Half-integer Shapiro steps in MgB_(2) focused He ion beam Josephson junctions

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 MgB_(2)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 MgB_(2)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.

Energy gap suppression and excess current in TI2Ba2CaCu208 intrinsic Josephson junctions

Intrinsic Josephson junctions in misaligned T12Ba2CaCu208 thin film were fabricated on LaA103 substrate. The temperature dependence of the critical current is investigated around liquid nitrogen temperature. In the current voltage characteristic, large voltage jump and lack of resistive branch are observed, which shows good consistency with the intrinsic Josephson junctions. By analyzing the large gap voltage in the curve, great suppression of the energy gap is found. Through discussing the temperature dependence of the gap voltage in liquid nitrogen temperature, it is shown that this phenomenon can be caused by the non-equilibrium quasiparticle injection. The temperature influence on the excess current also confirms the non-equilibrium effect.

Quantum Dynamics of Two Capacitively Coupled Superconducting Islands via josephson Junctions

In this paper, we consider a system consisting of two capacitively coupled superconducting islands viaJosephson junctions. We show that it can be reduced to two coupling harmonic oscillators under certain conditions,and can be solved exactly in terms of a displacing transformation, a beam-splitter-like transformation, and a squeezingtransformation. It is found that the system evolves by a rotated-squeezed-coherent state when the system is initially in acoherent state. Quantum dynamics of the Cooper pairs in the two superconducting islands are investigated. It is shownthat the number of the Cooper pairs in the two islands evolves periodically.

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted （RCL-shunted） Josephson junctions （RCLSJJs） and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.

Josephson vortices and intrinsic Josephson junctions in the layered iron-based superconductor Ca_(10)(Pt_(3)As_(8))((Fe_(0.9)Pt_(0.1))_(2)As_(2))_(5)

Modulated electronic state due to the layered crystal structures brings about moderate anisotropy of superconductivity in the iron-based superconductors and thus Abrikosov vortices are expected in the mixed state.However,based on the angular and temperature dependent transport measurements in iron-based superconductor Ca_(10)(Pt_(3)As_(8))((Fe_(0.9)Pt_(0.1))_(2)As_(2))_(5) with Tc(≌)12 K,we find clear evidences of a crossover from Abrikosov vortices to Josephson vortices at a crossover temperature T*(≌)7 K,when the applied magnetic field is parallel to the superconducting FeAs layers,i.e.,the angle between the magnetic field and the FeAs layers θ=0°.This crossover to Josephson vortices is demonstrated by an abnormal decrease(increase)of the critical current(flux-flow resistance)below T*,in contrast to the increase(decrease)of the critical current(flux-flow resistance)above T* expected for Abrikosov vortices.Furthermore,when θ is larger than 0.5°,the flux-flow resistance and critical current have no anomalous behaviors across T*.These anomalous behaviors can be understood in terms of the distinct transition from the well-pinned Abrikosov vortices to the weakly-pinned Josephson vortices upon cooling,when the coherent length perpendicular to the FeAs layers ξ⊥ becomes shorter than half of the interlayer distance d/2.These experimental findings indicate the existence of intrinsic Josephson junctions below T* and thus quasi-two-dimensional superconductivity in Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5,similar to those in the cuprate superconductors.

Fabrication of rhenium Josephson junctions

Rhenium is a superconductor with a relatively weak tendency to oxidize, which is advantageous in superconducting quantum circuit and qubit applications. In this work, Re/A1-A1Ox/Re Josephson tunnel junctions were fabricated using a selective film-etching process similar to that developed in Nb trilayer technology. The Re films had a superconducting transition temperature of 4.8 K and a transition width of 0.2 K. The junctions were found to be highly reproducible using the fabrication process and their characteristics had good quality with a low leakage current and showed a superconducting gap of 0.55 meV.

Flux qubit with a large loop size and tunable Josephson junctions

We present the design of a superconducting flux qubit with a large loop inductance. The large loop inductance is desirable for coupling between qubits. The loop is configured into a gradiometer form that could reduce the interference from environmental magnetic noise. A combined Josephson junction, i.e., a DC-SQUID is used to replace the small Josephson junction in the usual 3-JJ （Josephaon junction） flux qubit, leading to a tunable energy gap by using an independent external flux line. We perform numerical calculations to investigate the dependence of the energy gap on qubit parameters such as junction capacitance, critical current, loop inductance, and the ratio of junction energy between small and large junctions in the flux qubit. We suggest a range of values for the parameters.

Tunneling spectra of underdoped Bi_2Sr_2Ca_(1-x)Y_xCu_2O_(8+δ) intrinsic Josephson junctions

Mesa-structured submicron intrinsic Josephson junctions are successfully fabricated and well characterized on underdoped Bi2Sr2Ca1-xYxCu2O8＋δ single crystals with a Tc of 80 K. Tunneling spectra at the temperatures ranging from 4.2 K to 295 K are measured. A pulse technique is used to reduce sample heating for the measurement near pseudogap opening temperature T^＊ - 280 K. Our experimental results show that the superconducting gap, the peakdip separation, and the pseudogap opening temperature are all increased as compared with those from near optimally doped samples, which requires further theoretical analysis in the future.

Synchronization of chaos in resistive-capacitive-inductive shunted Josephson junctions

We present a scheme for chaotic synchronization in two resistive- capacitive-inductive shunted Josephson junctions （RCLSJJs） by using another chaotic RCLSJJ as a driving system. Numerical simulations show that whether the two RCLSJJs are chaotic or not before being driven, they can realize chaotic synchronization with a suitable driving intensity, under which the maximum condition Lyapunov exponent （MCLE） is negative. On the other hand, if the driving system is in different periodic states or chaotic states, the two driven RCLSJJs can be controlled into the periodic states with different period numbers or chaotic states but still maintain the synchronization.

Fabrication of Al/AlO_x/Al Josephson junctions and superconducting quantum circuits by shadow evaporation and a dynamic oxidation process

Besides serving as promising candidates for realizing quantum computing, superconducting quantum circuits are one of a few macroscopic physical systems in which fundamental quantum phenomena can be directly demonstrated and tested, giving rise to a vast field of intensive research work both theoretically and experimentally. In this paper we report our work on the fabrication of superconducting quantum circuits, starting from its building blocks： Al/AlOx/Al Josephson junctions. By using electron beam lithography patterning and shadow evaporation, we have fabricated aluminum Josephson junctions with a controllable critical current density （jc） and wide range of junction sizes from 0.01 μm2 up to 1 μm2. We have carried out systematical studies on the oxidation process in fabricating Al/AlOx/Al Josephson junctions suitable for superconducting flux qubits. Furthermore, we have also fabricated superconducting quantum circuits such as superconducting flux qubits and charge-flux qubits.

Energy gap suppression and excess current in Tl_2Ba_2CaCu_2O_8 intrinsic Josephson junctions

Intrinsic Josephson junctions in misaligned Tl2Ba2CaCu2O8 thin film were fabricated on LaAlO3 substrate. The temperature dependence of the critical current is investigated around liquid nitrogen temperature. In the current voltage characteristic, large voltage jump and lack of resistive branch are observed, which shows good consistency with the intrinsic Josephson junctions. By analyzing the large gap voltage in the curve, great suppression of the energy gap is found. Through discussing the temperature dependence of the gap voltage in liquid nitrogen temperature, it is shown that this phenomenon can be caused by the non-equilibrium quasiparticle injection. The temperature influence on the excess current also confirms the non-equilibrium effect.

Probing the minigap in topological insulator-based Josephson junctions under radio frequency irradiation

Recently,a contact-resistance-measurement method was developed to detect the minigap,hence the Andreev bound states(ABSs),in Josephson junctions constructed on the surface of three-dimensional topological insulators(3D TIs).In this work,we further generalize that method to the circumstance with radio frequency(rf)irradiation.We find that with the increase of the rf power,the measured minigap becomes broadened and extends to higher energies in a way similar to the rf power dependence of the outer border of the Shapiro step region.We show that the corresponding data of contact resistance under rf irradiation can be well interpreted by using the resistively shunted Josephson junction(RSJ)model and the Blonder–Tinkham–Klapwijk(BTK)theory.Our findings could be useful when using the contact-resistancemeasurement method to study the Majorana-related physics in topological insulator-based Josephson junctions under rf irradiation.

Bridge-free fabrication process for Al/AlO_x/Al Josephson junctions

We fabricate different-sized Al/AlO_x/Al Josephson junctions by using a simple bridge-free technique, in which only single-layer E-beam resist polymethyl methacrylate（PMMA） is exposed at low accelerate voltage（below 30 kV） and the size of junction can be varied in a large range. Compared with the bridge technique, this fabrication process is very robust because it can avoid collapsing the bridge during fabrication. This makes the bridge-free technique more popular to meet different requirements for Josephson junction devices especially for superconducting quantum bits.

Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V_(5)S_(8)

Introduction of spin-orbit coupling(SOC)in a Josephson junction(JJ)gives rise to unusual Josephson effects.We investigate JJs based on a newly discovered heterodimensional superlattice V_(5)S_(8) with a special form of SOC.The unique homointerface of our JJs enables elimination of extrinsic effects due to interfaces and disorder.We observe asymmetric Fraunhofer patterns with respect to both the perpendicular magnetic field and the current.The asymmetry is influenced by an in-plane magnetic field.Analysis of the pattern points to a nontrivial spatial distribution of the Josephson current that is intrinsic to the SOC in V_(5)S_(8).

Ac Josephson effect in Corbino-geometry Josephson junctions constructed on Bi_(2)Te_(3) surface

Recently, a Corbino-geometry type of Josephson junction constructed on the surface of topological insulators has been proposed for hosting and braiding Majorana zero modes. As a first step to test this proposal, we successfully fabricated Corbino-geometry Josephson junctions(JJs) on the surface of Bi_(2)Te_(3) flakes. Ac Josephson effect with fractional Shapiro steps was observed in the Corbino-geometry JJs while the flux in the junction area was quantized. By analyzing the experimental data using the resistively shunted Josephson junction model, we found that the Corbino-geometry JJs exhibit a skewed current-phase relation due to its high transparency. The results suggest that Corbino-geometry JJs constructed on the surface of topological insulators may provide a promising platform for studying Majorana-related physics.

Continuous Variable Entanglement of Two Mesoscopic Josephson Junctions Induced by a Thermal Radiation Field

The continuous-variable （CV） entanglement between two mesoscopic Josephson junctions is studied and the time-dependent characteristic function in Wigner representation for the Josephson junction subsystem driven by a singlemode thermal field is analytically obtained. It is found that an initial lowest energy state of the junction subsystem can evolve into a two-mode entangled Gaussian state through the interaction with the thermal radiation field. Furthermore, we investigate the influence of the temperature on the entanglement of the junctions and find that the CV entanglement of the two junctions shows the critical behavior with respect to the temperature.

External electric field control in the charge qubits including three Josephson junctions

Based on the standard canonical quantization principle, this paper gives the quantization scheme for the charge qubits mesoscopic circuit including three Josephson junctions coupled capacitively. By virtue of the Heisenberg equation, the time evolution of the phase difference operators across the polar plates and the number operators of the Cooper-pairs on the island are investigated and the modification of the Josephson equation is discussed. The time evolution of the phase difference operators is analysed when the Josephson junctions are irradiated by the external electrical field, which is referred to as also the obtainable controlling parameter.

Quadruple-stacked Nb/NbxSi1-x/Nb Josephson junctions for large-scale array application

Large-scale Josephson junction(JJ)arrays are essential in many applications,especially quantum voltage standards application for which hundreds of thousands of junctions are required to realize a high quantum voltage.For almost all applications,high-quality JJ arrays must be realized in a small chip area.This study proposes vertically quadruplestacked Nb/(NbxSi1-x/Nb)4 JJs to increase the integration density of junctions in an array.The current–voltage(I–V)characteristics of a single stack of Nb/(NbxSi1??x/Nb)4 JJs have been measured at 4.2 K.The uniformity of junctions in one stack and the uniformity of several stacks over the entire 2 inches wafer have been analyzed.By optimizing the fabrication parameters,a large-scale quadruple-stacked Nb/(NbxSi1??x/Nb)4 array consisting of 400000 junctions is realized.Good DC I–V characteristics are obtained,indicating the good uniformity of the large-scale array.

0-π transition induced by the barrier strength in spin superconductor Josephson junctions

The Andreev-like levels and the free energy of the spin superconductor/insulator/spin superconductor junction are obtained by using the Bogoliubov-de Gennes equation. The phase dependence of the spin supercurrents exhibits a 0-π transition by changing the barrier strength. The dependences of the critical current on the barrier strength and the temperature are also presented.

Two-Dimensional van der Waals Superconductor Heterostructures:Josephson Junctions and Beyond

The past few years have witnessed prominent progress in two-dimensional(2D)van der Waals heterostructures.Vertically assembled in an artificial manner,these atomically thin layers possess distinctive electronic,magnetic,and other properties,which have provided a versatile platform for both fundamental exploration and practical applications in condensed matter physics and materials science.Within various potential combinations,a particular set of van der Waals superconductor(SC)heterostructures,which is realized by stacking fabrication based on two-dimensional SCs,is currently attracting intense attention.For example,the Josephson junction,a specific structure in which a nonsuperconducting barrier is inserted between two proximity-coupled SCs,shows phenomena and outstanding properties with atomic-scale thickness.In this Perspective,we first review this emerging research area of van der Waals SC heterostructures,especially progress on the 2D van der Waals Josephson junctions,from the aspects of preparation,performance,and application,and also propose our vision for the future direction and potential innovation opportunities.