Nonlinear and nonlocal Meissner effect in superconducting wires

Abstract

The structure of the Meissner effect in a current-carrying cylindrical wire with arbitrary disorder is studied following a numerical procedure that is exact within the quasiclassical approximation. A distribution of current is found that is nonmonotonous as a function of the radial coordinate. For high currents, a robust gapless superconducting state develops at the surface of both clean and dirty leads. Our calculation provides a quantitative theory of the critical current in realistic wires.The Meissner effect is one of the most fundamental properties of the superconducting state. It originates from the existence of a dissipationless current density generated by the superfluid velocity distribution which characterizes the state of broken gauge symmetry. The current density j depends on the velocity v s through a complicated functional j͓v s ͔ which in general is nonlinear and nonlocal. 1 The Pippard approximation assumes a linear relation j(r) ϭ͐K(r,rЈ)•v s (rЈ)drЈ, which is valid for low enough superfluid velocities 2 and which in the local limit reduces to London's equation. A local yet nonlinear approximation to the full functional j͓v s ͔ is implemented, for instance, within the context of a Ginzburg-Landau description. 2 In this article, we present a fully nonlinear and nonlocal numerical study of the field and current distributions in a current-carrying cylindrical wire. Our calculation of the full functional j͓v s ͔ is exact within the framework of the quasiclassical approximation. We encounter a rich physical structure determined by the interplay between nonlinearity, nonlocality, and the global stability of the current configuration. In particular we find that, as a function of the distance to the central axis, the current density is nonmonotonous for currents close to the critical value, displaying a maximum near the surface. This configuration can be viewed as precursor of the intermediate state. 2 We also find that, for high total currents, the superfluid velocity near the surface acquires values so large that they cannot be realized in a quasi-onedimensional wire. In a three-dimensional wire, these large values of the superfluid velocity are possible because they are supported by the global stability of the current distribution. This causes a strong distortion of the local quasiparticle spectrum, which then develops a robust gapless form. The calculation presented here provides a quantitative theory of the critical current and represents an improvement over the phenomenological Silsbee's criterion. 3 We investigate the structure of currents and fields in a cylindrical wire made of a type I s-wave superconductor with an arbitrary degree of disorder due to nonmagnetic impurities. We have explored a broad range of temperatures and wire radii, and have found that the most interesting physics appears at low temperatures and for large wire radii ͑specifically, for radius RϾ 0 , 0 , where 0 and 0 are the zerotemperature coherence and penetration lengths͒. Thus we have focused on wires that are wide enough...

Supercurrent on a vortex core in 2H-NbSe2: Current-driven scanning tunneling spectroscopy measurements

“…It is useful to discuss our observations in relation to the de-pairing J d current. A simple, yet useful understanding of J d can be obtained by taking into account that the current Doppler-shifts the superconducting density of states [34,[47][48][49][50][51][52]. At the de-pairing current density J d the Doppler shift is of order of the gap and superconduc-tivity is lost.…”

“…A simple, yet useful understanding of J d can be obtained by taking into account that the current Doppler-shifts the superconducting density of states. [32][33][34][35][36][37][38] At the depairing current density J d the Doppler shift is of the order of the gap and superconductivity is lost. Unfortunately, the flow of a current through the cross section of a bulk superconducting sample is a difficult problem involving electrodynamics and vortex matter which is not fully solved.…”

Normal-metal–insulator–superconductor interferometer

“…It has been proposed [10] that oscillating behaviour in our geometry might originate from the modification of the energy gap and the density of states by the screening (and transport) currents when the flux threads the loop. Certainly, such effect should contribute to some extent, but a noticeable impact is only expected at high magnetic fields (currents) comparable to the critical ones [11]. More importantly, the periodicity should be equal to the usual 'superconducting' value h/2e.…”

“…Certainly, such effect should contribute to some extent, but a noticeable impact is only expected at high magnetic fields (currents) comparable to the critical ones [11]. More importantly, the periodicity should be equal to the usual 'superconducting' value h/2e.…”

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