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: 

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.

It should be noted that any perfect conductor (i.e. with zero electrical resistance) will maintain its internal magnetic state on account of the generation of surface currents.  If now we consider the case of cooling a superconductor through its transition temperature and into the superconducting state, then we observe an aspect of the Meissner effect that cannot be explained in terms of surface current generation.

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 and 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 once again the magnetic field inside the superconductor becomes zero.  This phenomenon cannot be explained in the simple terms given above, purely on the basis of zero electrical resistance.  Because no changes in the magetic field occur, electromagnetic induction cannot be invoked as the mechanism for generating surface currents that change the state of the internal field of the superconductor.  This is why the Meissner effect is considered to be a fundamental property of superconductors.

Next:  Type 1 and Type 2 Superconductors