Riedel Peak Research Articles

Josephson effect in multiterminal superconductor-ferromagnet junctions coupled via triplet components

On the basis of the Usadel equation we study a multi-terminal Josephson junction. This junction is composed by "magnetic" superconductors S$_{\text{m}}$ which have singlet pairing and are separated from the normal n~wire by spin filters so that the Josephson coupling is caused only by fully polarized triplet components. We show that there is no interaction between triplet Cooper pairs with antiparallel total spin orientations. The presence of an additional singlet superconductor S attached to the n wire leads to a finite Josephson current $I_{\text{Q}}$ with an unusual current--phase relation. The density of states in the n wire for different orientations of spins of Cooper pairs is calculated. We derive a general formula for the current $I_{\text{Q}}$ in a multi-terminal Josephson contact and apply this formula for analysis of two four-terminal Josephson junctions of different structures. It is shown in particular that both the "nematic" and the "magnetic" cases can be realized in these junctions. In a two-terminal structure with parallel filter orientations and in a three-terminal structure with antiparallel filter orientations of the "magnetic" superconductors with attached additional singlet superconductor, we find a nonmonotonic temperature dependence of the critical current. Also, in these structures, the critical current shows a Riedel peak like dependence on the exchange field in the "magnetic" superconductors. Although there is no current through the S/n interface due to orthogonality of the singlet and triplet components, the phase of the order parameter in the superconuctor S is shown to affect the Josephson current in a multi-terminal structure.

Identification of the±s-wave pairing state in iron-pnictide superconductors using the Riedel anomaly

We theoretically propose a method to identify $\ifmmode\pm\else\textpm\fi{}s$-wave order parameter in recently discovered Fe-pnictide superconductors. Our idea uses the Riedel anomaly in ac-Josephson current through a $\text{SI}(\ifmmode\pm\else\textpm\fi{}\text{S})$ (single-band $s$-wave superconductor/insulator/$\ifmmode\pm\else\textpm\fi{}s$-wave two-band superconductor) junction. We show that the Riedel peak effect leads to vanishing ac-Josephson current at some values of biased voltage. This phenomenon does not occur in the case when the $\ifmmode\pm\else\textpm\fi{}s$-wave superconductor is replaced by a conventional $s$-wave one so that the observation of this vanishing Josephson current would be a clear signature of $\ifmmode\pm\else\textpm\fi{}s$-wave pairing state in Fe-pnictide superconductors.

Sign Reversal of AC Josephson Current in a Ferromagnetic Josephson Junction

The ac Josephson effect in a ferromagnetic Josephson junction, which is composed of two superconductors separated by a ferromagnetic metal (FM), is studied by a tunneling Hamiltonian and Green's function method. We obtain two types of superconducting phase dependent currents, i.e., Josephson current and quasiparticle-pair-interference current (QPIC). These currents change their signs with thickness of the FM layer due to the 0–π transition characteristic to the ferromagnetic Josephson junction. As a function of applied voltage, the Josephson critical current shows a logarithmic divergence called the Riedel peak at the gap voltage, while the QPIC shows a discontinuous jump. The Riedel peak reverses due to the 0–π transition and disappears near the 0–π transition point. The discontinuous jump in the QPIC also represents similar behaviors to the Riedel peak. These results are in contrast to the conventional ones.

Theoretical study of ac Josephson effect in a double barrier Josephson junction

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 ( I c 1 ) and the amplitude of QPIC ( I c2 ) are functions of the thickness of NM and the applied voltage ( V ) . I c1 shows a logarithmic divergence called Riedel peak at the gap voltage, V = 2 Δ / e , where Δ is the superconducting gap, and I c2 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, I c1 and I c2 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 I c1 disappears at the 0–π transition and the 0–π transition occurs in I c2 similarly to I c1 .

Josephson effect in SFXSF junctions

We investigate the Josephson effect in S$_{\rm F}$XS$_{\rm F}$ junctions, where S$_{\rm F}$ is a superconducting material with a ferromagnetic exchange field, and X a weak link. The critical current $I_c$ increases with the (antiparallel) exchange fields if the distribution of transmission eigenvalues of the X-layer has its maximum weight at small values. This exchange field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S$_{\rm F}$IS$_{\rm F}$ junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference of the exchange fields $h_1-h_2$ in an S$_{\rm F}$IS$_{\rm F}$ junction corresponds to the potential difference $V_1-V_2$ in an SIS junction; i.e., the singularity in $I_c$ [in an S$_{\rm F}$IS$_{\rm F}$ junction] at $|h_1-h_2|=\Delta_1+\Delta_2$ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S$_{\rm F}$IS$_{\rm F}$ junctions.

Wigner-function approach to a single-electron tunnel junction.

We demonstrate that the Wigner function is suitable to describe single-electron tunneling in ultrasmall tunnel junctions. For a current-biased junction, we derive a master equation for the Wigner function which describes charging effects on Cooper-pair tunneling, quasiparticle-pair tunneling, and normal single-electron tunneling in an unified way. We obtain the current-voltage I-V characteristic for an ultrasmall Josephson junction that recovers those for the Josephson junction with no charging energy in the limit of e/C\ensuremath{\rightarrow}0. It is predicted that, due to charging effect in the ultrasmall Josephson, the position of the Riedel peak and the gap of the quasiparticle-pair interference term are changed from 2\ensuremath{\Delta}/e to 2\ensuremath{\Delta}/e-e/2C, while the quasiparticle current's onset changes from 2\ensuremath{\Delta}/e to 2\ensuremath{\Delta}/e+e/2C. \textcopyright{} 1996 The American Physical Society.

Measurements of the Riedel peak in superconducting aluminum tunnel junctions (mixers)

The Riedel singularity in thin-film aluminum tunnel junctions was measured from temperature behavior of the zero voltage step and the RF-induced Josephson steps at around the gap frequency. From these experiments the author derived a value of the imaginary gap parameter to be about 1% of the gap parameter value at the gap edge when the temperature was 0.7 of the transition temperature. The author believes that, using magnetic field for tuned superconductor-insulator-superconductor (SIS) mixers with relatively large area, the Riedel singularity should not play an important role for frequencies around the gap frequency at finite temperatures. >

Simulation of Shapiro Steps in a Josephson Junction Based on the Microscopic Theory of the Tunnel Junction

Shapiro steps in a Josephson tunnel junction were investigated by the simulation based on the microscopic theory of the tunnel junction. A nonzero pair-breaking parameter, δ=0.1, was assumed to make the computation tractable. The dependence of the step width of the zeroth- and the first-order Shapiro steps on the rf power was calculated for the frequency range, 0.2fg≦f≦1.5fg, where fg is the energy gap frequency. The steps are unstable at low frequencies, f\\lesssim0.7fg, and for large values of the junction capacitance. They become stable for larger frequencies. The steps are stable, on the whole, for small capacitance. The frequency dependence of the first maximum of the first-order Shapiro step, I1MAX, was obtained. It shows the Riedel peak, with even larger height than the prediction of the theory assuming a constant voltage source for a small capacitance.

Inverse ac Josephson effect at terahertz frequencies

The inverse ac Josephson effect occurs when a Josephson junction driven by a microwave source of frequency f produces constant-voltage steps at integer multiples of hf/2e. For low-leakage current hysteretic junctions driven at microwave frequencies below about 100 GHz, some of these steps can cross the zero dc bias current axis. These zero-crossing steps allow modern series array voltage standards to operate without individually biasing the junctions in the array. We reexamine the theory behind these steps and show that they can exist at frequencies much higher than thought previously. The Riedel singularity in the supercurrent response allows this effect to exist even up to terahertz frequencies. We describe a set of analytical calculations which provide limits on the amount of rounding of the Riedel peak which can be permitted while still allowing these zero-crossing steps to occur. We also discuss practical considerations such as microwave power levels required and parameters for device fabrication. This analysis is supported by numerical frequency-domain computations and time-domain simulations for a number of realistic I-V curves with rounded Riedel singularities and with quasiparticle subgap leakage currents.

Temperature dependence of submillimeter wave response in the point-contact Josephson junction

We have measured the magnitude of the first Shapiro step in both bridge-type (Ta-Ta and Ta-Sn) and tunnel-type (Ta-SnOx-Sn) point-contact Josephson junctions in the SMMW ( Submillimeter Wave ) region. By varying the temperature continuously with the frequency of the SMMW fixed (ω=2π/λ, λ = 699, 570 and 469μm) . we determined I_{1}^{\max}/I_{c} minutely as a function of the normalized frequency \omega/\omega_{g} (T), where I_{1}^{\max} is the maximum (half) height of the first Shapiro step as a function of the ac field power, I c is the critical current, and \omega_{g}(T)=4\Delta_{Ta}(T)/h or 2(\Delta_{Ta}(T)+\Delta_{Sn}(T))/h . By fitting the shape of the Riedel peak at \omega/\omega_{g}(T)=I with the theory of the tunnel junction, we have determined the damping factor δ. We obtained δ =0.02 for the Ta-SnOx-Sn tunnel- type junction, and δ=0.05 for both the Ta-Sn and Ta-Ta bridge - type junctions, respectively. At \omega/\omega_{g}(T)>1.5 , we have found that I_{1}^{\max}/I_{c} tends to saturate in both the tunnel-type and the bridge-type junctions as \omega/\omega_{g}(T) increases. For the tunnel-type junction, this agrees with the very slow decrease predicted by the theory of the tunnel junction. But for the bridge-type junction, this slow decrease is in marked contrast to the very rapid decrease found from the previous experiments, where the Shapiro step was measuared for a number of frequencies at a fixed temperature.

Time domain simulation of Shapiro steps in Josephson junctions

Using the time domain formulation of the theory of the tunnel junction, we investigated Shapiro steps by digital simulation, under the condition of a constant current source given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_{dc} + I_{rf} \sin \omegat</tex> . The integral kernels for the Josephson and the quasiparticle current were computed assuming a nonzero pair breaking parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\delta=0.1</tex> , and T = 0K. We obtained I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rf</inf> dependence of the zeroth and first Shapiro steps, I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , and the frequency dependence of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_{1}^{\MAX}</tex> , the maximum of the first Shapiro step as a function of I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rf</inf> , for a few values of the junction capacitance. we found the following results. (1) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_{1}^{\MAX}/I_{c}</tex> (I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> :the critical current), showed the Riedel peak at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega/\omega_{g} \simeq 1</tex> , where ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> is the gap frequency 4 Δ/h. (2) For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega/\omega_{g} &gt;1\cdot I_{1}^{\MAX}/I_{c}</tex> agrees well with that for the constant voltage bias. (3) As the frequency becomes smaller below <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{g} \cdot I_{1}^{\MAX}/I_{c}</tex> is severely depressed compared to that for the constant voltage bias.

Dynamics of Josephson tunnel junctions with a finite-width Riedel peak

The basic properties of high-current-density Josephson tunnel junctions are calculated from the microscopic theory taking into account a finite width 2δ of the Riedel peak. The calculated I-V curves for the finite values of the normalized capacitance β c , the Riedel peak halfwidth δ, and the parameter α of pair current suppression are in good agreement with published experimental results for the high-current-density tunnel junctions Pb(In)-oxide-Pb. The hysteresis parameter I R /I c calculated from the microscopic theory as a function of the normalized capacitance β c is compared with the dependence following from the RSJ and the RSJN models. In addition, the low-frequency spectral density S v (0) of the voltage fluctuations across the junction is numerically found and compared with that following from the simple shot-noise model.

Damping Factor of the Riedel Peak in Bridge-Type Josephoson Junctions

The Riedel peak in the Josephson current in bridge-type point-contact Josephson junctions has been studied by measuring the frequency dependence of the maximum height of the fundamental ( n =1) Shapiro-step in the energy range near \(\hbar\omega{\sim}4\varDelta_{0}\) with a submillimeter-wave laser, where Δ 0 is the real part of the energy gap. The imaginary part of the energy gap, Δ 2 , has been estimated from the observed rounding of the Riedel singularity. As a result, the damping factor \(\delta{=}\varDelta_{2}/\varDelta_{0}{\gtrsim}0.05\) has been obtained. The value of δ∼0.05 seems to be the lowest value which is intrinsic to bridge-type junctions. It has been also found that the value of δ is large in the junctions which show strong heating effects.

Electronic simulation of Josephson tunneling, including the effects of frequency, temperature, and the superconducting energy gap

An electronic device which simulates the Werthamer theory of Josephson tunneling is described. The simulator includes the effects of frequency, temperature, and the superconducting energy gap. The nonlinear quasi-particle resistance, and the related reactive term, are also modeled. Current-voltage characteristics obtained with the simulator are presented for a variety of temperatures under both current and voltage bias conditions. Phenomena such as subgap structure, the Riedel peak, and photon-assisted tunneling are also illustrated. Finally, brief evidence of a new form of oscillatory behavior associated with the Riedel peak is presented.

Direct observation of the Riedel singularity in a superconducting point contact

An heterodyne detection of the Josephson current in the gap region is performed using the oscillator-mixer mode of operation in a superconducting point contact. The direct observation of the Riedel peak in a Josephson device is realized. The measured peak height (∼3.5) in superconducting point contacts is of the same order of magnitude as for oxide barrier tunnel junctions. Consequently, strong similarities exist in the physical processes which occur in these two types of junctions and pair tunneling is believed to be a dominant mechanism in a point contact with Josephson behavior.

Ac Josephson current as a function of voltage

The superconductive current flowing through niobium point contacts was measured as a function of applied voltage using a bridge circuit. With the assumption that the de component of the superconductive current is proportional to the amplitude of the ac Josephson current, the latter was determined as a function of the voltage applied to the contact. For eV &amp;gt;2Δ the results agree qualitatively with theory. A maximum in the superconductive current (the Riedel peak) was observed in the superconducting current-voltage curves and in the curve of if signal amplitude versus voltage in experiments involving the mixing of two uhf signals.

Riedel singularity in tin-tin oxide-tin tunnel junctions

The Riedel peak in the Josephson supercurrent in Sn-Sn oxide-Sn tunnel junctions has been investigated by studying the amplitudes of microwave-induced steps. At low temperatures, the peak rises to a value approximately 2.8 times the zero-voltage supercurrent amplitude. This can be accounted for quantitatively in terms of the known bulk gap anisotropy of tin, reduced by a factor of 2–3 due to dirty-superconductor averaging and a further factor of about 17 due to preferred crystallographic orientation of the films comprising the junctions. At high temperatures, the truncation of the peak is in quantitative agreement with theoretical predictions of the effect of quasiparticle damping processes. Complementary measurements of the slope of the quasiparticle tunnel current at the gap voltage cannot be satisfactorily explained in a similar way, despite the common origin of the quasiparticle current jump at the gap voltage and the Riedel peak in the quasiparticle density-of-states peak at the gap edge. The quasiparticle current jump appears to be broadened by some mechanism which does not significantly affect the Riedel peak.

Renormalization of the expression for the superconducting tunnelling currents

The singularities of the expressions for the superconducting tunnelling currents are shown to be caused by the fact that they are derived via a perturbation calculation of finite order. A general formula for the current density valid for large tunnelling matrix elements and exterior electromagnetic fields is derived. Then it becomes possible to obtain a broadened quasiparticle current step and a finite Riedel peak. In addition, a renormalized second order quasiparticle current is shown to be finite for every DC voltage. The method employed is to sum the corresponding types of diagrams to infinite order.

Energy Gap, Microwave-Assisted Tunneling, and Josephson Steps in Thin-Film Weak Links at 63 and 302 GHz

We present experimental evidence for the occurrence of energy-gap structure and microwave-assisted tunneling in the IV curves for superconducting thin-film weak links. From measurements of the power and the temperature dependence of the Josephson steps we argue that also the Riedel peak is observable in weak links. (auth)