Measurements of the Kinetic Inductance of Superconducting Linear Structures

The kinetic inductance L_k is associated with the inertial mass of the current carriers. For a long superconductor of length l and very small cross-sectional area σ, L_k = (m* / n_se*²) (l/σ) and is the main contribution to the temperature-dependent inductance L_T. We have measured L_T in superconducting tin wires and thin film meander lines by a technique which uses a counter to determine frequency changes of a 15 MHz tunnel-diode oscillator whose tank circuit contains L_T. The measured frequency changes are proportional to z = [λ(t)/λ(0)]_BCS for wires and thick films; for thin films the frequency changes are proportional to z². This result agrees with calculations of L_T from the London theory and the values of λ(0) agree well with the values expected for these samples. This technique allows measurement of the carrier concentration or penetration depth in thin films over the whole H, T plane of the superconducting state and can be independent of the penetration law assumed. Frequency shifts observed with thin film alumimum meander lines have been used to detect changes of temperature of 5∼10^-7 °K, changes of magnetic field of 10^-5 G, and changes of current associated with one quantum in a flux quantum magnetometer.