Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 241

4.106 Critical Field in Superconductor (Stony Brook,

Chicago)

a) If the external field is smaller than the criticalfield, then the

B-field inside thesuperconductor is zero, and the magnetizationM

becomes

This meansthat the superconductordisplaysperfectdiamagnetism(with

magnetic susceptibility The change infree energy of the

superconductor due to the increase of the external field Hmay be written

as Therefore, the free energy of the

superconductor in a field is given by

The transition toa normal stateoccurswhen the freeenergy of the super-

conducting state isequal tothat of the normalstate:

Here weused the factthat,because of thenegligiblemagneticsusceptibility,

the free energy of thenormal state practicallydoes not depend on the

appliedfield. So, we have

where Now, it iseasy tocalculate theentropy discontinuity

since

so

If we recall that the dependence of thecriticalfield on the temperature can
be approximated by the formula where then
we can confirmthat asuperconducting state is amoreorderedstate,since
and hence