Upper critical field
Superconductivity is characterized both by perfect conductivity (zero resistance) and by the expulsion of magnetic fields (the Meissner effect). Changes in either temperature or magnetic field can cause the phase transition between normal and superconducting states. For a given temperature, the highest magnetic field under which a material remains superconducting is known as the critical field. The highest temperature under which the superconducting state is seen is known as the critical temperature. At that temperature even the smallest external magnetic field will destroy the superconducting state, so 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 () at the critical temperature ():
There is also a direct relation between the critical field and the critical current - the maximum electric current density that a given superconducting material can carry, before switching into the normal state. According to Ampère's law any electric current induces a magnetic field, but superconductors exclude that field. On a microscopic scale the magnetic field is not quite zero at the edges of any given sample - a penetration depth applies. For a type I superconductor, the current must remain zero within the superconducting material (to be compatible with zero magnetic field), but can then go to non-zero values at the edges of the material on this penetration-depth length-scale, as the magnetic field rises. As long as the induced magnetic field at the edges is less than the critical field, the material remains superconducting, but at higher currents the field becomes too strong and the superconducting state is lost. This limit on current density has important practical implications in applications of superconducting materials - despite zero resistance they cannot carry unlimited quantities of electric power.
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