Little–Parks Effect

A superconducting loop with a repeating temperature story: one flux quantum at a time.

The Physics

In 1962 William Little and Roland Parks threaded a magnetic field through a hollow superconducting cylinder and watched its transition temperature oscillate. A circulating supercurrent costs kinetic energy and depresses the transition temperature between peaks. The peaks occur at integer multiples of the superconducting flux quantum; the h/2e period identifies paired charge carriers.

T_c(Φ) = T_c(Φ + Φ₀), Φ₀ = h/(2e) ≈ 2.067 833 848 × 10⁻¹⁵ Wb.

• T_c: superconducting transition temperature (K).
• Φ: axial magnetic flux through the cylinder’s hole (Wb).
• Φ₀: superconducting flux quantum (Wb).
• h: Planck constant, 6.626 070 15 × 10⁻³⁴ J s.
• e: elementary charge, 1.602 176 634 × 10⁻¹⁹ C.
• n in Φ = nΦ₀: integer winding number (dimensionless).

Honest caveat: This description is for a thin-walled superconducting cylinder, with wall thickness smaller than the penetration depth. T_c is maximal at Φ = nΦ₀; the suppression vanishes there. The thin-cylinder curve consists of parabolic arcs, not a sine wave. The period is h/2e, not h/e.

Sources

• W. A. Little & R. D. Parks, “Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder,” Phys. Rev. Lett. 9, 9–12 (1962), doi:10.1103/PhysRevLett.9.9.
• R. D. Parks & W. A. Little, “Fluxoid Quantization in a Multiply-Connected Superconductor,” Phys. Rev. 133, A97–A103 (1964), doi:10.1103/PhysRev.133.A97.
• NIST: SI 2019 definitions of h and e.

On the shirt

Approved physics print block:

“LITTLE–PARKS EFFECT”

“T_c(Φ) = T_c(Φ + Φ₀), Φ₀ = h/2e”

“Φ₀ ≈ 2.07 × 10⁻¹⁵ Wb”

“Thread magnetic flux through a tiny superconducting ring and its critical temperature rises and falls, repeating every flux quantum h/2e.”

Printed front and back. Physics. Personified.