For type I superconductors (with only the Meissner effect and no vortices), it is all or nothing. If the magnetic field is weak, it is completely expelled. If it is too strong, the system will not develop the necessary supercurrents, there will be no superconductivity and the sample will simply become normal metal again. The critical magnetic field over which the material cannot be superconducting even if it is cooled down is called Bc.
It is represented in this phase diagram.
Under the bell curve, the sample is superconducting; above, it is not. The value of this critical magnetic field depends on the temperature because it is easier to quench the superconductor when the temperature is high than when it is low.
The type II superconductor phase diagram is slightly more complex. Below its critical temperature and when no external magnetic field is involved, the sample is superconducting, just like type I superconductors. When a small magnetic field is applied, surface currents develop and create a screen preventing the magnetic field from entering the majority of the sample; this is called the Meissner state. This state exists until the strength of the applied magnetic field reaches the first critical value (called Bc1). Above this value, the system enters the mixed state and the first vortex penetrates the sample. The sample still creates a screen against the external magnetic field, but the screen is not perfect since part of the magnetic field can go through the vortex.
When the magnetic field is raised again, more and more vortices appear in the superconductor; the latter becomes less and less diamagnetic. When the external magnetic field reaches a second critical field, Bc2, the compromise no longer works and the sample becomes normal metal again. This critical field occurs when the vortices become so numerous that there is no space left for superconductivity.
In this phase diagram, we show a situation of weak pinning during which the vortices can easily go through the sample. This situation describes the most energetically favourable state for the system, when the best compromise is reached. In case of strong pinning, the situation becomes more complicated and the state of the system strongly depends on the temperature and the magnetic field applied to the sample. If you apply the magnetic field first and then cool the sample, vortices will form during the superconducting state and will become pinned.
This procedure is called “Field Cooling”, and this is what is used for the most impressive superconducting levitation experiments. Inversely, if you cool the sample first and then raise the magnetic field, strong pinning will prevent the vortices from forming in the superconductor: the stronger the trap, the fewer the vortices. Really strong pinning will enable the sample to expel the magnetic field almost completely, similar to the Meissner effect, even if the energetic compromise represented by the vortices is normally a more favourable state. This procedure is called “Zero Field Cooling”. The following videos illustrate these effects:
See the following videos :
