Superconductivity

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# 2.3 The Meissner effect

The second defining characteristic of a superconducting material is much less obvious than its zero electrical resistance. It was over 20 years after the discovery of superconductivity that Meissner and Ochsenfeld published a paper describing this second characteristic. They discovered that when a magnetic field is applied to a sample of tin, say, in the superconducting state, the applied field is excluded, so that B = 0 throughout its interior. This property of the superconducting state is known as the Meissner effect.

The exclusion of the magnetic field from a superconductor takes place regardless of whether the sample becomes superconducting before or after the external magnetic field is applied. In the steady state, the external magnetic field is cancelled in the interior of the superconductor by opposing magnetic fields produced by a steady screening current that flows on the surface of the superconductor.

It is important to recognise that the exclusion of the magnetic field from inside a superconductor cannot be predicted by applying Maxwell's equations to a material that has zero electrical resistance. We shall refer to a material that has zero resistance but does not exhibit the Meissner effect as a perfect conductor, and we shall show that a superconductor has additional properties besides those that can be predicted from its zero resistance.

Consider first the behaviour of a perfect conductor. We showed in the previous subsection that the flux enclosed by a continuous path through zero resistance material – a perfect conductor – remains constant, and this must be true for any path within the material, whatever its size or orientation. This means that the magnetic field throughout the material must remain constant, that is, ∂﻿B/∂﻿t = 0. The consequences of this are shown in Figure 10 parts (a) and (b).

Figure 10 A comparison of the response of a perfect conductor, (a) and (b), and a superconductor, (c) and (d), to an applied magnetic field.

In part (a) of this figure, a perfect conductor is cooled in zero magnetic field to below the temperature at which its resistance becomes zero. When a magnetic field is applied, screening currents are induced in the surface to maintain the field at zero within the material, and when the field is removed, the field within the material stays at zero. In contrast, part (b) shows that cooling a perfect conductor to below its critical temperature in a uniform magnetic field leads to a situation where the uniform field is maintained within the material. If the applied field is then removed, the field within the conductor remains uniform, and continuity of magnetic field lines means there is a field in the region around the perfect conductor. Clearly, the magnetisation state of the perfect conductor depends not just on temperature and magnetic field, but also on the previous history of the material.

Contrast this with the behaviour of a superconductor, shown in Figure 10 parts (c) and (d). Whether a material is cooled below its superconducting critical temperature in zero field, (c), or in a finite field, (d), the magnetic field within a superconducting material is always zero. The magnetic field is always expelled from a superconductor. This is achieved spontaneously by producing currents on the surface of the superconductor. The direction of the currents is such as to create a magnetic field that exactly cancels the applied field in the superconductor. It is this active exclusion of magnetic field – the Meissner effect – that distinguishes a superconductor from a perfect conductor, a material that merely has zero resistance. Thus we can regard zero resistance and zero magnetic field as the two key characteristics of superconductivity.

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