Figure 158: The critical magnetic fieldHc(T)as a function of temperatureT. ForT =Tcwe have
Hc(Tc) = 0. Hc(T)separates the normal (above the curve) from the superconducting
(below the curve) state.
16.2.2 Meissner - OchsenfeldEffect
In 1933MeissnerandOchsenfeldobserved that if a superconductor within an external magnetic
fieldBis cooled below the transition temperatureTc, then the magnetic field is pushed out of the
interior of the superconductor, i.e.B= 0 within the superconductor. Note that this effect is reversible.
This observation has several consequences. For instance, in case of a superconducting wire we can
immediately deduce that current cannot flow within the superconductor due toAmpere’s law∇×B=
μ 0 J. The current must therefore flow in the surface of the wire.
A second consequence is that a superconductor is not equal to an ideal conductor. For an ideal
conductor we obtain fromOhm’s lawE=ρJ, withEthe electrical field andρthe resistivity, that
E→ 0 in the limitρ→ 0 , sinceJ<∞within the superconductor. However, fromMaxwell’s
equations we now deduce thatB ̇ ∼∇×E= 0. This is not equivalent to the observation byMeissner
andOchsenfeldsince in the case of an ideal conductor we obtain that the magnetic field must not
change on cooling through the transition temperature. Hence, we obtain that perfect diamagnetism
is an essential property of the superconducting state.
We now explicitly write the magnetic field within the superconductor
B=Ba+μ 0 M, (265)whereMis the magnetization. SinceB= 0 forBa<Bacwe have in the one-dimensional case
M
Ba=−
1
μ 0
=−ε 0 c^2 , (266)whereε 0 is the dielectric constant of vacuum andcis the vacuum speed of light. In Fig. 159(a) this
relation is illustrated. Note that the superconductor undergoes a first order phase transition atHcfor
T 6 =Tc. However, such behavior is only observed in a a certain class of materials, which are nowadays