The Meissner effect is a fundamental phenomenon observed in superconductors when transitioning into their superconducting state below the critical temperature (TC). It describes the expulsion of a magnetic field from the interior of a superconductor.
When a material becomes superconducting, it transitions into a state of perfect diamagnetism, meaning it completely excludes any external magnetic field from penetrating its interior. On the contrary, when a magnetic field is applied to a superconductor above its critical temperature, it penetrates the material.
German physicists Walther Meissner and Robert Ochsenfeld discovered this phenomenon in 1933, and it is considered one of the defining characteristics of superconductivity.
Theory of Meissner Effect
The theoretical explanation for the Meissner effect is based on the London equations developed by brothers Fritz and Heinz London in 1935.
These equations describe the electrodynamics of superconductors and provide a framework for understanding the perfect diamagnetism observed in the Meissner effect.
According to the London equations, the magnetic field inside a superconductor decays exponentially from the surface, with a characteristic length scale known as the London penetration depth.
This decay results from the formation of persistent supercurrent loops within the superconductor, which generate a magnetic field that opposes the applied field, effectively expelling it from the interior.
The Meissner effect is a direct consequence of the thermodynamics of superconductors. When a material transitions into the superconducting state, it undergoes a phase transition accompanied by a decrease in the system’s free energy.
The expulsion of the magnetic field allows the superconductor to minimize its free energy and achieve a more stable thermodynamic state.
How Dose Meissner Effect Works
Above the critical temperature, Tc, a superconductor has no notable effect when a magnetic field is applied, as the magnetic field is able to pass through the superconductor unhindered.
If the superconductor is below its critical temperature, the applied magnetic field is expelled from the inside of the superconductor and bent around it, as seen in Figure.
These magnetic fields are expelled because under the influence of a magnetic field, surface currents that flow without resistance develop to create magnetization within the superconductor.
This magnetization is equal and opposite to the magnetic field, resulting in cancelling out the magnetic field everywhere within the superconductor. This results in the superconductor having a magnetic susceptibility of -1, meaning it exhibits perfect diamagnetism.
While many materials exhibit some small amount of diamagnetism, superconductors are strongly diamagnetic. Since diamagnetics have a magnetization that opposes any applied magnetic field, the superconductor is repelled by the magnetic field.
When a magnet is placed above a superconductor, this repelling force can be stronger than gravity, allowing the magnet to levitate above the superconductor.
This is not an entirely stable configuration, giving the magnet the freedom to spin above the superconductor while it tries to orient its magnetic poles.
If the magnetic field is removed or the superconductor raises above the critical temperature, the surface currents and magnetization disappear, and the magnet will no longer levitate.
Critical Temperature
The critical temperature is the temperature that marks the difference between superconducting and non-superconducting properties within a superconducting material. Above this temperature, the superconductor will behave normally.
In the case of metals, the resistance will decrease with a drop in temperature, similar to non-superconducting metals. When the critical temperature is reached, the resistance suddenly drops to zero, and the material behaves as a superconductor.
This temperature is not constant for all superconductors, but varies depending on the material, with some superconductors have a lower critical temperature than others.
Those with a critical temperature above 30K are called high temperature superconductors, such as Y-Ba-Cu-O with a critical temperature of 90 K.
High temperature superconductors are especially useful due to it being easier to achieve super conductance in these materials because they do not need to be cooled to such low temperatures.
Significance of Meissner Effect
Meissner effect can explain two important magnetic phenomena – magnetic levitation and flux pinning.
Magnetic Levitation
Magnetic levitation, often called Maglev, exploits the Meissner effect to achieve levitation and frictionless motion.
In a Maglev system, the superconducting material is often used to construct the vehicle, while the magnetized track is embedded with powerful magnets.
As the superconducting vehicle passes over the magnetized track, the Meissner effect generates a repulsive force between the superconductor and the magnetic field, causing the vehicle to levitate above the track.
By controlling the magnetic fields along the track and the orientation of the superconductor, the levitating vehicle can be propelled forward, allowing for efficient and frictionless transportation.
Overall, magnetic levitation through the Meissner effect enables the development of high-speed, energy-efficient transportation systems with minimal contact between the vehicle and the track, offering numerous advantages over traditional wheeled transportation methods.
Type I and Type II Superconductors
While superconductors may appear to react the same when in an applied magnetic field, there are differences that separate superconductors into two categories depending on how they react.
For all superconductors, there is a maximum magnetic field, called the critical magnetic field, Bc, that can be applied before the magnetization opposing the magnetic field reaches a maximum and the superconductor reverts to its nonsuperconducting state.
For a Type I superconductor, this direct relationship between the applied magnetic field and the opposing magnetization follows until the critical magnetic field is reached and superconduction no longer occurs.
Read Also: What is Type I and Type II Superconductor?
When this point is reached, the Meissner effect, which would occur within the superconductor up until the critical magnetic field, vanishes, and the magnetic field is able to pass through the superconductor unhindered. The range of the Meissner effect for a Type I superconductor can be seen in Figure .
For Type II superconductors, there is an additional state that occurs between the Meissner state and the normal state. This state, called the mixed state or the vortex state, is noted by the mixing of the normal and Meissner states.
The magnetic field is allowed to pass through the superconductor at specific parts where the normal state is occurring, while the rest of the superconductor exhibits the Meissner effect and expels the magnetic field.
The shift from the Meissner effect to the vortex state occurs at a lower critical magnetic field, Bc1. This vortex state continues to occur to the upper critical magnetic field, Bc2, where the magnetic field becomes too strong for the superconductor to expel and the superconductor allows all magnetic fields to pass through it, returning it to its normal state.
Between these two extremes the vortex state occurs, where small tubular regions develop within the superconductor, inside which the superconductor is in the normal state. The range of states for a Type II superconductor can be seen in Figure.
Through these flux tubes or vortices, the magnetic field is allowed to pass. As with the edge of the superconductor, currents develop on the inside of the flux tubes, preventing the magnetic field from passing into the Meissner state sections of the superconductor. It is within this vortex state that flux pinning occurs.
Flux Pinning
Flux pinning is a phenomenon observed in superconductors where magnetic flux lines become trapped or pinned within the material, even when it transitions into its superconducting state below the critical temperature.
This phenomenon occurs due to imperfections or defects in the superconducting material, such as impurities, dislocations, or grain boundaries.
Meissner effect is typically dominant in pristine, defect-free superconductors. However, if imperfections are present, the Meissner effect can be partially or completely suppressed, allowing magnetic flux lines to penetrate the material.
When magnetic flux lines enter a superconductor, they induce currents called screening currents that circulate the flux lines to shield the interior of the superconductor from the magnetic field.
In the presence of defects, these screening currents can become trapped or pinned, immobilizing the magnetic flux lines within the material.