Meissner Effect

The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples. The samples, in the presence of an applied magnetic field, were cooled below what is called their superconducting transition temperature. Below the transition temperature the samples cancelled nearly all magnetic fields inside. They detected this effect only indirectly, because the magnetic flux is conserved by a superconductor, when the interior field decreased the exterior field increased. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconducting state. Despite having been known for over 80 years, no dynamical explanation of the Meissner effect exists within the conventional understanding of superconductivity.

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

Explanation

In a weak applied field, a superconductor “expels” nearly all magnetic flux. It does this by setting up electric currents near its surface. The magnetic field of these surface currents cancels the applied magnetic field within the bulk of the superconductor. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called persistent currents) do not decay with time. Therefore the conductivity can be thought of as infinite: a superconductor.

Near the surface, within a distance called the London penetration depth, the magnetic field is not completely cancelled. Each superconducting material has its own characteristic penetration depth.

A magnet levitating above a superconductor cooled by liquid nitrogen.

Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary electromagnetic induction at zero resistance. The Meissner effect is distinct from this: when an ordinary conductor is cooled so that it makes the transition to a superconducting state in the presence of a constant applied magnetic field, the magnetic flux is expelled during the transition. This effect cannot be explained by infinite conductivity alone. Its explanation is more complex and was first given in the London equations by the brothers Fritz and Heinz London. It should thus be noted that the placement and subsequent levitation of a magnet above an already superconducting material does not demonstrate the Meissner effect, while an initially stationary magnet later being repelled by a superconductor as it is cooled through its critical temperature does.

Consequences

The discovery of the Meissner effect led to the phenomenological theory of superconductivity by Fritz and Heinz London in 1935. This theory explained resistanceless transport and the Meissner effect, and allowed the first theoretical predictions for superconductivity to be made. However, this theory only explained experimental observations — it did not allow the microscopic origins of the superconducting properties to be identified. Nevertheless, it became a requirement on all microscopic theories to be able to reproduce this effect. This was done successfully by the BCS theory in 1957. Both phenomenological Londons’ theory and microscopic BCS one describe the Meissner effect in its steady state only and cannot explain the transient stage when the supercurrent grows from zero to its steady value. Indeed, under initial conditions of the Meissner effect, Lorentz force equals to zero, and there are no other electromotive forces in superconductor to accelerate the electrons. This fundamental problem of the conventional theory of the Meissner effect has been pointed out by J. E. Hirsch in The Lorentz force and superconductivity. He has also proposed the dynamical explanation of the Meissner effect in Spin Meissner effect in superconductors and the origin of the Meissner effect.

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