Josephson Phase Research Articles

Explicit-time Floquet topological superconductivity in a microwave/infrared frequency AC voltage-driven Josephson junction

Anomalous Floquet topological superconductivity with chirality can be achieved by applying a dc-bias voltage across the Josephson junction with a sandwiched magnetic topological insulator (TI), in which the intrinsic Josephson phase provides a time-dependent periodic driving [R.-X. Zhang and S. Das Sarma, ]. In this work, we remove the bias voltage and connect the magnetic TI to an external AC voltage source to modulate the chemical potential, thus bringing about an explicit-time Floquet periodic driving. In the context of the driving, the system is similarly found to convert into a two-dimensional anomalous Floquet topological superconductor with chirality. By tuning the AC voltage source's frequency, we obtain a rich variety of novel Floquet topological superconducting phases with chirality. Particularly, by manipulating such static parameters as Zeeman field and superconducting pairing potential, a series of topological superconducting phase transitions are also exhibited, accompanied by exotic Floquet topological superconducting phases with chirality. Published by the American Physical Society 2024

Anomalies-Rich Floquet superconductivities induced by joint modulation of dynamic driving and static parameters

Current theoretical and experimental endeavors to realize an anomalous Floquet chiral topological superconductor (TSC), which is characterized by chiral Majorana edge modes independent of the Chern number, remain insufficient. Herein, we propose a new scheme that involves jointly tuning dynamic driving and static parameters within a magnetic topological insulator-superconductor sandwich structure to achieve this goal. The Josephson phase modulation induced by an applied bias voltage across the structure is utilized as a Floquet periodic drive. It is found that the interplay between the two kinds of tunings can bring about a lot more exotic Floquet TSC phases than those caused by only tuning the dynamic driving parameter (frequency ω or period τ). More importantly, just tuning static parameters (the chemical potential µ, Zeeman field gz , and proximity-induced superconducting energy gap Δb ) also can induce a series of novel topological phase transitions. Particularly, the features in the context of the three tunings are different from each other, originating from the combination of intrinsic and different extrinsic mechanisms. In addition, jointly tuning τ and µ (gz ) can have its own unique TSC phases. The proposed scheme should be readily accessible in experiments, and thus the family of anomalous Floquet TSC phases may be considerably enriched.

Optimization of Adiabatic Superconducting Logic Cells by Using π Josephson Junctions

Adiabatic superconducting logic circuits can ensure the practical implementation of operations with the energy dissipation below the Landauer limit. However, applications of the existing solutions are limited because of two contradictory requirements of a high energy efficiency and a sufficiently fast response of devices. Josephson junctions with a negative critical current (π junctions) allow one to obtain a certain form of the potential energy of superconducting circuits and, as a result, a practically required degree of control of dynamic processes in the proposed reversible logic cells. The features of the current transport and balance of Josephson phases in circuits with π junctions make it possible to improve the coupling between the parts of a reversible computer by a factor more than 2. At the same time, the continuous evolution of the state is ensured at higher critical currents and higher characteristic voltages of the main Josephson junctions of adiabatic superconducting logic cells, which allows an increase in the response rate.

Josephson effects between the Kitaev ladder superconductors

The two-leg ladder system consisting of the Kitaev chains is known to exhibit a richer phase diagram than that of the single chain. We theoretically investigate the variety of the Josephson effects between the ladder systems. We consider the Josephson phase difference \thetaθ between these two ladder systems as well as the phase difference \phiϕ between the parallel chains in each ladder system. The total energy of the junction at T = 0T=0 is calculated by a numerical diagonalization method as functions of \thetaθ, \phiϕ, and also a transverse hopping t_{\perp}t⊥ in the ladders. We find that, by controlling t_{\perp}t⊥ and \phiϕ, the junction exhibits not only the fractional Josephson effect for the phase difference \thetaθ, but also the usual 0-junction and even \piπ-junction properties.

Terahertz Radiations and Switching Phenomena of Intrinsic Josephson Junctions in High-Temperature Superconductors: Josephson Phase Dynamics in Long- and Short-Ranged Interactions

Terahertz Radiations and Switching Phenomena of Intrinsic Josephson Junctions in High-Temperature Superconductors: Josephson Phase Dynamics in Long- and Short-Ranged Interactions

Terahertz third harmonic generation in c -axis La1.85Sr0.15CuO4

Terahertz nonlinear optics is a viable method to interrogate collective phenomena in quantum materials spanning ferroelectrics, charge-density waves, and superconductivity. In superconductors this includes the Higgs amplitude and Josephson phase modes. We have investigated the nonlinear $c$-axis response of optimally doped ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}\mathrm{Cu}{\mathrm{O}}_{4}$ using high-field THz time domain spectroscopy at field strengths up to $\ensuremath{\sim}80$ kV/cm. With increasing field, we observe a distinct redshift of the Josephson plasma edge and enhanced reflectivity (above the plasma edge) arising from third harmonic generation. The nonmonotonic temperature-dependent response is consistent with nonlinear drive of the Josephson plasma mode (JPM) as verified with comparison to theoretical expectations. Our results add to the understanding that, using THz light, the JPM (in addition to the Higgs mode) provides a route to interrogate and control superconducting properties.

Influence of Anharmonic and Frustration Effects on Josephson Phase Qubit Characteristics

This study is devoted to the investigation of the Josephson phase qubit spectrum considering the anharmonic current-phase relation of the junction. The change in energy difference in the spectrum of phase qubits based on single-band/multiband Josephson junctions is also analyzed. It was shown that the presence of the anharmonic term in the current-phase relation and frustration effects in the junction electrodes leads to changing effective plasma frequencies in the different cases and results in an energy spectrum.

Transport Theory for Topological Josephson Junctions with a Majorana Qubit.

We construct a semiclassical theory for the transport of topological Josephson junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit-induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influence of these dynamical phenomena on the transport signatures of the junction. We apply the theory to study the Shapiro steps of the junction, and find the suppression of the first Shapiro step due to the dynamical feedback of the Majorana qubit.

Quantum dynamics of a 4π kink in Josephson junction parallel arrays with large kinetic inductance

We present a theoretical study of the quantum dynamics of two magnetic fluxons trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The Josephson phase distribution of two trapped magnetic fluxons satisfies a topological constraint, i.e., the total variation of Josephson phases along a JJPA is $4\ensuremath{\pi}$. In such JJPAs the characteristic length of the Josephson phase distribution (``the size'' of magnetic fluxon) is drastically reduced to be less than a single cell size. Two extreme dynamic patterns will be distinguished: two weakly interacting and two merged magnetic fluxons, i.e., a $4\ensuremath{\pi}$ kink. Taking into account the repulsive interaction between two magnetic fluxons located in the same or adjacent cells, we obtain the energy band spectrum ${E}_{4\ensuremath{\pi}}(p)$ for a quantum $4\ensuremath{\pi}$ kink. The coherent quantum dynamics of $4\ensuremath{\pi}$ kinks demonstrates the quantum beats with the frequency and amplitude strongly deviating from those observed for two independent magnetic fluxons. In the presence of applied dc and ac bias currents of frequency $f$ a weakly incoherent quantum dynamics of a $4\ensuremath{\pi}$ kink results in the Bloch oscillations and the seminal current steps with values ${I}_{4\ensuremath{\pi}}^{(n)}=enf$ which are two times less than those for two independent magnetic fluxons.

Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose–Einstein condensates

The spontaneous symmetry breaking (SSB) induced by a specific component of a linearly coupled binary Bose–Einstein condensate was analyzed. The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and double-well potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground states were obtained, and an induced asymmetry in the partner field was observed. In this sense, it is adequately demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between the atomic species, as well as the appearance of the Josephson and SSB phases.

Tuning the topological state of a helical atom chain via a Josephson phase

By solving the Bogoliubov-de Gennes equations, we study the quasiparticle spectrum of a magnetic atom chain placed inside a short constriction-type Josephson junction. A helical magnetic order of the atomic spins is assumed, so that a topologically nontrivial state with Majorana edge modes at the ends of the chain can appear. It is found that in the presence of a nonzero Josephson phase the subgap spectrum of an infinite chain consists of four branches (Shiba bands). This spectrum is almost certainly gapped if the atomic spins form a coplanar spiral. The Majorana number of the given system is calculated analytically. It is demonstrated that a Josephson phase shift can be used to drive the system into a topologically nontrivial state and to tune the size of the topological gap. The spatial structure of Majorana edge modes is studied as well. We generalize the effective model based on discrete Bogoliubov-de Gennes equations developed by Pientka et al. for a bulk superconductor to the case of a Josephson junction. Using these discrete equations, the wave functions of Majorana zero modes are calculated analytically for a coplanar atomic spin spiral with arbitrary pitch. The wave functions exhibit an intermediate asymptotic behavior with a nonexponential fall-off with distance from the edge of the atomic chain.

Anomalous Josephson coupling and high-harmonics in non-centrosymmetric superconductors with S-wave spin-triplet pairing

We study the Josephson effects arising in junctions made of non-centrosymmetric superconductors with spin-triplet pairing having s-wave orbital-singlet symmetry. We demonstrate that the orbital dependent character of the spin-triplet order parameter determines its non-trivial texture in the momentum space due to the inversion symmetry breaking and spin-orbit interactions. The emergence of this pattern is responsible for the occurrence of an anomalous Josephson coupling and a dominance of high-harmonics in the current phase relation. Remarkably, due to the spin-orbital couplings, variations in the electronic structure across the heterostructure can generally turn the ground state of the junction from 0- to a generic value of the Josephson phase, thus realizing the so-called φ-junction. Hallmarks of the resulting Josephson behavior, apart from non-standard current-phase relation, are provided by an unconventional temperature and magnetic field dependence of the critical current. These findings indicate the path for the design of superconducting orbitronics devices and account for several observed anomalies of the supercurrent in oxide interface superconductors.

Signatures of Majorana bound states and parity effects in two-dimensional chiral p -wave Josephson junctions

We characterize topological features of Josephson junctions formed by coupled mesoscopic chiral $p$-wave superconducting islands. Through analytic and numerical studies of the low-lying BdG (Bogoliubov-de Gennes) spectrum, we identify localized MBS (Majorana bound states) nucleated in Josephson vortices by the application of a perpendicular magnetic field. Additionally, we demonstrate the existence of an extended MBS that is delocalized around the outer perimeter of the coupled islands, which has measurable consequences on the Josephson supercurrent and phase dynamics of the junction. In particular, we predict a change in the critical current diffraction pattern in which the odd integer-flux nodes are lifted in a fermion parity-dependent fashion. We model the competing stochastic effects of thermal noise and macroscopic quantum tunneling within the RCSJ framework and show the emergence of a bimodal critical current distribution. We demonstrate that increasing the parity transition rate suppresses the bimodal nature of the distribution, thus strongly emphasizing the non-trivial parity dependent nature of the many-body ground state. Finally, we consider a trijunction geometry with three islands and discuss possible schemes to braid Majorana bound states by moving the Josephson vortices to which they are bound.

Frustration-driven Josephson phase dynamics

The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets switched on by driving the changeover among different ground states, which can be induced by varying the parameters that set the phase state. Remarkably, the character of the transitions in the Josephson phase space allows different types of dynamics, with few or several harmonics. This result sets out a characteristic mark of any superconducting system with frustrated Josephson couplings and can be exploited to disentangle the complexity of the underlying phases.

Terahertz phase slips in striped La2−xBaxCuO4

Interlayer transport in high-$T_C$ cuprates is mediated by superconducting tunneling across the CuO$_2$ planes. For this reason, the terahertz frequency optical response is dominated by one or more Josephson plasma resonances and becomes highly nonlinear at fields for which the tunneling supercurrents approach their critical value, $I_C$. These large terahertz nonlinearities are in fact a hallmark of superconducting transport. Surprisingly, however, they have been documented in La$_{2-x}$Ba$_x$CuO$_4$ also above $T_C$ for doping values near $x=1/8$, and interpreted as an indication of superfluidity in the stripe phase. Here, Electric Field Induced Second Harmonic (EFISH) is used to study the dynamics of time-dependent interlayer voltages when La$_{2-x}$Ba$_x$CuO$_4$ is driven with large-amplitude terahertz pulses, in search of other characteristic signatures of Josephson tunnelling in the normal state. We show that this method is sensitive to the voltage anomalies associated with 2$\pi$ Josephson phase slips, which near $x=1/8$ are observed both below and above $T_C$. These results document a new regime of nonlinear transport that shares features of fluctuating stripes and superconducting phase dynamics.

Critical Current Modulation in Josephson Junctions Contacted by Redundant Vias

We study the impact of redundant via placement on Fraunhofer interference patterns in superconductor–insulator–superconductor Josephson junctions with thin counter electrodes. By varying the number and location of contact vias to the counter electrode in otherwise equivalent junctions and studying the magnetic field dependence of the critical current, we observe a variety of unconventional features in the interference patterns, including a lifting of critical current minima and differences in node positions and side lobe amplitudes. We attribute these features to local changes in the Josephson phase gradient arising from the nonuniform magnetic thickness resulting from the vias. Our findings highlight the significant role that contact vias on thin counter electrodes play in the response of Josephson junctions to applied magnetic fields.

Resonator-induced quantum phase transitions in a hybrid Josephson junction

We investigate the Josephson current through a suspended carbon nanotube double quantum dot which, at sufficiently low temperatures, is characterized by the ground state of the electronic subsystem. Depending on parameters like a magnetic field or the inter-dot coupling, the ground state can either be a current-carrying singlet or doublet, or a blockaded triplet state. Since the electron-vibration interaction has been demonstrated to be electrostatically tuneable, we study in particular its effect on the current-phase relation. We show that the coupling to the vibration mode can lift the current-suppressing triplet blockade by inducing a quantum phase transition to a ground state of a different total spin. Our key finding is the development of a triple point in the Josephson current parameterized by the resonator coupling and the Josephson phase. The quantum phase transitions around the triple point are directly accessible through the critical current and resilient to moderately finite temperatures. The proposed setup makes the mechanical degree of freedom part of a superconducting hybrid device which is interesting for ultra-sensitive displacement detectors.

Collective magnetic and plasma excitations in Josephson ψ junctions

We show that Josephson $\ensuremath{\psi}$ junctions with a half-metallic (HM) weak link coupled to superconducting (S) electrodes through ferromagnetic (F) layers host collective excitations of the magnetic moment and the Josephson phase. This results in a shift of the ferromagnetic resonance frequency, anomalies in the current-voltage characteristics, and the appearance of additional magnetic anisotropy in the F layers. In contrast to previously studied S/F/S junctions, coupling between magnetic and plasma modes emerges even in the long wavelength limit. Such coupling is shown to enable controllable magnetization reversal in the F layer governed by a dc current pulse, which provides an effective mechanism for the magnetic moment manipulation in the devices of superconducting spintronics.

Dynamic Spin-Triplet Order Induced by Alternating Electric Fields in Superconductor-Ferromagnet-Superconductor Josephson Junctions.

Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here, we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling, and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the spin-orbital coupling, into dynamic s-wave equal-spin-triplet correlations. We demonstrate that the critical current of Josephson junctions hosting these states is proportional to the electromagnetic power, supplied either by the external irradiation or by the ac current source. Based on these unusual properties we propose the scheme of a Josephson transistor which can be switched by the ac voltage and demonstrates an even-numbered sequence of Shapiro steps. Combining the photoactive Josephson junctions with recently discovered Josephson phase batteries we find photomagnetic SQUID devices which can generate spontaneous magnetic fields while being exposed to irradiation.

Ballistic SNS sandwich as a Josephson junction

The paper develops the theory of the ballistic SNS sandwich, in which the Josephson effect exists without the proximity effect. The theory takes into account restrictions imposed by the charge conservation law and the incommensurability of the superconducting gap with the Andreev level energy spacing. This resulted in revisions of some conclusions of previous works. In the one-dimensional case the Josephson phase of the ground state of the ballistic SNS sandwich is not necessarily zero but may have any value from 0 to $\pi$. If this value is $\pi$ this is a $\pi$ junction, which was well known before. The suppression of the supercurrent at temperatures on the order or higher than the Andreev level energy spacing, which was predicted in previous investigations, does not take place in the one-dimensional case. At zero temperature the ballistic SNS sandwich of any dimensionality is not a weak link. This leads to unusual properties: the absence of the Josephson plasma mode localized at the normal layer and the Meisner effect with the same London penetration depth in the normal and the superconducting layers.