Critical temperature

The critical temperature T_c of a superconductor is the threshold below which the material transitions abruptly from normal electrical conduction to the superconducting state. Above T_c, resistivity follows the ordinary metallic temperature dependence. At T_c, resistance drops discontinuously to zero — experimentally indistinguishable from zero, with persistent currents in superconducting rings observed to decay with time constants longer than the age of the universe. Simultaneously, the Meißner effect switches on: any magnetic flux threading the sample is actively expelled.

The first superconductors discovered by Kamerlingh Onnes in 1911 had tiny T_c values: mercury 4.15 K, lead 7.2 K, tin 3.7 K — all accessible only with liquid helium. For seventy-five years this defined the experimental cost of superconductivity: helium is expensive to produce, lose, and handle, which is why superconducting MRI magnets and accelerator magnets remained the only widely-deployed technologies through the mid-1980s. Nb₃Sn at 18 K and Nb₃Ge at 23 K were the practical limits reached by 1973.

The 1986 discovery of cuprate superconductors by Bednorz and Müller broke the barrier: La-Ba-Cu-O with T_c ≈ 35 K, then YBa₂Cu₃O₇ at 92 K (above the 77 K boiling point of liquid nitrogen, transforming the economics of the technology), then mercury-barium-calcium-copper-oxides reaching 135 K at atmospheric pressure and 164 K under pressure. In the late 2010s, ultra-high-pressure hydride materials pushed T_c above 250 K (H₃S, 203 K at 150 GPa; LaH₁₀, 250 K at 170 GPa), with room-temperature superconductivity now appearing plausible if not yet routine. The theoretical upper limit — whether there is one, and what sets it — remains one of the open questions of condensed-matter physics.