Phase Sensitive Detection Applied to Superconducting Transport Measurements*

Measurements of superconducting transitions in materials under very high pressures (e.g., in diamond anvil cells) can be challenging due to the very small samples involved. Phase sensitive detection methods are used in both electrical resistance and magnetic susceptibility measurements in order to extract signatures of superconductivity (i.e., T_c) in such samples. The background signals in such measurements are often not well understood, leading to controversies in the literature.  We present a method of extracting evidence for both zero-resistivity and the Meissner effect in a single electrical measurement for small samples within diamond-anvil cells, in particular, through the observation of a transient inductance at T_c . A framework for differentiating a superconducting transition from instrumental or environmental artifacts is developed and data from superconducting samples that have been well characterized using other techniques along with data for proposed near-ambient superconductivity in the Lu-N-H system.