Shapiro Steps Research Articles

Quantized current steps due to the synchronization of microwaves with Bloch oscillations in small Josephson junctions.

Synchronization of Bloch oscillations in small Josephson junctions (JJs) under microwave radiation, which leads to current quantization, has been proposed as an effect that is dual to the appearance of Shapiro steps. This current quantization was recently demonstrated in superconducting nanowires in a compact high-impedance environment. Direct observation of current quantization in JJs would confirm the synchronization of Bloch oscillations with microwaves and help with the realisation of the metrological current standard. Here, we place JJs in a high-impedance environment and demonstrate dual Shapiro steps for frequencies up to 24 GHz (I = 7.7 nA). Current quantization exists, however, only in a narrow range of JJ parameters. We carry out a systematic study to explain this by invoking the model of a JJ in the presence of thermal noise. The findings are important for fundamental physics and application in quantum metrology.

Doubled Shapiro steps in a dynamic axion insulator Josephson junction

Dynamic axion insulators feature a time-dependent axion field that can be induced by antiferromagnetic resonance. Here, we show that a Josephson junction incorporating this dynamic axion insulator between two superconductors exhibits striking doubled Shapiro steps wherein all odd steps are completely suppressed in the joint presence of a DC bias and a static magnetic field. The resistively shunted junction simulation confirms that these doubled Shapiro steps originate from the distinctive axion electrodynamics driven by the antiferromagnetic resonance, which thus not only furnishes a hallmark to identify the dynamic axion insulator but also provides a method to evaluate its mass term. Furthermore, the experimentally feasible differential conductance is also determined. Our work holds significant importance in condensed matter physics and materials science for understanding the dynamic axion insulator, paving the way for its further exploration and applications.

Interfering Josephson diode effect in Ta2Pd3Te5 asymmetric edge interferometer

Edge states in topological systems have attracted great interest due to their robustness and linear dispersions. Here a superconducting-proximitized edge interferometer is engineered on a topological insulator Ta2Pd3Te5 with asymmetric edges to realize the interfering Josephson diode effect (JDE), which hosts many advantages, such as the high efficiency as much as 73% at tiny applied magnetic fields with an ultra-low switching power around picowatt. As an important element to induce such JDE, the second-order harmonic in the current-phase relation is also experimentally confirmed by half-integer Shapiro steps. The interfering JDE is also accompanied by the antisymmetric second harmonic transport, which indicates the corresponding asymmetry in the interferometer, as well as the polarity of JDE. This edge interferometer offers an effective method to enhance the performance of JDE, and boosts great potential applications for future superconducting quantum devices.

Demonstration of dual Shapiro steps in small Josephson junctions.

Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I=±n×2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I≈3 nA. Inspired by today's voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.

Feasibility of the Josephson voltage and current standards on a single chip

The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.

From nonreciprocal to charge-4e supercurrent in Ge-based Josephson devices with tunable harmonic content

Hybrid superconductor(S)-semiconductor(Sm) devices bring a range of functionalities into superconducting circuits. In particular, hybrid parity-protected qubits and Josephson diodes were recently proposed and experimentally demonstrated. Such devices leverage the nonsinusoidal character of the Josephson current-phase relation (CPR) in highly transparent S-Sm-S junctions. Here, we report an experimental study of superconducting quantum-interference devices (SQUIDs) embedding Josephson field-effect transistors fabricated from a SiGe/Ge/SiGe heterostructure grown on a 200-mm silicon wafer. The single-junction CPR shows up to three harmonics with gate-tunable amplitude. In the presence of microwave irradiation, the ratio of the first two dominant harmonics, corresponding to single and double Cooper-pair transport processes, is consistently reflected in relative weight of integer and half-integer Shapiro steps. A combination of magnetic-flux and gate-voltage control enables tuning the SQUID functionality from a nonreciprocal Josephson-diode regime with 27% asymmetry to a π-periodic Josephson regime suitable for the implementation of parity-protected superconducting qubits. These results illustrate the potential of Ge-based hybrid devices as versatile and scalable building blocks of superconducting quantum circuits. Published by the American Physical Society 2024

Shapiro Steps in Driven Atomic Josephson Junctions.

We study driven atomic Josephson junctions realized by coupling two two-dimensional atomic clouds with a tunneling barrier. By moving the barrier at a constant velocity, dc and ac Josephson regimes are characterized by a zero and nonzero atomic density difference across the junction, respectively. Here, we monitor the dynamics resulting in the system when, in addition to the above constant velocity protocol, the position of the barrier is periodically driven. We demonstrate that the time-averaged particle imbalance features a plateau behavior that is the analog of Shapiro steps observed in driven superconducting Josephson junctions. The underlying dynamics reveals an intriguing interplay of the vortex and phonon excitations, where Shapiro steps are induced via suppression of vortex growth. We study the system with a classical-field dynamics method, and benchmark our findings with a driven circuit dynamics.

Dynamic metastable vortex states in interacting vortex lines

The electron transport in current-biased superconducting nano-bridges is determined by the motion of the quantum vortex confined in the internal disorder landscape. Here we consider theoretically a simple case of a single or two neighbouring linear defects crossing a nano-bridge. The strong anharmonicity of the vortex motion along the defect leads, upon radio frequency (RF) excitation, to fractional Shapiro steps. In the case of two defects, the vortex motion becomes correlated, characterised by metastable states that can be locked to the RF-drive. The lock-unlock process causes sudden voltage jumps and drops in the voltage-current characteristics that can be observed in experiments. We analyse the parameters that promote these metastable dynamic states and discuss their possible experimental realisations.

Toolkit in Python for Simulation of Shapiro Step on the Current–Voltage Characteristic of a Josephson Junction

Toolkit in Python for Simulation of Shapiro Step on the Current–Voltage Characteristic of a Josephson Junction

Half-integer Shapiro steps in MgB2 focused He ion beam Josephson junctions

Abstract Half-integer microwave induced steps (Shapiro steps) have been observed in many different Josephson junction systems, which have attracted a lot of attention because they signify the deviation of current phase relation (CPR) and uncover many unconventional physical properties. In this article, we first report the discovery of half-integer Shapiro steps in MgB2 focused He ion beam (He-FIB) Josephson junctions. The half-integer steps’ dependence on microwave frequency, temperature, microwave power, and magnetic field is also analyzed. We find that the existence of half-integer steps can be controlled by the magnetic field periodically, which is similar to that of high temperature superconductor (HTS) grain boundary junctions, and the similarity of the microstructures between gain boundary junctions and He-FIB junctions is discussed. As a consequence, we mainly attribute the physical origin of half-integer steps in MgB2 He-FIB junctions to the model that a He-FIB junction is analogous to a parallel junctions’ array. Our results show that He-FIB technology is a promising platform for researching CPR in junctions made of different superconductors.

MgB[formula omitted] Josephson Junctions fabricated by Focused Helium Ion Beam with different irradiation doses on SiC and MgO substrates

Recently, high quality MgB2 single junctions and junction arrays fabricated by Focused Helium Ion Beam irradiation (He-FIB) have been reported. However, the effects of irradiation doses and substrates on junction properties have not been analysed systematically. In this work, 30 nm MgB2 thin films were deposited on SiC (0001) and MgO (111) substrates using Hybrid Physical–Chemical Vapour Deposition (HPCVD) technique and then etched into 2–4 μm wide microbridges. 2000–6000 ions/nm doses of He-FIB were irradiated across these microbridges, creating narrow junction barriers. R–T curves exhibit a clear foot-like structure that enlarges as irradiation dose increases. Temperature dependence of junction properties (critical current Ic, junction normal state resistance Rn, characteristic voltage Vc) shows that all junctions in our experiment exhibit superconductor–normal–superconductor (SNS) like behaviour and higher irradiation doses create thicker junction barriers. Furthermore, we analyse junction properties dependence on irradiation doses which yields an exponential change law. Finally, Fraunhofer diffraction-like patterns and Shapiro steps of junctions are also measured. Our results show MgB2 Josephson Junctions with adjustable properties can be fabricated by He-FIB on SiC and MgO substrates, which provides a solid foundation for future application devices research.

Large second-order Josephson effect in planar superconductor-semiconductor junctions

We investigate the current-phase relations of Al/InAs-quantum well planar Josephson junctions fabricated using nanowire shadowing technique. Based on several experiments, we conclude that the junctions exhibit an unusually large second-order Josephson harmonic, the \sin(2\varphi)sin(2φ) term. First, superconducting quantum interference devices (dc-SQUIDs) show half-periodic oscillations, tunable by gate voltages as well as magnetic flux. Second, Josephson junction devices exhibit kinks near half-flux quantum in supercurrent diffraction patterns. Third, half-integer Shapiro steps are present in the junctions. Similar phenomena are observed in Sn/InAs quantum well devices. We perform data fitting to a numerical model with a two-component current phase relation. Analysis including a loop inductance suggests that the sign of the second harmonic term is negative. The microscopic origins of the observed effect remain to be understood. We consider alternative explanations which can account for some but not all of the evidence.

Co-doped BaFe2As2 Josephson junction fabricated with a focused helium ion beam

Josephson junction plays a key role not only in studying the basic physics of unconventional iron-based superconductors but also in realizing practical application of thin-film based devices, therefore the preparation of high-quality iron pnictide Josephson junctions is of great importance. In this work, we have successfully fabricated Josephson junctions from Co-doped BaFe2As2 thin films using a direct junction fabrication technique which utilizes high energy focused helium ion beam (FHIB). The electrical transport properties were investigated for junctions fabricated with various He+ irradiation doses. The junctions show sharp superconducting transition around 24 K with a narrow transition width of 2.5 K, and a dose correlated foot-structure resistance which corresponds to the effective tuning of junction properties by He+ irradiation. Significant J c suppression by more than two orders of magnitude can be achieved by increasing the He+ irradiation dose, which is advantageous for the realization of low noise ion pnictide thin film devices. Clear Shapiro steps are observed under 10 GHz microwave irradiation. The above results demonstrate the successful fabrication of high quality and controllable Co-doped BaFe2As2 Josephson junction with high reproducibility using the FHIB technique, laying the foundation for future investigating the mechanism of iron-based superconductors, and also the further implementation in various superconducting electronic devices.

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.

Shapiro Steps at the Sliding of Charge Density Waves: Oscillations, Frequency Mixing, and Features in High Electric Fields

Shapiro Steps at the Sliding of Charge Density Waves: Oscillations, Frequency Mixing, and Features in High Electric Fields

Shapiro Steps and Surface Acoustic Waves in Charge Density Wave Dynamics

Shapiro Steps and Surface Acoustic Waves in Charge Density Wave Dynamics

O printsipial'nom otlichii vozdeystviya elektricheskikh i mekhanicheskikh kolebaniy na dinamiku volny zaryadovoy plotnosti

The effects of radio-frequency electric and strain fields on the depinning and sliding of a charge density wave in the quasi-one-dimensional conductor TaS3 have been compared. The amplitude dependence of the threshold voltage Vt (zeroth Shapiro step) has been studied for both fields. The threshold voltage Vt decreases with increasing radio-frequency electric field Erf at increasing rate |dVt/dErf|, whereas with increasing strain field, the decrease in the threshold voltage Vt is saturated, approaching a constant value. This result indicates a qualitative difference between the mechanisms of influence of the electric and strain fields on the dynamics of the charge density wave and is explained by the modulation of the sliding velocity of the charge density wave and pinning potential in the former and latter cases, respectively. In practice, the result allows one to distinguish the mechanical impact on the dynamics of the charge density wave from the influence of electrical interference at the same frequency.

Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors.

Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi2Sr2CaCu2O8+x crystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.

Electric-field modulation of the charge-density-wave quantum condensate in h-BN/NbS3 quasi-2D/1D heterostructure devices

We report on the field-effect modulation of the charge-density-wave quantum condensate in the top-gated heterostructure devices implemented with quasi-one-dimensional NbS3 nanowire channels and quasi-two-dimensional h-BN gate dielectric layers. The charge-density-wave phases and collective current in quasi-1D NbS3 nanowires were verified via temperature dependence of the resistivity, non-linear current–voltage characteristics, and Shapiro steps that appeared in the device response under radio frequency excitation mixed with the DC bias. It was demonstrated that the electric field of the applied gate bias can reversibly modulate the collective current of the sliding charge-density-wave condensate. The collective current reduces with more positive bias, suggesting a surface effect on the condensate mobility. The single-particle current, at small source–drain biases, shows small-amplitude fluctuation behavior, attributed to the variations in the background potential due to the pinned or creeping charge-density-wave condensate. The knowledge of the electric-field effect on the charge density waves in quasi-1D NbS3 nanowires is useful for potential electronic applications of such quantum materials.

On-chip ac driving for dual Shapiro steps

On-chip ac driving for dual Shapiro steps