We have studied the normal-to-superconducting phase transition in optimally-doped YBa$_2$Cu$_3$O$_{7-delta}$ in zero external magnetic field using a variety of different samples and techniques. Using DC transport measurements, we find that the dynamical critical exponent $z=1.54pm0.14$, and the static critical exponent $ u=0.66pm0.10$ for both films (when finite-thickness effects are included in the data analysis) and single crystals (where finite-thickness effects are unimportant). We also measured thin films at different microwave frequencies and at different powers, which allowed us to systematically probe different length scales to avoid finite-thickness effects. DC transport measurements were also performed on the films used in the microwave experiments to provide a further consistency check. These microwave and DC measurements yielded a value of z consistent with the other results, $z=1.55pm0.15$. The neglect of finite-thickness, finite-current, and finite-frequency effects may account for the wide ranges of values for $ u$ and $z$ previously reported in the literature.
The suspension and levitation of superconductors by permanent magnets is one of the most fascinating consequences of superconductivity, and a wonderful instrument for generating interest in low temperature physics and electrodynamics. We present a novel classroom demonstration of the levitation/suspension of a superconductor over a magnetic track that maximizes levitation/suspension time, separation distance between the magnetic track and superconductor and also insulator aesthetics. The demonstration as described is both inexpensive and easy to construct.
