Critical field

For a given temperature, the critical field refers to the maximum magnetic field strength below which a material remains superconducting. Superconductivity is characterized both by perfect conductivity (zero resistance) and by the complete expulsion of magnetic fields (the Meissner effect). Changes in either temperature or magnetic flux density can cause the phase transition between normal and superconducting states. The highest temperature under which the superconducting state is seen is known as the critical temperature. At that temperature even the weakest external magnetic field will destroy the superconducting state, so the strength of the critical field is zero. As temperature decreases, the critical field increases generally to a maximum at absolute zero.

For a type-I superconductor the discontinuity in heat capacity seen at the superconducting transition is generally related to the slope of the critical field ($H_{\text{c}}$) at the critical temperature ($T_{\text{c}}$):

$C_{\text{super}}-C_{\text{normal}}={T \over 4\pi }\left({\frac {dH_{\text{c}}}{dT}}\right)_{T=T_{\text{c}}}^{2}$

The geometry of the superconducting sample complicates the practical measurement of the critical field – the critical field is defined for a cylindrical sample with the field parallel to the axis of radial symmetry. With other shapes (spherical, for example), there may be a mixed state with partial penetration of the exterior surface by the magnetic field (and thus partial normal state), while the interior of the sample remains superconducting.