A Ginzburg-Landau equation with non-local correction for superconductors in zero magnetic field

Abstract

A form of Ginzburg-Landau theory with non-local correction is derived which is useful in numerical calculation of the spatial variation of the order parameter for superconductors in zero magnetic field. This form of theory is obtained as an extension of the low-temperature modifications of G-L theory developed by Werthamer and others, and is valid over a considerably wider range of values of temperature and order parameter. Boundary conditions at the interface between two metals applicable under rather general conditions are obtained, and the numerical calculation of the one-electron eigenstates in the presence of a spatially varying order parameter is discussed briefly in an appendix.

Design of a test for the electromagnetic coupling of non-local wavefunctions

“…In fact, it is reasonable to expect that only a small fraction η of the current of the junction crosses the junction by strong tunnelling, i.e., without local conservation. For example, the non-local corrections to the Ginzburg-Landau equation in the proximity effect are small, of the order of 1% or less of the order parameter [14]. As a consequence, the effect of the missing B s field on the total field will be small, of the same magnitude order.…”

“…Such sources are not present in the standard formalism based on the Schrödinger equation (and its nonlinear extensions) or in quantum field theory with local interactions. Nevertheless, non-locally conserved currents arise for some effective wavefunctions, like those describing nuclear scattering [8,9], systems with long range interactions and anomalous diffusion [10][11][12], superconductors in the general non-local Gorkov theory [13,14], or fractional quantum mechanics [15,16].…”

“…II, III). Namely, we consider a brief pulse of supercurrent which crosses multiple normal barriers thanks to the proximity effect, in the assumption that the macroscopic wavefunction of the superconducting charge carriers satisfies a Ginzburg-Landau equation with non-local terms [14]. We find the anomalous corrections to the magnetic field of the supercurrent and propose a scheme for a possible detection procedure (Sect.…”

Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current

“…We summarize here the local approximation procedure given by Waldram [33,34]. Let us suppose that the order parameter F varies slowly in space (this is true for low-T c superconductors, but not for high-T c superconductors, which have a very short coherence length).…”

High-Frequency Electromagnetic Emission from Non-Local Wavefunctions

“…3. For the proximity effect in superconductors, especially in thick SNS junctions in cuprates, where the Gorkov equation cannot be properly approximated by a local Ginzburg-Landau equation [9,17,30,31].…”