Contradiction between the results of observations of resistance and critical current quantum oscillations in asymmetric superconducting rings

Abstract

Magnetic field dependences of critical current, resistance, and rectified voltage of asymmetric (half circles of different widths) and symmetrical (half circles of equal widths) aluminum rings were measured in the temperature region close to the superconducting transition. All these dependences are periodic magnetic field functions with periods corresponding to the flux quantum in the ring. The periodic dependences of critical current measured in opposite directions were found to be close to each other for symmetrical rings and shifted with respect to each other by half the flux quantum in asymmetric rings with ratios between half circle widths of from 1.25 to 2. This shift of the dependences by a quarter of the flux quantum as the ring becomes asymmetric makes critical current anisotropic, which explains the rectification effect observed for asymmetric rings. Shifts of the extrema of the periodic dependences of critical current by a quarter of the flux quantum contradict directly to the results obtained by measuring asymmetric ring resistance oscillations, whose extrema are, as for symmetrical rings, observed at magnetic fluxes equal to an integer and a half of flux quanta.

Asymmetric nanowire SQUID: Linear current-phase relation, stochastic switching, and symmetries

“…Nanowire networks [12] and loops [13][14][15][16][17][18][19][20] are qualitatively distinct from conventional Josephson junction and SQUIDS due to the linear nature of the nanowire CPR [13]. In contrast, conventional Josephson junctions obey a sinusoidal CPR.…”

Development of a Superconducting Differential Double Contour Interferometer

“…The measurements [9] corroborate that the quantum number of the ring corresponds to the minimal kinetic energy ∝ v 2 with the predominant probability after its coming back in superconducting state. The oscillations of the critical current of a symmetric superconducting ring, Fig.5, observed for example in [13], are similar to the one of a conventional dc SQUID, i.e. superconducting loop with two Josephson junctions [3].…”

“…The two states n and n + 1 have the opposite velocity v and equal kinetic energy E k ∝ v 2 . The picture below on the right: Measurements of the critical current of symmetric aluminum ring with the radius r ≈ 2 µm [13] corroborate the predominant probability of the n state in the interval (n − 0.5)Φ0 < Φ < (n + 0.5)Φ0. must be valid for any contour l along which the wave function Ψ = |Ψ|e iϕ is defined, according to this requirement.…”

“…The observation of these jumps has the critical importance for the opportunity to use the DDCI for high sensitive detection of magnetic flux. The conventional theory [7] and numerous experiments [9,10,[12][13][14][15] testify to the sharpness of the change of the probability P (n) of the n state of superconducting loop with enough big value of the persistent current I p,A . The theory predicts the jump of the critical current with the n change at Φ = (n + 0.5)Φ 0 not only of the double contour interferometer but also, for example, of a superconducting ring with asymmetric link-up of current leads.…”

“…The numerous measurements of the critical current [9,12,13] and other parameters [14,15] testify that the loop comes back in the superconducting state with the quantum number n corresponding to the minimal kinetic energy (2) at the (n − 0.5)Φ 0 < Φ < (n + 0.5)Φ 0 with the predominant probability P (n) ≈ 1.The probability P (n) of the n state should change in a narrow interval of magnetic flux ∆Φ ≈ Φ 0 /ǫ near Φ = (n + 0.5)Φ 0 when a segment of the continuous superconducting loop is switched in the normal state by the short pulses of an external current I sw with a frequency f . Such switching may be provided with the help of the additional current leads shown on Fig.1.…”