy Andreev states (ZES) formed at the junction interface. Consequently, anomalies such as half-integer Shapiro steps should be observed. Both ZES formation and J2 are expected to be highly anisotropic as we change the tunneling orientation in the ab plane reaching their maximum for tunneling close to [110] direction and their minimum for [100] or [010] directions. We performed experiments on junctions between untwinned d-wave YBa2Cu3O7-x and Nb and found clear evidence of ZES formation for all 72 different tunneling directions in the ab plane investigated. However, in contrast to the theoretical predictions, we found no trace of half-integer Shapiro steps. That suggests J2 is insignificantly small compared to the first Josephson harmonic for all of the orientations. We believe that microscopic scale roughness, or diffusive reflection at a scale that is much smaller than the Fermi wavelength, dramatically suppresses J2 due to scattering processes. Our findings suggest that YBa2Cu3O7-x/Nb d-wave junctions have a purely sinusoidal current-phase relation which is essential to take into consideration for their implementation as qubits or π-junctions in digital circuits.

Josephson current in a superconductor-ferromagnet junction with two noncollinear magnetic domains

We study the Josephson effect in a superconductor-ferromagnet-superconductor (SFS) junction with ferromagnetic domains of noncollinear magnetization. As a model for our study we consider a diffusive junction with two ferromagnetic domains along the junction. The superconductor is assumed to be close to the critical temperature ${T}_{c}$, and the linearized Usadel equations predict a sinusoidal current-phase relation. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. As a function of those parameters, the junction may undergo transitions between $0$ and $\ensuremath{\pi}$ phases. We find that the presence of domains reduces the range of junction lengths at which the $\ensuremath{\pi}$ phase is observed. For the junction with two domains of the same length, the $\ensuremath{\pi}$ phase totally disappears as soon as the misorientation angle exceeds $\frac{\ensuremath{\pi}}{2}$. We further comment on the possible implication of our results for experimentally observable $0$-$\ensuremath{\pi}$ transitions in SFS junctions.

Probing the intrinsic Josephson coupling potential inBi2Sr2CaCu2O8+δsuperconductors by thermal activation

We study thermal fluctuation phenomena in small Bi-2212 intrinsic Josephson junctions. Being able to measure switching currents of a {\it single} intrinsic junction, we observe that it's statistics can be very well described by thermal activation from a periodic Josephson potential with the sinusoidal current-phase relation. This is a direct evidence for the dc-intrinsic Josephson effect and the first unambiguous confirmation of the tunnelling nature of interlayer transport in strongly anisotropic high temperature superconductors. Furthermore, the fluctuation-free critical current, extracted from the analysis of switching current statistics, exhibits a temperature dependence typical for superconductor- insulator- superconductor tunnel junctions.

The influence of the second harmonic in the current-phase relation on the voltage-current characteristic of high TC�DC�SQUID

A theory for the voltage-current characteristic in high TC DC SQUIDs, which accounts for a second harmonic in the junction current-phase relation, is developed. The comparison with experiment is performed. It is shown that if the second harmonic is prevailed, the theory can explain the large deviations of the experimental voltage modulation from theoretical predictions and computer simulations based on conventional sinusoidal current-phase relation.

Supercurrent–phase relation of a Nb/InAs(2DEG)/Nb Josephson junction

Using an RF-SQUID configuration we have measured the temperature dependence of the current–phase relation (CPR) of Nb/InAs(2DEG)/Nb (two-dimensional electron gas, 2DEG) Josephson junctions with high interface transparency. At low temperatures, significant deviations from a sinusoidal CPR are observed. The experimental results are fitted by the scattering matrix theory of Brouwer and Beenakker, additionally taking into account the proximity effect between the Nb and the 2DEG in the inversion layer on p-type bulk InAs. We have studied also the influence of an external gate voltage applied to the InAs(2DEG) channel. It is shown that the amplitude of RF-SQUID oscillations can be controlled by gate voltage with only modest deterioration of the SQUID signal.