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Superconducting topological systems formed by a strong 3D topological insulator (TI) in proximity to a conventional s-wave superconductor (SC) have been intensely studied, as they may host Majorana zero modes. However, there are limited experimental realizations of TI-SC systems in which robust superconducting pairing is induced on the surface states of the TI and a topological superconducting state is established. Here, we fabricate a TI-SC system by depositing, via a focused ion beam, tungsten (W) nanoscale clusters on the surface of TI Bi0.91Sb0.09. We find that the resulting heterostructure supports phase-slip lines (PSLs) that act as effective Josephson junctions (JJs). We probe the response of the system to microwave radiation. We find that for some ac frequencies, and powers, the resulting Shapiro steps' structure of the voltage–current characteristic exhibits a missing first step and an unexpectedly wide second Shapiro step. The theoretical analysis of the measurements shows that the unusual Shapiro response arises from the interplay between a static JJ and a dynamic one and allows us to identify the conditions under which the missing first step can be attributed to the topological nature of the JJs formed by the PSLs. Our results suggest an approach to induce superconductivity in a TI, a route to realizing highly transparent topological JJs, and show how the response of superconducting systems to microwave radiation can be used to infer the dynamics of PSLs. Highly transparent topological junctions are promising candidates to realize vector field sensors with very high sensitivity. In addition, due to the nontrivial Berry phase of the TI's surface states such junctions can be in a topological state which is ideal to create topologically protected qubits. [ABSTRACT FROM AUTHOR]

We suggest a nanoelectromechanical setup and corresponding time-protocol for controlling parameters in order to demonstrate nanomechanical manipulation of superconducting charge-qubit quantum network. We illustrate it on an example reflecting important task for quantum information processing — transmission of quantum information between two charge-qubits facilitated by nanomechanics. The setup is based on terminals utilizing the AC Josephson effect between bias voltage-controlled bulk superconductors and mechanically vibrating mesoscopic superconducting grain in the regime of the Cooper pair box, controlled by the gate voltage. The described manipulation of quantum network is achieved by transduction of quantum information between charge-qubits and intentionally built nanomechanical coherent states, which facilitate its transmission between qubits. This performance is achieved using quantum entanglement between electrical and mechanical states. • Superconducting NEMS featuring charge qubit is resonantly coupled to nanomechanics by the AC Josephson effect. • Time-protocol of NEMS setup is used to build entangled qubit with nanomechanical coherent states. • Nanomechanically facilitated transmission of quantum information between charge qubits is achieved. [ABSTRACT FROM AUTHOR]

We suggest a nanoelectromechanical setup and corresponding time-protocol of its manipulation by which we transduce quantum information from charge qubit to nanomechanical cat-state. The setup is based on the AC Josephson effect between bulk superconductors and mechanically vibrating mesoscopic superconducting island in the regime of the Cooper pair box. Starting with a pure state with quantum information initially encoded into superposition of the Cooper pair box states, applying a specially tailored time-protocol upon bias voltage and gate electrodes, we obtain a new pure state with information finally encoded into superposition of nanomechanical coherent states constituting the cat-state. This performance is achieved using quantum entanglement between electrical and mechanical states. Nanomechanical cat-states serve as a "storage" of quantum information, motivated by significantly longer decoherence time with respect to the charge qubit states, from which the information can be transdued back to the charge qubit applying the reverse time-protocol. • Superconducting NEMS featuring charge qubit is resonantly coupled to nanomechanics by the AC Josephson effect. • Time protocol of NEMS setup is used to build cat-states consisting of nanomechanical coherent states. • Quantum information is encoded into pure charge qubit state and transduced into pure nanomechanical cat-state using the entanglement between electrical and nanomechanical states. [ABSTRACT FROM AUTHOR]

• Joule heating phenomenon is incorporated in the AC Josephson effect. • The phase and temperature dynamic states are discussed for various parameters. • Device state diagrams are realized for Josephson weak-link – shunted and unshunted. • A useful thermal model as a guide for the experiments with weak-link-based devices. Superconducting weak-link (WL), behaving like a Josephson junction (JJ), is fundamental to many superconducting devices such as nanoSQUIDs, single-photon detectors, and bolometers. The interplay between unique nonlinear dynamics and inevitable Joule heating in a JJ leads to new characteristics. Here, we report a time-dependent model incorporating thermal effect in the AC Josephson regime for a Josephson WL shunted by a resistor together with an inductor to investigate the dynamics as well as the resulting current-voltage characteristics. We find that the dynamic regime where phase and temperature oscillate simply widens due to a pure resistive shunt. However, a significant inductive time-scale in the shunt loop, competing with the thermal time-scale, introduces high-frequency relaxation oscillations in the dynamic regime. Based on numerical analysis, we present state diagrams for different parameter regimes. Our model is a guide for better controlling the parameters in the experiments of WL-based devices. [ABSTRACT FROM AUTHOR]

Abstract: In this study, we investigate numerically the terahertz radiation from the mesa-structured intrinsic Josephson junctions (IJJs). The Sine–Gordon equation for inside of the mesa, and the Maxwell equation for outside of the mesa, are solved simultaneously. We consider the influence of a hot spot in the mesa where locally decreases, and calculate the radiation power as a function of the voltage. We observe strong radiation when the ac Josephson frequency satisfies the cavity resonance condition. For this strong radiation from the IJJs mesa, we calculate the radiation patterns. The radiation patterns reflect the existence of two types of internal modes: a uniform background mode and a cavity resonance mode. Furthermore, the radiation patterns are strongly affected by the diffraction at substrate edges. [Copyright &y& Elsevier]

Recently terahertz wave emission from intrinsic Josephson junctions without external magnetic fields has been intensively studied, and some emission states have been proposed numerically or theoretically. For the surface impedance Z=1, the McCumber-like state with small spatial dependence of the electric field in the junction becomes stable, while for large and complex Z, the π-phase kink state characterized by translational symmetry breaking along the layered structure becomes stable. In the present study, the relations between these two extreme cases are clarified numerically by solving the coupled equations of the Josephson relations and the Maxwell equations for an experimental width of the junction, 86 μm. The dynamical phase diagram in the surface impedance ( Z)–current ( J) plane and the optimal value of Z for the strongest emission are evaluated. [ABSTRACT FROM AUTHOR]

The AC Josephson effect in the interface between a superconducting dot with dx2-y2 symmetry (d-dot) and its surrounding s-wave superconductor is investigated in the presence of an external magnetic field parallel to the interface. We derive the dynamical equations for the phase difference in this d-dot system for two different shapes of d-dot, i.e., square and triangle. The effect of the d-wave symmetry is incorporated in terms of the orientation-dependent Josephson critical current density. We solve numerically the dynamical equations and clarify the dynamics of vortices with half-flux quantum. [Copyright &y& Elsevier]

When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect─the phase of the junction locks to the drive frequency. As a result, the I - V curves of the junction acquire "Shapiro steps" of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multiterminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest that multiterminal Josephson junctions are a playground to study highly connected nonlinear networks with novel topologies.

We have studied the features of intrinsic Josephson junction stacks in the c-axis direction in highly Pb-substituted (Bi/sub 1-x/Pb/sub x/)/sub 2/Sr/sub 2/CaCu/sub 2/O/sub y/ (with x/spl ges//spl sim/0.2) single crystals exhibiting multiple branches with hysteresis on the I-J characteristics. For the mesa of the single crystal with x=/spl sim/0.2, as the self-field effects on the fluxon motion in the Intrinsic Josephson junctions, the flux flow branch and the zero field step were successfully observed in addition to the supercurrent at zero voltage and the multiple resistive branches. Moreover, their ac Josephson effect was also confirmed by observation of the microwave-induced Shapiro step. These results imply the existence of intrinsic Josephson effects in the single crystals with x/spl ges//spl sim/0.2. [ABSTRACT FROM PUBLISHER]

The ac Josephson effect for a current-driven Josephson junction enhanced by a non-monochromatic input signal is studied based on an analog simulation. The obtained rf-induced step-height in the current-voltage characteristic which is a measure of this effect suggest that the use of either a pulse train or a biharmonic consisting of fundamental and second harmonic sinusoidal functions is effective for the enhancement, if compared to a monochromatic signal drive. It is revealed that the individual phase locking between the rf-signal and the Josephson oscillation is much more stabilized by use of the pulse train-like signal and can be explained qualitatively by a pendulum motion, i.e., the relatively slow motion of the pendulum near the position of rest. [ABSTRACT FROM PUBLISHER]

Abstract: We study an ac Josephson effect in a SC/I/X/I/SC junction, where SC is an s-wave superconductor, I is an insulator, and X is either a normal metal (NM) or a ferromagnetic metal (FM). Using a tunneling Hamiltonian and Green’s function method, we obtain two types of superconducting phase dependent current. One is the Josephson current and the other is the quasiparticle-pair-interference current (QPIC). In a SC/I/NM/I/SC junction, the Josephson critical current and the amplitude of QPIC are functions of the thickness of NM and the applied voltage . shows a logarithmic divergence called Riedel peak at the gap voltage, , where is the superconducting gap, and shows a discontinuous jump at the gap voltage. These behaviors are similar to these of SC/I/SC junctions. On the other hand, in a SC/I/FM/I/SC junction, and exhibit the strong dependence on the thickness of FM and changes their signs by crossing the 0–π transition point due to the magnetic exchange splitting between the up- and down-spin bands in FM. It is predicted that the Riedel peak in disappears at the 0–π transition and the 0–π transition occurs in similarly to . [Copyright &y& Elsevier]

The AC Josephson effect manifests itself in the form of "Shapiro steps" of quantized voltage in Josephson junctions subject to radiofrequency (RF) radiation. This effect presents an early example of a driven-dissipative quantum phenomenon and is presently utilized in primary voltage standards. Shapiro steps have also become one of the standard tools to probe junctions made in a variety of novel materials. Here we study Shapiro steps in a widely tunable graphene-based Josephson junction in which the high-frequency dynamics is determined by the on-chip environment. We investigate the variety of patterns that can be obtained in this well-understood system depending on the carrier density, temperature, RF frequency, and magnetic field. Although the patterns of Shapiro steps can change drastically when just one parameter is varied, the overall trends can be understood and the behaviors straightforwardly simulated, showing some key differences from the conventional RCSJ model. The resulting understanding may help interpret similar measurements in more complex materials.