KAHIBARO
Table of Contents
Defining the phenomenon
The Meissner effect is the expulsion of magnetic field from the interior of a material when it enters the superconducting state. If a sample is cooled below its critical temperature while a magnetic field is present, the magnetic field is pushed out of most of the material. This behavior is one of the clearest signatures of superconductivity.
This is not just very good conductivity. An ordinary perfect conductor would prevent changes in magnetic flux, but the Meissner effect shows something stronger. A superconductor actively settles into a state in which the magnetic field inside is essentially zero, except near the surface.
A key fact is that a superconductor in the superconducting state behaves as an ideal diamagnet:
$$B_{\text{inside}} \approx 0$$
for magnetic fields below a critical value and away from the surface.
Why it matters
The Meissner effect tells us that superconductivity is a distinct thermodynamic phase of matter, not merely a material with zero electrical resistance. The magnetic response changes qualitatively at the transition. This is why magnetic behavior is used to identify superconductors in experiments.
If a magnet is brought near a superconducting sample, currents appear on the surface of the superconductor. These surface currents create their own magnetic field that opposes and cancels the applied field inside the material.
Surface currents and field exclusion
The magnetic field is not removed by charges sitting still. Instead, circulating currents near the surface produce the effect. These are called screening currents. They flow without resistance and generate a magnetic field opposite to the applied one.
The field does not usually drop to zero instantly at the boundary. It decreases over a short distance inside the material. This distance is called the penetration depth, usually written as $\lambda$.
A simple description is
$$B(x) = B_0 e^{-x/\lambda}$$
where $x$ is the distance measured inward from the surface, $B_0$ is the magnetic field at the surface, and $\lambda$ is the penetration depth.
The magnetic field inside a superconductor is excluded only over distances larger than the penetration depth. Very near the surface, some field can remain.
Distinguishing it from perfect conductivity
To see the difference, imagine two materials placed in a magnetic field and then cooled.
A perfect conductor would preserve whatever magnetic field configuration existed before it became resistance free. A superconductor, by contrast, expels the field as it enters the superconducting state, provided the applied field is not too large.
This distinction is central.
| Material idea | What happens to magnetic field inside after cooling below transition |
|---|---|
| Ideal perfect conductor | Existing magnetic flux could remain trapped |
| Superconductor | Magnetic field is expelled, this is the Meissner effect |
Critical field and loss of the effect
The Meissner effect occurs only while superconductivity survives. If the applied magnetic field becomes too strong, the superconducting state can be destroyed.
For a simple superconductor, if the applied field exceeds a critical magnetic field $H_c$, the material returns to the normal state and magnetic field can enter freely.
The Meissner effect is observed only below the critical temperature and below the critical magnetic field.
Magnetic levitation
One striking consequence of the Meissner effect is magnetic levitation. A small magnet can float above a superconductor because the induced surface currents create a repulsive magnetic interaction.
This is often the most visible demonstration of superconductivity for beginners. The superconductor excludes the magnetic field, and this exclusion can balance the weight of the magnet.
An ideal diamagnetic response
In magnetism, diamagnetic materials oppose an applied magnetic field weakly. A superconductor does this in the strongest possible way. In simple terms, its magnetic susceptibility is
$$\chi = -1$$
in SI language for perfect flux expulsion, when described ideally. This means the induced magnetization fully opposes the applied field inside.
This ideal diamagnetism is exactly what makes the Meissner effect so special.
A simple picture to remember
A useful mental image is that the superconductor does not like magnetic field lines passing through its bulk. When the material becomes superconducting, it develops surface currents that rearrange the field so that the interior becomes nearly field free.
Final idea
The Meissner effect is the defining magnetic property of a superconductor. When superconductivity appears, magnetic field is expelled from the interior by resistance free surface currents, except within a thin penetration layer near the surface. This is why superconductors are not just perfect conductors, but a separate and remarkable state of matter.