Observation of a Phase-Dependent Conductivity in Superconducting Point Contacts

Abstract

Phys. Rev. Lett. _15, 964 (1965). 2 J. W. Halley, Phys. Rev. _181, 338 (1969). 3 M. J. Stephen, Phys. Rev. JJ37, 279 (1969). The analogous scattering in solid helium has been considered byThe total current density for a superconducting tunnel junction was calculated by Josephson 1 to be j =j e sine? + cr 0 (F, T)V+ a x (V 9 T)Vcos<p.(1)A vast number of experiments have shown that the behavior of diverse types of weakly linked superconductors, not only tunnel junctions, are well described by the first two terms in Eq.(1), The phase-dependent conductivity contained in the third term was recently observed for the first time by Pedersen, Finnegan, and Langenberg 2 through measurements of the Q of the Josephson plasma resonance of tunnel junctions. An observation of the contribution of this term to the current in thin-film bridges was reported very recently by Falco, Parker, and Trullinger 3 from measurements of the effects of thermal noise on the I-V curves. Interpreted in terms of Eq. (1), both these experiments show that a= CT^CFQ is negative and has magnitude slightly less than 1, This value for a is in agreement with several calculations 4 ' 6 ; however, recent examinations of the microscopic theory have raised some question about the sign. 3 ' 7 In this Letter we report evidence for N. R. Werthamer, ibid. .185, 348 (1969). 4 T.a phase-dependent conductivity of superconducting point contacts from measurements of the impedance of phase-biased point contacts. Our data require a negative value for a and are most consistent with Q?»-1. Our experiments in essence measure the impedance of a niobium point contact and determine the parameters of an equivalent-circuit representation like that shown in Fig. 1(a). This equivalent circuit is justified by the following considerations: From Eq. (1) we can write i = i p + i q , where the pair current i p =i c sm<p and the quasiparticle current i Q = G 0 (l+ acos<p)V. We assume that G 0 and a are independent of V. The current i is then the total current through the pair of elements shown in Fig. 1(a), where i q flows through a phase-dependent conductance G(<p) = G 0 (l+ acos<p) and develops a voltage V. The same voltage appears across a phase-dependent inductance £ = L 0 /cos<p carrying the current i p . The identification of the inductance £ follows from combining the Josephson relation (p = 2eV/H with the expression for the pair current i p =i c sincp. Solving for <p from the second equation, differentiating it, and inserting the result into the first equation

Superconducting Memristors

“…The ratio ε between the PDC and the leakage conductance has been investigated in a number of experiments on tunnel junctions [8,12], point contacts [9,11] and weak links [10,13] finding consistently ε ∼ −1 at low temperature, while BCS theory predicts ε > 0 [4,35]. As shown in Appendix A the exponential regularization gives ε ≈ −1/3, with the sign in agreement with experimental results.…”

“…The measured value of the PDC in tunnel junctions [8,12], point contacts [9,11] and weak links [10,13,14] can not be explained by BCS theory. Several effects that can account for the discrepancy have been discussed in Ref.…”

Phase-dependent noise in Josephson junctions

“…The ratio ε has been investigated in a number of experiments on tunnel junctions [11,12], weak links [13,14], and point contacts [15,16], consistently finding ε ∼ −1 at low temperatures in disagreement with BCS theory which predicts ε > 0. This discrepancy may be accounted for by including frequency broadening in the BCS result [4] as we have done with the exponential factors in equations (4) and (5).…”

“…BCS theory cannot account for the measured value of the PDC in tunnel junctions [11,12], point contacts [13,14] or weak links [15][16][17]. Several effects may account for such discrepancy (see, e.g., Ref.…”

Josephson flux-flow oscillator: The microscopic tunneling approach

“…One of them, the famous cos ϕ problem [7,8], puzzled the scientific community for many decades. Various experiments of the time [9][10][11][12][13][14] observed the sign of phase-dependent dissipative current, also known as the "cosine" or quasiparticle-pair interference term, to disagree from the prediction of the MTT [15]. It was later suggested that, in fact, either sign is possible, while the disagreement between the theory and experiments can be explained by broadening mechanisms which result in smearing of the Riedel peaks [16,17].…”