[Paper Review] Experimental investigations of the change with magnetic flux of quantum number in superconducting ring

A. V. Burlakov, В. Л. Гуртовой+3 more|arXiv (Cornell University)|Mar 16, 2011

Physics of Superconductivity and Magnetism3 citations

TL;DR

This study investigates quantum number transitions in superconducting aluminum rings with asymmetric current leads, measuring critical current dependencies under varying magnetic flux. Despite theoretical predictions of a discontinuous jump in critical current at half-integer flux quanta due to quantum number changes, experiments show smooth, continuous variations—challenging standard quantum formalism and revealing a paradoxical absence of expected jumps near Φ = (n+0.5)Φ₀.

ABSTRACT

The magnetic dependencies of the critical current of aluminum ring with asymmetric link-up of current leads have been measured in order to clear up the essence of the paradoxical absence of the jump of the critical current at the quantum number change revealed before at the measurements of asymmetric superconducting ring. The measurements have shown that the experimental and theoretical dependencies agree in the region of magnetic field corresponding to integer numbers of the flux quantum and disagree at the half of the flux quantum. The jump is not observed as well as in the asymmetric rings.

Motivation & Objective

• To resolve the paradox of the missing jump in critical current during quantum number transitions in asymmetric superconducting rings.
• To investigate whether the discontinuity predicted by quantum formalism at Φ = (n+0.5)Φ₀ is experimentally observable.
• To examine the role of asymmetric current lead geometry in modifying critical current behavior under magnetic flux variation.
• To compare experimental critical current dependencies with theoretical models near integer and half-integer flux quanta.
• To explore the origin of a previously observed 1/4 flux quantum shift in critical current anisotropy, which defies conventional explanation.

Proposed method

• Fabricated aluminum superconducting rings with radius ≈1 μm and asymmetric current lead geometry (l_sh ≈ 0.35×2πr, l_long ≈ 0.65×2πr).
• Measured magnetic flux dependence of critical current I_c+ and I_c- in opposite current directions at T ≈ 0.900T_c and T ≈ 0.933T_c.
• Used theoretical model I_c± = I_c0 ± I_p,A(n − Φ/Φ₀) to predict expected jump of ΔI_c = I_p,A at Φ = (n+0.5)Φ₀.
• Compared experimental I_c(Φ/Φ₀) curves with theoretical predictions, focusing on agreement near Φ = nΦ₀ and disagreement near Φ = (n+0.5)Φ₀.
• Analyzed critical current anisotropy I_c,an(Φ/Φ₀) = I_c+(Φ/Φ₀ + Δφ) − I_c−(Φ/Φ₀ − Δφ) to detect shifts in periodicity.
• Assessed the influence of persistent current direction reversal on critical current behavior during quantum number transitions.

Experimental results

Research questions

• RQ1 Why is there no observable jump in critical current at half-integer flux quanta (Φ = (n+0.5)Φ₀) despite theoretical prediction of a discontinuity due to quantum number n change?
• RQ2 How does asymmetric current lead geometry affect the magnetic flux dependence of critical current in superconducting rings?
• RQ3 What causes the experimentally observed 1/4 flux quantum shift (Δφ ≈ 1/4) in the critical current anisotropy, which contradicts standard quantum formalism?
• RQ4 Why do experimental and theoretical critical current dependencies agree near integer flux quanta (Φ = nΦ₀) but disagree near half-integer quanta?
• RQ5 To what extent does the smooth variation of critical current near Φ = (n+0.5)Φ₀ contradict the expectation of abrupt changes due to persistent current reversal?

Key findings

• The measured critical current I_c+ and I_c− vary smoothly with magnetic flux near Φ = (n+0.5)Φ₀, with no observable jump despite theoretical prediction of ΔI_c = I_p,A.
• Experimental data agree well with theoretical predictions near integer flux quanta (Φ ≈ nΦ₀), confirming the model’s validity in that regime.
• Discrepancy between experiment and theory emerges specifically near Φ ≈ (n+0.5)Φ₀, where the expected discontinuity is absent.
• The amplitude of the persistent current I_p,A is sufficiently large (I_p,A / I_c0 < 0.25) to make the absence of a jump statistically significant and not due to measurement limitations.
• The observed 1/4 flux quantum shift in critical current anisotropy (Δφ ≈ 1/4) is inconsistent with standard quantum mechanical expectations and remains unexplained.
• The smooth behavior of I_c(Φ/Φ₀) near half-integer flux quanta suggests a fundamental suppression of discontinuities, possibly due to quantum coherence or non-adiabatic effects not captured by the standard model.