Integer Shapiro Steps Research Articles

Josephson dynamics and Shapiro steps at high transmissions: current bias regime.

We investigate Josephson dynamics of highly transparent superconducting nanojunctions at subgap voltages and temperatures. In this limit, intrinsic dissipation in such junctions turns out to be sub-Ohmic, which yields a linear dependence of the average voltage on the bias current I slightly exceeding the critical one Ic. We demonstrate a strong impact of intrinsic sub-Ohmic dissipation on integer Shapiro steps appearing on the I-V curve in the presence of external microwave radiation.

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.

Supercurrent in Bi4Te3 Topological Material-Based Three-Terminal Junctions

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi4Te3 and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators' weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current-phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

Microwave response of NbSe2 van der Waals Josephson junctions

van der Waals Josephson junctions utilize the interface between two superconducting ${\mathrm{NbSe}}_{2}$ crystal flakes as a tunnel barrier. We fabricate such junctions by a dry-transfer procedure and characterize them by electric transport experiments at various temperatures and under microwave irradiation at frequencies up to 224 GHz. We observe integer Shapiro steps in the current-voltage characteristics indicating a sinusoidal Josephson current-phase relation and the possibility to use this kind of junction even in the terahertz frequency range.

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 Effect in MgB2/Pd/Nb Trilayer Josephson Junctions

This paper reports fabrication techniques and results of MgB2/Pd/Nb trilayer Josephson junctions. The MgB2 bottom electrode was co-evaporated by molecular beam epitaxy (MBE) technique from both magnesium and boron sources at a low substrate temperature ~ 300 °C, while the interlayer and the top niobium electrode (Pd/Nb bilayer) were deposited ex-situ using RF sputtering. The junctions exhibited and Josephson effect as well as a modulation of the critical current in a magnetic field applied in a direction normal to the junction plane. Fractional and integer Shapiro steps were observed at voltages corresponding to the frequency of the applied microwave radiation field. The products of the junctions compare well with the previously reported values. The results suggest that it should be possible to fabricate all-MgB2 and MgB2 as one of the electrodes Superconductor/Normal/Superconductor (SNS), Superconductor/Insulator/Superconductor (SIS) or even Superconductor/Ferromagnet/Superconductor (SFS) tunnel junctions with interesting characteristics and for various applications.
 Keywords: MgB2; all-MgB2; Josephson Tunnel junctions; trilayer devices; Niobium

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.

Hybrid Nb/Al/Ba0.5K0.5Fe2As2 sandwich Josephson junctions

We fabricated hybrid Josephson junctions between a Ba0.5K0.5Fe2As2 (BKFA) single crystal and the conventional superconductor Nb with normal metal Al as the barrier. An in situ process was used to create clean BKFA/Al/Nb interfaces. Current transport is along the c-axis of BKFA. The current–voltage characteristics are slightly hysteretic at low temperatures. Except for some features indicative of resonant modes the shape of the current–voltage characteristics can be well described by the resistively and capacitvely shunted junction (RCSJ) model, with a product of the Josephson critical current and the normal state resistance of the junction exceeding 180 μV at low temperatures. The temperature dependence of the Josephson current is linear for temperatures down to 2 K. Under 40 GHz microwave irradiation integer Shapiro steps are observed. The power dependence of the Shapiro step-height is in good agreement with RCSJ simulations. Possible relations of our data with the symmetry of the superconducting order parameter of BKFA are discussed.

Dynamical detection of Majorana fermions in current-biased nanowires

We analyze the current-biased Shapiro experiment in a Josephson junction formed by two one-dimensional nanowires featuring Majorana fermions. Ideally, these junctions are predicted to have an unconventional $4\pi$-periodic Josephson effect and thus only Shapiro steps at even multiples of the driving frequency. Taking additionally into account overlap between the Majorana fermions, due to the finite length of the wire, renders the Josephson junction conventional for any dc-experiments. We show that probing the current-phase relation in a current biased setup dynamically decouples the Majorana fermions. We find that besides the even integer Shapiro steps there are additional steps at odd and fractional values. However, different from the voltage biased case, the even steps dominate for a wide range of parameters even in the case of multiple modes thus giving a clear experimental signature of the presence of Majorana fermions.

Integer and half-integer Shapiro steps in p-SQUIDs

We study the I-V characteristics of π-SQUID's in the presence of an rf radiation, adopting a perturbation approach to first order in the parameter β. We find that integer and half integer Shapiro steps appear in the I-V characteristics of these devices. In particular, half-integer Shapiro steps are seen to have amplitude proportional to β, while integer Shapiro steps are seen not to depend on β, except for applied magnetic fluxes being integer multiples of Φ0

Dynamics of underdamped Josephson junctions with nonsinusoidal current-phase relation

Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.

Dynamics of underdamped Josephson junctions with non-sinusoidal current-phase relation

Results on analytical and computational investigations of high-frequency dynamics of Josephson junctions, characterized by non-zero capacitance and the second harmonic in the current-phase relation are presented. These attributes each have influence on the behaviour of integer Shapiro steps and lead to the formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for the so-called high-frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.

Shapiro steps in symmetric π-SQUID’s

Integer and half-integer Shapiro steps amplitudes in the current–voltage characteristics of symmetric superconducting quantum interference devices containing one π-junction are calculated, in the absence of noise and for small values of the parameter β, by means of a reduced two-junction interferometer model. We find that, to first order in the parameter β, half-integer Shapiro steps are seen to have amplitude proportional to β, itself, while integer Shapiro steps are seen not to depend on β, except for applied fluxes being integer multiples of the elementary flux quantum Φ 0.

Fabrication of Josephson superconductor-normal metal-superconductor series arrays using a focused ion beam

A new fabrication method for superconductor-normal metal-superconductor junctions employing focused ion beam patterning of a superconductor-normal metal bilayer has been used to make series junction arrays. We investigated their current-voltage (I-V) characteristic and examined their response to microwaves at 4.2 K. Multiple integer Shapiro steps were observed in the I-V response of an array to microwaves. In addition, we found that the properties of each junction in a double-junction series array did not change in the junction spacing range studied (0.2-8 µm). Modelling the I-V characteristic of large arrays showed the junction variation of the critical current was 20%.

Characterization of grain boundaries in YBa/sub 2/Cu/sub 3/O/sub y/ bicrystal junctions [SQUIDs

I-V, V-/spl Phi/ characteristics and atomic force images of grain boundary Josephson junctions fabricated on SrTiO/sub 3/ bicrystal substrates were investigated. The half integer Shapiro steps and I/sub c/ versus B curves show evidence of the inhomogeneous current distribution along the grain boundary junction. The dc SQUID formed on the grain boundary shows the expected V-/spl Phi/ curve. The AFM images, R-T curves and I/sub c/R/sub n/ product reveal sequential destructive deterioration of the junction originating from the underlying grooved substrate. The results are discussed.

Characteristics of Aharonov–Bohm Electron Interference in Two-Mode Squeezed Vacuum

Electron interference related to Aharonov–Bohm effect in the presence of the two-mode quantized radiation field is investigated. Characteristics of Shapiro steps, the visibility of the interference fringe and the temporal behavior of electron interference in correlated and uncorrelated two-mode radiation field are discussed. It is shown that for the correlated two-mode squeezed vacuum the integer Shapiro steps are obtained and the time evolution of the intensity of electron interference can exhibit very interesting periodic spontaneous collapse and revival (CR), while for the uncorrelated two-mode coherent state the fractional Shapiro steps are obtained and the CR phenomenon does not occur. In addition, the relation between CR and the quantum fluctuation in electron interference is also discussed.

Effects of magnetic fields and microwave irradiation on step-edge and bi-epitaxial YBa/sub 2/Cu/sub 3/O/sub y/ SQUIDs

Current-voltage (I-V) curves of step-edge YBa/sub 2/Cu/sub 3/O/sub y/ junctions, SQUIDs, and Junctions in parallel in a magnetic field and under microwave irradiation were measured. I/sub c/-/spl Phi/ curves for a single Josephson junctions show Fraunhofer diffraction pattern. The voltage of SQUIDs and Josephson junctions in parallel at a constant bias current is modulated by external magnetic fields. In additional to integer Shapiro steps, non-integer constant-voltage steps were observed under microwave irradiation in bi-epitaxial SQUIDs. The non-integer voltage steps can be modulated by the microwave power and the applied magnetic field.

Screening in Josephson-junction ladders.

Both critical current and Shapiro steps in Josephson ladders are found to show effects of vortex exclusion below a critical magnetic field. Vortices are excluded even though the flux itself is not screened out. When current is injected perpendicular to the ladder edges, the critical current is unchanged from its $f=0$ value up to a penetration field of ${f}_{c1\ensuremath{\perp}}\ensuremath{\approx}0.12$ flux quanta per plaquette. Similarly, there are only integer Shapiro steps below a critical ${f}_{c1\ensuremath{\perp}}^{*}$, where vortices first penetrate. A narrower critical current plateau also appears to form near $f=\frac{1}{2}$. No such plateaus occur when current is injected in the parallel direction. We attribute the exclusion in the perpendicular geometry to screening currents which flow along the edges of the ladder.

Observation of half-integer Shapiro steps in step-edge YBa 2Cu 3O y Josephson junctions

Current-voltage (I–V) characteristics of step-edge YBa 2Cu 3O y junctions on MgO(001) substrates were measured over various temperature and frequency ranges to examine the effects of microwave irradiation and magnetic fields on the I–V behaviors of the junctions. In addition to the usual integer Shapiro steps, half-integer Shapiro steps were observed under microwave irradiation. Both the integer and half-Integer Shapiro steps were sensitive to the applied magnetic field and the microwave power. The results are discussed.

Transverse Shapiro steps in a radio frequency driven superconducting Wheatstone bridge

We study the current-voltage characteristics of a superconducting Wheatstone bridge in the presence of radio frequency current sources. Besides the regular integer Shapiro steps in the current-voltage characteristics observed when the voltage is measured between the input and output leads of the dc biasing current, we also found additional integer steps in the transverse voltage for large value of the dc biasing current. An explanation for these steps is given in terms of competing circulating currents in the bridge.