Meissner effect

{c}

For a bulk <type-II superconductor> with negligible <demagnetizing field>, raising the applied <magnetic field intensity> past the lower critical value $H_{c1}$ favors a <superconducting mixed state> containing <quantum vortex> lines; <superconductivity> survives until the upper critical value $H_{c2}$. The <magnetic field> extends around each vortex over a penetration scale, not solely inside its core. Thus a nonzero average <magnetic flux density> can coexist with <superconductivity>. Below $H_{c1}$, a <type-II superconductor> also supports a <Meissner state>; a vortex-free state above the equilibrium entry field may instead be <metastable>. <University Physics Volume 3 by Samuel J. Ling and others/9.8 Superconductivity>[§9.8, type-II critical-field and mixed-state paragraphs; the source uses B_c1 and B_c2 for applied-field scales]{ref}

Real preparation histories may leave <quantum vortex> lines held in place by material inhomogeneities, retaining <magnetic flux> and producing <hysteresis>. This <flux pinning> restricts access to equilibrium: it is different from the arbitrary frozen interior <magnetic field> of the ideal <perfect conductor> model. Harvard's vortex-imaging work illustrates strong pinning to bulk disorder in a <type-II superconductor>. <Scanning Tunneling Microscopy Research by Hoffman Laboratory>[Vortex Imaging in Iron Pnictide Superconductor, Fig. 2 and the discussion of disordered vortices and bulk pinning]{ref} Separately, <flux conservation in a superconducting loop> and <fluxoid and flux quantization in a superconductor> explain why a hole can retain <magnetic flux>. Neither bore retention, vortex penetration nor weak screening in a thin sample should be silently identified with the equilibrium <Planar London screening> calculation.


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 Incoming links: Limits of Meissner screening