Meissner Effect in Superconductors


Meissner Effect in Superconductors

The Meissner effect is a hallmark characteristic of superconductivity, where a superconductor expels magnetic fields from its interior when cooled below its critical temperature in the presence of a magnetic field. This effect leads to the iconic demonstration of levitating magnets above a superconducting material. It is a unique demonstration of how superconductors differ from ordinary conductors or magnetic materials.

What Is the Meissner Effect?

Discovered in 1933 by German physicists Walther Meissner and Robert Ochsenfeld, the Meissner effect occurs when a superconductor transitions to its superconducting state and actively repels magnetic fields, creating a field-free region within the material. This repulsion results from the formation of persistent surface currents that create an opposing magnetic field that expels the external magnetic field from the superconductor.

Meissner Effect Demonstration

Meissner effect levitating magnet
Levitation of a magnet over a superconductor is the classic demonstration of the Meissner effect. (Mai-Linh Doan, CC 3.0)

The most famous demonstration of the Meissner effect is the levitation of a magnet above a superconducting disk. If you have the materials, the project is easy:

  • A superconducting material (such as Yttrium Barium Copper Oxide or YBCO)
  • A cryogenic coolant like liquid nitrogen
  • A small magnet
  • A non-metallic container for the liquid nitrogen

Here’s how to observe the Meissner effect:

  1. Prepare the Superconducting Disk: Cool the superconducting disk in a container of liquid nitrogen until it reaches its critical temperature.
  2. Introduce the Magnet: Carefully place a small magnet on top of the cooled superconducting disk. Due to the Meissner effect, the superconductor expels the magnetic field, making the magnet levitate above the disk. You can even gently spin or push the floating magnet, demonstrating the stability and effectiveness of magnetic levitation.

History

Walther Meissner and Robert Ochsenfeld discovered the Meissner effect in 1933 while studying superconductivity in lead and tin. So, sometimes the phenomenon is called the Meissner-Ochsenfeld effect. They noticed that cooling these materials below their critical temperatures in the presence of a magnetic field resulted in the expulsion of the magnetic flux from their interiors. They realized that superconductivity is not just about zero electrical resistance but also involves magnetic field exclusion.

How Does the Meissner Effect Work?

The Meissner effect arises from the formation of persistent currents on the surface of a superconductor. These currents create a magnetic field that opposes and ultimately cancels the external magnetic field within the superconductor. This phenomenon is governed by the London equations, which describe how magnetic fields penetrate superconductors and why they are expelled in the superconducting state.

Superconductivity gets its lack of electrical resistance due to Cooper pairs. Cooper pairs are pairs of electrons with opposite spins and momenta. These pairs form a coherent quantum state that generates the surface currents that expel magnetic fields, leading to the Meissner effect.

Type I and Type II Superconductors

There are two types of superconductors: Type I and Type II. They differ in their critical temperatures, the magnetic field strength they withstand, and the degree of the Meissner effect they exhibit.

  • Type I Superconductors: When cooled below their critical temperature (Tc), Type I superconductors become perfect electrical conductors and exhibit a complete Meissner effect, expelling all magnetic fields from their interiors. However, they typically have very low Tc values and only maintain superconductivity below a fairly low critical magnetic field strength. Beyond this threshold, they lose their superconducting properties and magnetic fields freely penetrate them. Common examples of Type I superconductors are elemental metals like lead, aluminum, and mercury.
  • Type II Superconductors: Type II superconductors are superconductive at higher temperatures and work under higher magnetic fields than Type I superconductors. However, Type II superconductors only exhibit a partial Meissner effect. In the presence of a strong magnetic field, they enter a mixed state. Magnetic vortices penetrate the material and let some magnetic field lines through while retaining superconductivity. Examples include Yttrium Barium Copper Oxide (YBCO) and niobium-titanium (Nb-Ti).

Practical Applications

Levitating a magnet is a cool physics demonstration, but there are also numerous practical applications of the Meissner effect:

  • Magnetic Levitation (Maglev): In maglev trains, the Meissner effect enables levitation, which reduces friction and increases speed.
  • Magnetic Resonance Imaging (MRI): Provides high-field strength for medical imaging without energy loss, improving diagnostic quality.
  • Particle Accelerators: Uses superconducting magnets to steer and focus high-energy particles for experiments in physics.
  • Superconducting Quantum Interference Devices (SQUIDs): Measures extremely small magnetic fields, which is useful in geophysical surveys and quantum computing.
  • Energy Storage and Transmission: Allows efficient energy storage in superconducting magnetic energy storage (SMES) and reduces transmission losses in superconducting cables.
  • Quantum Computing: Superconductivity and the Meissner effect form the basis for superconducting qubits in quantum computers.

Perfect Diamagnetism vs. Superconductivity

Although superconductors and perfect diamagnets both repel magnetic fields, they operate differently. A perfect diamagnet achieves diamagnetism by rearranging its electrons to counteract external magnetic fields, creating a weak repulsion. Superconductors, on the other hand, maintain superconductivity by forming Cooper pairs and expelling magnetic fields through persistent surface currents. This results in a much stronger and complete repulsion.

Meissner Effect vs. Flux Pinning or Quantum Locking

While the Meissner effect demonstrates magnetic field expulsion, flux pinning or quantum locking is a different phenomenon observed in Type II superconductors. In this case, magnetic flux vortices penetrate the superconductor and form regions where the magnetic field is locked. These vortices “pin” the superconductor in a specific position relative to the magnetic field, allowing for stable levitation at fixed heights or even complex movements along a predefined path. The vortices form where there are imperfections or grain boundaries in the superconductor.

References

  • Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (1957). “Microscopic Theory of Superconductivity”. Physical Review. 106 (1175): 162–164. doi:10.1103/physrev.106.162
  • Callaway, D. J. E. (1990). “On the remarkable structure of the superconducting intermediate state”. Nuclear Physics B. 344 (3): 627–645. doi:10.1016/0550-3213(90)90672-Z
  • Landau, L. D.; Lifschitz, E. M. (1984). Electrodynamics of Continuous Media. Course of Theoretical Physics. Vol. 8 (2nd ed.). Butterworth-Heinemann. ISBN 0-7506-2634-8.
  • Meissner, W.; Ochsenfeld, R. (1933). “Ein neuer Effekt bei Eintritt der Supraleitfähigkeit”. Naturwissenschaften. 21 (44): 787–788. doi:10.1007/BF01504252