Meissner Effect · aiwiki.page

The Meissner effect is the expulsion of a magnetic field from the bulk of a material when it enters the appropriate low-field state of superconductivity. The field is excluded from the interior but penetrates a thin surface layer in which screening currents flow. Discovered by Walther Meissner and Robert Ochsenfeld in 1933, the effect established that superconductors are not merely conductors with zero resistance: they possess a distinctive equilibrium magnetic response. Complete exclusion applies in the Meissner state, not under every condition in which a material remains superconducting. (nobelprize.org)

Physical meaning

A superconducting sample placed in a sufficiently weak external field develops an electric current near its surface. The magnetic field generated by this screening current opposes the applied field, making the magnetic induction $\mathbf B$ approximately zero sufficiently far inside a large sample. This is a form of perfect diamagnetism, rather than the much weaker magnetic response of ordinary diamagnetic materials. (nobelprize.org)

In the International System of Units, the relation between magnetic induction, field strength, and magnetization is

\mathbf B=\mu_0(\mathbf H+\mathbf M).

Consequently, ideal bulk exclusion implies $\mathbf M=-\mathbf H$ , or an intrinsic magnetic susceptibility of $\chi=-1$ . Here $\mathbf H$ is the internal magnetic field strength; a susceptibility calculated using the externally applied field also depends on sample shape and its demagnetizing field. These relations describe the ideal bulk limit rather than the field within the surface penetration layer. (nobelprize.org)

Why zero resistance is not enough

Perfect conductivity and the Meissner effect impose different conditions on magnetic fields. In an ideal stationary conductor, zero electrical resistance permits persistent currents. With zero electric field in its interior, Faraday’s law of induction gives

\frac{\partial\mathbf B}{\partial t}=0.

This preserves an existing magnetic field rather than requiring its removal. A field already present when an ordinary conductor hypothetically becomes perfectly conducting can therefore remain inside it. (nobelprize.org)

A superconductor instead favors a field-excluding state under suitable conditions, including when it is cooled through its superconducting transition in an applied field. The distinction is between maintaining an initial magnetic configuration and establishing a characteristic state of thermodynamic equilibrium. Real samples can nevertheless retain flux because of pinning, geometry, or other barriers to equilibration. (nobelprize.org)

London theory and penetration depth

In 1935, Fritz and Heinz London introduced a phenomenological description of superconducting electrodynamics. Its second London equation relates the superconducting current density $\mathbf j_s$ to magnetic induction:

\nabla\times\mathbf j_s =-\frac{\mathbf B}{\mu_0\lambda_L^2}.

Combining it with the static Maxwell equations yields

\nabla^2\mathbf B=\frac{\mathbf B}{\lambda_L^2}.

The parameter $\lambda_L$ , the London penetration depth, sets the distance over which magnetic fields are screened. For a planar surface bordering a semi-infinite superconductor, with a field parallel to the surface, the solution is

B(x)=B(0)e^{-x/\lambda_L},

where $x$ is distance into the material. Magnetic exclusion is therefore not an abrupt disappearance at the boundary: it is a rapid decay into the interior. (api.repository.cam.ac.uk)

In the simple isotropic London model,

\lambda_L=\sqrt{\frac{m^*}{\mu_0 n_s q^{*2}}},

where $n_s$ , $m^*$ , and $q^*$ are the density, effective mass, and charge of the superconducting carriers, using a consistent carrier convention. For Cooper pairs, the charge magnitude is $2e$ . Penetration depth depends on material properties and temperature; the simple local model also requires refinement for anisotropic or nonlocal responses. (api.repository.cam.ac.uk)

The London equations describe the magnetic response without supplying a microscopic pairing mechanism. BCS theory subsequently provided a microscopic account of conventional superconductivity, while Ginzburg–Landau theory describes superconductivity through an order parameter and spatial variations in the superconducting state. (harvest.aps.org)

Type-I and type-II superconductors

Both principal classes of superconductors possess a Meissner state, but their responses differ as the applied field increases:

Type-I superconductors exclude magnetic induction in their bulk below the thermodynamic critical field $H_c$ . Depending on sample geometry, they can form an intermediate state containing normal and superconducting regions before becoming fully normal.
Type-II superconductors have a low-field Meissner state below the lower critical field $H_{c1}$ . Between $H_{c1}$ and the upper critical field $H_{c2}$ , magnetic flux enters as Abrikosov vortices, producing a mixed state. Superconductivity persists between vortices even though complete magnetic exclusion no longer holds. (nobelprize.org)

An isolated, singly quantized vortex carries one magnetic flux quantum,

\Phi_0=\frac{h}{2e}.

This penetration of flux does not contradict the Meissner effect: it marks a different superconducting state. It is therefore inaccurate to describe all superconductors as excluding all magnetic fields, or to say that type-II superconductors never exhibit the effect. (nobelprize.org)

Experimental interpretation and limitations

Finite size matters. If a sample dimension is comparable to its penetration depth, the field may penetrate a substantial fraction of the material even without vortices. Thin films also have screening behavior strongly influenced by their geometry. Complete bulk exclusion is an approximation most directly applicable to samples much larger than the relevant penetration length. (arxiv.org)

In type-II materials, defects can immobilize vortices through flux pinning. A sample cooled in a field may consequently retain magnetic flux instead of reaching an ideal field-excluding equilibrium. Magnetic behavior can depend on cooling history and field history; incomplete expulsion alone does not establish that superconductivity is absent. (arxiv.org)

Magnetic measurements provide evidence complementary to measurements of zero resistance. Historically, establishing the Meissner response was an important test of whether newly investigated materials genuinely exhibited superconductivity rather than only an anomalous decrease in resistance. (aps.org)

Levitation and applications

Meissner screening can produce repulsive forces between a superconductor and a magnet. However, many familiar demonstrations involving high-temperature superconductors rely importantly on vortex pinning. Pinning can stabilize levitation or even suspend a magnet beneath a superconductor. Such “quantum locking” is not synonymous with the Meissner effect, because it involves retained flux rather than complete exclusion. (bulk-sucon.eng.cam.ac.uk)

Superconducting magnetic screening is relevant to field-sensitive devices and their geometry, including superconducting quantum interference devices. By contrast, high-field superconducting magnets generally exploit the mixed state of type-II materials: their operation depends on superconductivity surviving substantial flux penetration, not on maintaining complete Meissner exclusion. (arxiv.org)

References

J. R. Schrieffer – Nobel Lecturenobelprize.org
Advanced information on the Nobel Prize in Physics 2016nobelprize.org
Advanced information on the Nobel Prize in Physics 2003nobelprize.org
Theory of Type-II Superconductors with Finite London Penetration Deptharxiv.org
The Nonlinear Meissner Effect in Unconventional Superconductorsarxiv.org
This month in physics history: April 1986aps.org
Bulk Superconductivity Group – Superconductivity Outreachbulk-sucon.eng.cam.ac.uk
Cambridge Engineers Break Superconductor World Recordeng.cam.ac.uk
Press release: The 2003 Nobel Prize in Physicsnobelprize.org