Direct Measurement of Penetration Length in Ultra-Thin and/or Mesoscopic Superconducting Structures

As the dimensions of thin superconducting structures become comparable with or less than the penetration length of magnetic flux into the structures, it becomes increasingly necessary to devise experimental tests of available theoretical models. One approach which we shall describe, enables penetration lengths to be derived from the measurement of the effective area of planar, thin-film structures with linear dimensions in the range 1 to 100μm. The effective area is defined by measurement of the inductive coupling of the structures to dc or low-frequency magnetic fields. The structures described consist of two parts: (1) An ultra-thin annular superconducting film with transition temperature Tca (“washer”); and (2) surrounding the washer is a superconducting ring with transition temperature Tcs. Because the films are prepared in such a way that Tca < Tcs , the ring-washer combination acts as a dc SQUID (Superconducting Quantum Interference Device) up to and beyond Tca, enabling the effective area of the washer to be measured over a wide temperature range. Results for the temperature dependence of the Pearl penetration length Λ(T), derived directly from measurements of the effective area, are compared both with theory and with other experimental data. Whereas alternative methods may be restricted to narrow-band, high-frequency fields and require sample dimensions of order 10 mm or greater, the method is inherently broad-band and is applicable to dimensions ≥ 1 μm.