1.4 Superconducting thermodynamics Ë 5partially penetrate into the superconductor, and the field is only partially excluded,
i.e. diamagnetism is not perfect.
Movement of vortices in a type II superconductor can cause heat dissipation, i.e.
a finite resistivity, called flux flow resistivity, the superconductor is no longer in the
superconducting state of type I superconductor. If the current is sufficiently small,
the vortices are stationary, and the resistivity is zero. The resistance below the critical
current densityJcis negligible compared with that of normal conductors. Indeed,
there is no complete Meissner-Ochsenfeld effect in type II superconductors aboveHc1,
since in the mixed state, the magnetic field penetrates into the superconductor in the
shape of the vortices.
Interaction between the magnetic field and type I superconductor in Meissner-
Ochsenfeld state produces a magnetic levitation force, but this force is much smaller
than that of a type II superconductor in the mixed state. This is a very important matter,
but also confusing. Maglev in type II superconductor looks similar to the Meissner-
Ochsenfeld effect, but there is a critical difference. The Meissner-Ochsenfeld effect
completely excludes the magnetic fields belowHc1to the field penetrating depth휆
on the superconductor surface, and it gives rise to a small levitation forces. In the
mixed state of a type II superconductors, the pinning forces hold the superconductor
in a place, thereby allowing it to levitate stably. The levitation forces of type II
superconductors in the mixed state are much larger than the levitation force in a pure
Meissner-Ochsenfeld state in type I superconductors.
Svedlindh et al. [13] reported the observation of a paramagnetic Meissner-
Ochsenfeld effect (PME) [14] in a BiSrCaCuO superconductor. The Meissner-
Ochsenfeld effect is characterized by a diamagnetic response of the superconducting
material when a magnetic field is applied, but in several cases, this magnetic response
in FC experiments can be paramagnetic, challenging the conventional Meissner-
Ochsenfeld effect.
1.4 Superconducting thermodynamics [15]
The phase transition from the normal state to the superconducting state can be dealt
with the general principles of thermodynamics. Considering the magnetization effect
for a magnetic medium, the Gibbs free energyGcan be expressed as
G=U−TS+pV−휇 0 HM. (1.2)Here,Uis the internal energy,Tis the temperature,Sis the entropy,pis pressure,
Vis the volume,휇 0 is the permeability of free space, andMis the magnetization.
At constant temperature and constant pressure conditions,
dG= −휇 0 MdH. (1.3)