Little-parks effect in a system of asymmetric superconducting rings

Abstract

Little-Parks oscillations are observed in a system of 110 series-connected aluminum rings 2 µm in diameter with the use of measuring currents from 10 nA to 1 µA. The measurements show that the amplitude and character of the oscillations are independent of the relation between the measuring current and the amplitude of the persistent current. By using asymmetric rings, it is demonstrated that the persistent current has clockwise or contra-clockwise direction. This means that the total current in one of the semi-rings may be directed against the electric field at measurement of the Little-Parks oscillations. The measurements at zero and low measuring current have revealed that the persistent current, like the conventional circulating current, causes a potential difference on the semi-rings with different cross sections in spite of the absence of the Faraday's voltage.

The Meissner effect puzzle and the quantum force in superconductor

“…This paradoxical phenomenon was observed first in the Little-Parks experiment [7]. The observations of the quantum oscillations of the resistance, ∆R ∝ I 2 p [7][8][9] and magnetic susceptibility ∆Φ Ip = LI p [10] give evidence that the persistent current can not decay in spite of non-zero resistance without the Faraday electrical field −dA/dt = 0. It is well known that an electrical current must rapidly decay I(t) = I 0 exp −t/τ RL in a ring with a resistance R > 0 if magnetic flux inside the ring does not change in time dΦ/dt = 0.…”

“…This relation resembles (7). One may say that the azimuthal quantum force F q maintains the persistent current observed at R > 0 and dΦ/dt = 0 [7][8][9][10] instead of the electrical force F e = qE. The relation between the quantum force and of the product of the ring resistance and the current on average in time…”

“…Little and R. D. Parks [7] at measurements of the resistance of thin cylinder in the temperature region corresponding to its superconducting resistive transition. Later on, the quantum oscillations of the ring resistance ∆R ∝ I 2 p [8,9], its magnetic susceptibility ∆Φ Ip = LI p [10], the critical current I c (Φ/Φ 0 ) = I c0 − 2|I p (Φ/Φ 0 )| [11] and the dc voltage V dc (Φ/Φ 0 ) ∝ I p (Φ/Φ 0 ) measured on segments of asymmetric rings [8,9,[12][13][14][15] were observed.…”

“…The observations of the oscillations of the magnetic susceptibility ∆Φ Ip = LI p [10] corroborate that I p = 0 both at Φ = nΦ 0 and Φ = (n + 0.5)Φ 0 . The maximum of the resistance is observed at Φ = (n + 0.5)Φ 0 [7][8][9] because ∆R ∝ I 2 p :…”

“…The observations of the periodicity in magnetic field of the resistance ∆R ∝ I 2 p [7][8][9] and the magnetic susceptibility ∆Φ Ip = LI p [10] are evidence of the strong discreteness ∆E n,n+1 ≫ k B T of the spectrum of superconducting state with the closed wave function, Fig.1, even in the region T c −δT c /2 < T < T c +δT c /2 where the pair density is not zero n s > 0 because of thermal fluctuations. These observations testify to non-zero average values of the persistent current I p = I p,A 2(n − Φ/Φ 0 ) = 0, the dissipation force F dis and the quantum force F q = 0 at Φ = nΦ 0 and Φ = (n + 0.5)Φ 0 .…”