Superconductivity
= Superconductivity
{wiki}
<Superconductivity> is a phase of matter that supports steady <electric current> with zero bulk <electrical resistivity> and exhibits the <Meissner effect>: equilibrium screening of a sufficiently weak, static <magnetic field> from the interior. It occurs below a material-dependent <superconducting transition temperature>, provided the <electric current> and applied <magnetic field> are also sufficiently small. https://arxiv.org/abs/cond-mat/0409402[Milind N. Kunchur (2004), limits on dissipation-free superconducting current]{ref} Bulk expulsion means that a sample much thicker than its <London penetration depth> has an almost field-free interior; the <magnetic field> need not vanish at its surface. Conventional <BCS theory> explains <superconductivity> through correlated <electrons> forming <Cooper pairs>. https://hoffman.physics.harvard.edu/materials/SCintro.php[Hoffman laboratory, introduction to superconductivity]{ref}
The two observations answer different questions. A <resistance-versus-temperature experiment for superconductivity> asks whether a steady <electric current> requires a measurable <electric potential difference>. A <Field-cooled Meissner experiment> asks whether a <magnetic field> already present in the material is expelled when it enters <superconductivity>. An ideal <perfect conductor> with zero <electrical resistivity> can preserve that pre-existing <magnetic field>; zero <electrical resistance> alone therefore does not establish the <Meissner effect>.
The usefulness follows directly from <Joule heating>, $P=I^2R$: maintaining a steady <electric current> through a segment with zero <electrical resistance> produces no resistive heating in that segment. This makes persistent <electric currents> attractive for producing steady <magnetic fields>. The beauty is that one phase has both a transport property and an equilibrium magnetic response, and the second cannot be inferred just by making an ordinary <electrical resistance> very small. The <London equations> encode this extra magnetic response. https://doi.org/10.1098/rspa.1935.0048[F. and H. London (1935), The electromagnetic equations of the supraconductor]{ref}