Previous:  Superconductivity

In the previous section we discussed one of the fundamental properties of the superconducting state, namely that the application of a magnetic field, above a material-specific and temperature-dependent threshold field B_C, brings about the return of the normal conducting state.  In this section we are concerned with what happens to the superconducting state when the applied magnetic field is below the threshold value, thus retaining the material under consideration in the superconducting state. 

Consider the application of an external magnetic field to a cylindrical material that is already in its superconducting state.  That is, we assume that the temperature of our material is less than the transition temperature for superconductivity, i.e. T < T_C.  A schematic representation of the processes that take place when the magnetic field is switched on are shown in the following diagram: 

(Note:  the assumption that the material is already in its superconducting state is an important one, as we will discuss at the end of this article).

When the external magnetic field is switched on, there will be a short period of time where our superconducting material is subject to a time-varying magnetic field (as the field changes from zero to its final value).  Now, the laws of electromagnetism tell us that when a conductor is subject to a time-varying magnetic field, electric currents are induced in the conductor. 

Further, Lenz’s law tells us that such currents flow so as to produce effects that oppose those of the “driving” agency.  In the situation we are considering, the driving agency is the external magnetic field acting on our superconductor.  The flows in our superconducting material are restricted to a thin surface layer, and flow around the cylinder as shown in the left-hand side of the above diagram. 

The laws of electromagnetism tell us that current flow of this type induces a magnetic field inside the superconducting cylinder.  The field generated in this way has an equal magnitude to the applied field, but acts in the opposite direction, as shown on the right-hand side of the above figure.  The magnitude of the induced magnetic field is equal to that of the external field.  Thus, the total magnetic field in the cylinder, while the induced currents are flowing, is equal to the sum of the internal and external fields.  That is, the total magnetic field inside the cylinder is zero. 

Now we know that when a material is in the superconducting phase, it exhibits zero resistivity.  Thus, the induced currents persist, because there are no scattering mechanisms to dissipate the currents.  Therefore, the internal field in the cylinder also persists, and the total magnetic field inside the cylinder remains at zero. 

This zero magnetic field inside the superconducting cylinder is referred to as the Meissner effect.  It is another fundamental property of superconductors.  The Meissner effect, and the situation when the external field exceeds the threshold or critical field B_C, is summarised in the following diagram. 

When the external field B exceeds the threshold field strength B_C, the superconducting material behaves like a normal conductor.  Thus, when the external field is switched on, currents are induced in the material but these soon dissipate because of the non-zero resistivity of the material.  In this situation, no internal magnetic field is generated and so the magnetic field inside the conductor equals the external field. 

As discussed above, when the external field is below the threshold field strength, an equal and opposite field is generated because of the persistent surface currents, and the magnetic field inside the superconductor is zero. 

Throughout, we have assumed that the temperature of our material is less than the transition temperature for superconductivity, i.e. T < T_C.  If we assume that we start with T > T_C then a slightly different situation applies.  If we apply a magnetic field to such a material, then surface currents are generated, but do not persist because of the non-zero resistivity of the material (when T > T_C the material is not in its superconducting state and therefore behaves like a normal conductor). 

If we were to now cool the material so as to push it into its superconducting state (i.e. T < T_C and the external field B < B_C), then we would still observe a magnetic field inside our material.  Why?  Because no surface currents are generated through this cooling process.  If the magnetic field were now to be switched off, persistent surface currents would be generated in our superconducting material, and an internal magnetic field would be generated because of those persistent currents.  That is, we would have a magnetic field that is “locked” into our superconducting material, because the surface currents (and hence the internal magnetic field) will persist for as long as the material remains in the superconducting state.

Next:  Type 1 and Type 2 Superconductors