Dc Josephson Effect Research Articles

Josephson effect in superconducting wires supporting multiple Majorana edge states

We study superconducting-normal-superconducting (SNS) Josephson junctions in one-dimensional topological superconductors which support more than one Majorana end mode. The variation of the energy spectrum with the superconducting phase is investigated by combining numerical diagonalizations of tight-binding models describing the SNS junction together with an analysis of appropriate low-energy effective Hamiltonians. We show that the four pi-periodicity characteristic of the fractional dc Josephson effect is preserved. Additionally, the ideal conductance of a NS junction with a topological supraconductor, hosting two Majorana modes at its ends, is doubled compared to the single Majorana case. Last, we illustrate how a nonzero superconducting phase gradient can potentially destroy the phases supporting multiple Majorana end states.

Stationary Josephson effect in a short multiterminal junction

We study the dc Josephson effect and the density of states in a multiterminal structure of cross-type geometry that consists of four superconducting electrodes connected by one-dimensional normal or ferromagnetic wires. We find that the Josephson current ${I}_{Jz}$ has a sinusoidal dependence on the phase difference ${\ensuremath{\phi}}_{z}$ between the superconductors in the horizontal wire with a critical current ${I}_{c}$ that can be varied by changing the phase difference ${\ensuremath{\phi}}_{y}$ between the superconductors in the vertical wire. The period of the function ${I}_{Jz}({\ensuremath{\phi}}_{z})$ depends on the ratio of the interface resistances ${R}_{Sn,z}/{R}_{Sn,y}$ being equal to $2\ensuremath{\pi}$ if this ratio is small and equal to $4\ensuremath{\pi}$ in the opposite limit. We also calculate the amplitudes of both the singlet and the odd-frequency triplet components in the system under consideration. The triplet component amplitude may be significantly larger than the amplitude of the singlet component.

Nb lateral Josephson junctions induced by a NiFe cross strip

We fabricated lateral junctions by crossing superconducting Nb strips in metallic contact with a ferromagnetic NiFe strip. Transport measurements on the Nb lateral junctions exhibit modulations of the critical current with a varying perpendicular magnetic field similar to a Fraunhofer interference pattern, which demonstrates the dc Josephson effect. The modulations of the critical current could be attributed to an effective weak link embedded in the Nb strip and formed a Josephson junction. Appearance of Shapiro steps on the current-voltage curves of these junctions when microwaves irradiation is applied proves the ac Josephson effect. The underlying physics of the effective weak link induced by the NiFe strip is discussed.

Nb Lateral Josephson Junction Induced by Inverse Proximity Effect With NiFe

We utilize the inverse proximity effect in superconductor-ferromagnet bilayer to generate lateral Josephson junctions. The weak link is created by a ferromagnetic NiFe strip across a superconductor Nb bridge due to the inverse proximity effect. The critical currents of the junctions were measured at different temperatures and magnetic fields. The junctions exhibit a modulation of the critical current in perpendicular magnetic field similar to a Fraunhofer interference pattern which proves the dc Josephson effect. The weak link region induced by the NiFe in Nb persists down to 2 K.

Josephson effect in a CeCoIn5 microbridge

We report DC Josephson effects observed in a microbridge prepared from an individual crystalline growth domain of CeCoIn5 thin film. Josephson effects were observed by periodic voltage modulations under external magnetic field ΔV(B) with the expected periodicity and by the temperature dependence of the Josephson critical current Ic(T). The shape of ΔV(B) was found to be asymmetric, as it is expected for microbridges. The dependence Ic(T) follows the Ambegaokar–Baratoff relation, which is unexpected for microbridges. Features in the dynamical resistance curves were attributed to the periodic motion of Abricosov vortices within the microbridge.

Spin-flip scattering and critical currents in ballistic half-metallicd-wave Josephson junctions

We analyze the dc Josephson effect in a ballistic superconductor/half-metal/superconductor junction by means of the Bogoliubov de Gennes equations. We study the role of spin-active interfaces and compare how different superconductor symmetries, including d-wave pairing, affect the Josephson current. We analyze the critical current as a function of junction width, temperature, and spin-flip strength and direction. In particular, we demonstrate that the temperature dependence of the supercurrent in the dxy symmetry case differs qualitatively from the s and dx2-y2 symmetries. Moreover, we have derived a general analytical expression for the Andreev bound-state energies that shows how one can either induce 0-{\pi} transitions or continuously change the ground-state phase of the junction by controlling the magnetic misalignment at the interfaces.

Superfluidity of Bose-Einstein condensates in toroidal traps with nonlinear lattices

Superfluid properties of Bose-Einstein condensates (BEC) in toroidal quasi-one-dimensional traps are investigated in the presence of periodic scattering length modulations along the ring. The existence of several types of stable periodic waves, ranging from almost uniform to very fragmented chains of weakly interacting and equally spaced solitons, is demonstrated. We show that these waves may support persistent atomic currents and sound waves with spectra of Bogoliubov type. Fragmented condensates can be viewed as arrays of Josephson junctions and the current as a BEC manifestation of the dc-Josephson effect. The influence of linear defects on BEC superfluidity has been also investigated. We found that for subcritical velocities, linear defects that are static with respect to the lattice (while the condensate moves in respect to both the optical lattice and the defect) preserve the BEC superfluidity.

Magnetic field modulated Josephson oscillations in a semiconductor microcavity

We theoretically study an exciton-polariton Josephson junction in a planar semiconductor microcavity. When an external magnetic field is applied normal to the plane of the microcavity, remarkable competition is found between the Zeeman energy and the interactions of exciton polaritons. We can determine a critical magnetic field, below which there is only the dc Josephson effect, and above which the ac Josephson effect appears. The ac oscillations of extrinsic and intrinsic Josephson currents have the same frequency, which linearly increases with the magnetic field, analogous to the linear voltage dependence of the Josephson frequency in conventional superconducting junctions. The spontaneous polarization separation and the macroscopic quantum self-trapping can be realized by regulating the magnetic field. These results may be experimentally confirmed by investigating the magnetic-field modulated Josephson oscillations in semiconductor microcavities.

Josephson effects in one-dimensional supersolids

We demonstrate that superflow past an obstacle is possible in a solid phase in the one-dimensional Gross-Pitaevskii equation with a finite-range two-body interaction. The phenomenon we find is analogous to the dc Josephson effect in superconductors, and we deduce the ``Josephson relation'' between the current and phase difference of the condensates separated by the obstacle. We also discuss persistent currents and nonclassical rotational inertia in annular containers with a penetrable potential barrier. The phase diagram in the plane of the current and the interaction strength is given. Our result provides a simple theoretical example of supersolidity in the presence of an obstacle.

Quasiclassical description of a superconductor with a spin density wave

We derive equations for the quasiclassical Green's functions $\mathrm{g\ifmmode \check{}\else \v{}\fi{}}$ within a simple model of a two-band superconductor with a spin density wave (SDW). The elements of the matrix $\mathrm{g\ifmmode \check{}\else \v{}\fi{}}$ are the retarded, advanced, and Keldysh functions, each of which is an $8\ifmmode\times\else\texttimes\fi{}8$ matrix in the Gor'kov-Nambu, the spin, and the band space. In equilibrium, these equations are a generalization of the Eilenberger equation. On the basis of the derived equations, we analyze the Knight shift, the proximity, and the dc Josephson effects in the superconductors under consideration. The Knight shift is shown to depend on the orientation of the external magnetic field with respect to the direction of the vector of the magnetization of the SDW. The proximity effect is analyzed for an interface between a superconductor with the SDW and a normal metal. The function describing both superconducting and magnetic correlations is shown to penetrate the normal metal or a metal with the SDW due to the proximity effect. The dc Josephson current in an ${S}_{\text{SDW}}/N/{S}_{\text{SDW}}$ junction is also calculated as a function of the phase difference $\ensuremath{\varphi}$. It is shown that in our model, the Josephson current does not depend on the mutual orientation of the magnetic moments in the superconductors ${S}_{\text{SDW}}$ and is proportional to $\mathrm{sin}\ensuremath{\varphi}$. The dissipationless spin current ${j}_{\text{sp}}$ depends on the angle $\ensuremath{\alpha}$ between the magnetization vectors in the same way (${j}_{\text{sp}}~\mathrm{sin}\ensuremath{\alpha}$) and is not zero above the superconducting transition temperature.

Josephson effect in S/F/S junctions: Spin bandwidth asymmetry versus Stoner exchange

We analyze the dc Josephson effect in a ballistic superconductor/ferromagnet/superconductor junction by means of the Bogoliubov--de Gennes equations in the quasiclassical Andreev approximation. We consider the possibility of ferromagnetism originating from a mass renormalization of carriers of opposite spin, i.e., a spin bandwidth asymmetry. We provide a general formula for Andreev levels that is valid for arbitrary interface transparency, exchange interaction, and bandwidth asymmetry, and we analyze the current-phase relation, free energy, and critical current in the short junction regime. We compare the phase diagrams and the critical current magnitudes of two identical junctions differing only in the mechanism by which the midlayer becomes magnetic. We show that a larger number of $0\ensuremath{-}\ensuremath{\pi}$ transitions caused by a change in junction width or polarization magnitude is expected when ferromagnetism is driven by spin bandwidth asymmetry compared to Stoner magnetism. Moreover, we show that these features can be present also for ferromagnets of the Stoner type having only a partial bandwidth asymmetry.

Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects

We consider light transmission in a two-dimensional (2D) photonic crystal waveguide coupled with two identical nonlinear defects positioned symmetrically aside the waveguide. With the coupled mode theory, we show three scenarios for the transmission. The first one inherits the linear case and preserves the symmetry. In the second scenario, the symmetry is broken because of different light intensities at the defects. In the third scenario, the intensities at the defects are equal but phases of complex amplitudes are different. That results in a vortical power flow between the defects similar to the dc Josephson effect if the input power over the waveguide is applied and the defects are coupled. All of these phenomena agree well with computations based on an expansion of the electromagnetic field into optimally adapted photonic Wannier functions in a 2D photonic crystal.

Odd spin-triplet superconductivity in a multilayered superconductor-ferromagnet Josephson junction

We study the dc Josephson effect in a diffusive multilayered ${\text{SF}}^{\ensuremath{'}}{\text{FF}}^{\ensuremath{'}}\text{S}$ structure, where S is a superconductor and F and ${\text{F}}^{\ensuremath{'}}$ are different ferromagnets. We assume that the exchange energies in the ${\text{F}}^{\ensuremath{'}}$ and F layers are different ($h$ and $H$, respectively) and the middle F layer consists of two layers with parallel or antiparallel magnetization vectors $M$. The $M$ vectors in the left and right ${\text{F}}^{\ensuremath{'}}$ layers are generally not collinear to those in the F layer. In the limit of a weak proximity effect we use a linearized Usadel equation. Solving this equation, we calculate the Josephson critical current for arbitrary temperatures, arbitrary thicknesses of the ${\text{F}}^{\ensuremath{'}}$ and F layers (${L}_{h}$ and ${L}_{H}$) in the case of parallel and antiparallel $M$ orientations in the F layer. The part of the critical current ${I}_{c\text{SR}}$ formed by the short-range singlet and $S=0$ triplet condensate components decays on a short length ${\ensuremath{\xi}}_{H}=\sqrt{D/H}$, whereas the part ${I}_{c\text{LR}}$ due to the long-range triplet $|S|=1$ component decreases with increasing ${L}_{H}$ on the length ${\ensuremath{\xi}}_{N}=\sqrt{D/\ensuremath{\pi}T}$. Our results are in a qualitative agreement with the experiment [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, Jr., and N. O. Birge, Phys. Rev. Lett. 104, 137002 (2010)].

Generalized dc and ac Josephson effects in antiferromagnets and in antiferromagneticd-wave superconductors

The Josephson effect is generally described as Cooper pair tunneling, but it can also be understood in a more general context. The DC Josephson effect is the pseudo-Goldstone boson of two coupled systems with a broken continuous abelian U(1) symmetry. Hence, an analog should exist for systems with broken continuous non-Abelian symmetries. To exhibit the generality of the phenomenon and make predictions from a realistic model, we study tunneling between antiferromagnets and also between antiferromagnetic d-wave superconductors. Performing a calculation analogous to that of Ambegaokar and Baratoff for the Josephson junction, we find an equilibrium current of the staggered magnetization through the junction that, in antiferromagnets, is proportional to s_L X s_R where s_L and s_R are the Neel vectors on either sides of the junction. Microscopically, this effect exists because of the coherent tunneling of spin-one particle-hole pairs. In the presence of a magnetic field which is different on either sides of the junction, we find an analog of the AC Josephson effect where the angle between Neel vectors depends on time. In the case of antiferromagnetic d-wave superconductors we predict that there is a contribution to the critical current that depends on the antiferromagnetic order and a contribution to the spin-critical current that depends on superconducting order. The latter contributions come from tunneling of the triplet Cooper pair that is necessarily present in the ground state of an antiferromagnetic d-wave superconductor. All these effects appear to leading order in the square of the tunneling matrix elements.

Planar S-(S/F)-S Josephson junctions induced by the inverse proximity effect

We present a utilization of the inverse proximity effect in superconductor-ferromagnet (S-F) bilayer to generate lateral Josephson junctions. The weak link is created by a Pd0.95Fe0.05 strip across a Nb bridge. Close to TC and in perpendicular magnetic field the junctions exhibit a modulation of the critical current IC(B) similar to a Fraunhofer interference pattern which proves the dc Josephson effect. The structure contains three weak links (two different areas) in series which result in the observation of two periods scalable with the areas penetrated by magnetic flux. Measurements of Shapiro steps prove the presence of the ac Josephson effect.

DC and AC Josephson effects with superfluid Fermi atoms across a Feshbach resonance

We show that both DC and AC Josephson effects with superfluid Fermi atoms in the BCS-BEC crossover can be described at zero temperature by a nonlinear Schrodinger equation (NLSE). By comparing our NLSE with mean-field extended BCS calculations, we find that the NLSE is reliable in the BEC side of the crossover up to the unitarity limit. The NLSE can be used for weakly-linked atomic superfluids also in the BCS side of the crossover by taking the tunneling energy as a phenomenological parameter.

Dc Josephson effect with Fermi gases in the Bose-Einstein regime

We show that the dc Josephson effect with ultracold fermionic gases in the Bose-Einstein-condensate (BEC) regime of composite molecules can be described by a nonlinear Schr\odinger equation (NLSE). By comparing our results with Bogoliubov--de Gennes calculations [Phys. Rev. Lett. 99, 040401 (2007)] we find that our superfluid NLSE, which generalizes the Gross-Pitaevskii equation taking into account the correct equation of state, is reliable in the BEC regime of the BCS-BEC crossover up to the limit of very large (positive) scattering length. We also predict that the Josephson current displays relevant beyond-mean-field effects.

Josephson current in ballistic heterostructures with spin-active interfaces

We develop a general microscopic theory of dc Josephson effect in hybrid superconductor--normal-metal--superconductor structures with ballistic electrodes and spin-active normal-metal--superconductor (NS) interfaces. We establish a direct relation between the spectrum of Andreev levels and the Josephson current which contains complete information about nontrivial interplay between Andreev reflection and spin-dependent interface scattering. The system exhibits a rich structure of properties sensitive to spin-dependent barrier transmissions, spin-mixing angles, relative magnetization orientation of interfaces, and the kinematic phase of scattered electrons. We analyze the current-phase relations and identify the conditions for the presence of a $\ensuremath{\pi}$-junction state in the systems under consideration. We also analyze resonant enhancement of the supercurrent in gate-voltage-driven nanojunctions. As compared to the nonmagnetic case, this effect can be strongly modified by spin-dependent scattering at NS interfaces.

Josephson current and Andreev states in superconductor–half metal–superconductor heterostructures

We develop a detailed microscopic theory describing dc Josephson effect and Andreev bound states in superconducting junctions with a half metal. In such systems, the supercurrent is caused by triplet pairing states emerging due to spin-flip scattering at the interfaces between superconducting electrodes and the half metal. For sufficiently clean metals, we provide a detailed nonperturbative description of the Josephson current at arbitrary transmissions and spin-flip scattering parameters for both interfaces. Our analysis demonstrates that the behavior of both the Josephson current and Andreev bound states crucially depends on the strength of spin-flip scattering, showing a rich variety of features which can be tested in future experiments.

Coherence effects in S/I/N/I/FS tunnel junctions

The dc Josephson effect in superconductor / insulator / normal metal / insulator /ferromagnetic superconductor junctions has been studied. We calculate the dc Josephson current based on the Bogoliubov de Gennes equation. The Josephson current is derived as a function of exchange field in ferromagnetic superconductor, normal metal thickness and insulating barrier strength. It is found that there exists an oscillation relation between the critical Josephson current and the normal metal thickness. The oscillation amplitude decreases as the thickness of the normal metal increases or the exchange field augments.