Meissner effect , also called Meissner-Ochsenfeld effect, consists of the total disappearance of the magnetic field flux inside a superconducting material below its critical temperature. It was discovered by Walter Meissner and Robert Ochsenfeld in 1933 by measuring the flow distribution outside of lead and tin samples cooled below their critical temperature in the presence of a magnetic field.
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- 1 Origin
- 2 The London equation
- 3 The Pippard equation
- 4 The Meissner effect near critical temperature
- 5 Typical values of penetration length
- 6 Sources
Meissner and Ochsenfeld found that the magnetic field completely cancels out inside the superconducting material and that the magnetic field lines are ejected from inside the material, making it behave like a perfect diamagnetic material. The Meissner effect is one of the properties that define superconductivity and its discovery served to deduce that the appearance of superconductivity is a phase transition to a different state.
The expulsion of the magnetic field from the superconducting material enables the formation of curious effects, such as the levitation of a magnet on a superconducting material at low temperature shown in the figure.
The London equation
The first phenomenological theory that explains the Meissner effect is based on the Beaner equation:
where λL depends on the number ns of electrons (per unit volume, that is, density) that are in the superconducting state:
The equation, developed by the brothers Fritz and Heinz London in 1935,1 explains the shape that a magnetic field must have in order for the fundamental conditions given in the Meissner effect to be fulfilled, which are:
- that the magnetic field is null inside the superconductor, 2. that the electric currents are limited to the surface of the superconductor, in a layer with a thickness of the order of what is known as the penetration length? L, being void inside.
The London brothers developed their theory thinking that the charge carriers were electrons, which was found to be wrong several decades later. However, despite this initial mistake, the experimental results were not much affected because the penetration length is essentially the same in both cases:
The first to realize the error was Lars Onsager in 1953 investigating the quantization of the magnetic flux that passes through a superconducting ring: the minimum value of the flux was exactly half what it should be, which is in accordance with a 2e charge. Based on this idea Cooper would expose the idea that the charge carriers are not actually electrons, but pairs of electrons (known as Cooper pairs), as explained in detail in the BCS theory later.
Quantization of the magnetic field in a superconducting ring.
The London equation (1) has several limitations. The main one is that it does not respect the fundamental principle of physics according to which two events far enough from each other cannot interfere with each other. In other words, it is a non-local theory. This is because the two electrons that make up the Cooper pair are relatively far from each other. However, at the time the London brothers could not know this, since they did not even know that it was two electrons together instead of one.
To solve this Brian Pippard presented in 1953 the Pippard equation, which is more general than that of the London brothers, and was corroborated a little later by the BCS theory.
The Meissner effect near critical temperature
Due to the dependence of the penetration length on the electron density in the superconducting state, it is easy to see that the closer the sample temperature approaches the critical temperature, the fewer electrons there will be in the superconducting state and therefore the magnetic field It will penetrate more and more into the superconductor. When the superconductor reaches the critical temperature, the penetration length tends to infinity, which means that the magnetic field can penetrate the sample without opposition, that is, the Meissner effect disappears.
Historically, it was difficult to understand why the penetration length increased with temperature, since it was not known until later that electrons in a superconducting state (that is, those that are two by two forming Cooper pairs) coexist with electrons in normal state (that is, unpaired), and that the density of electrons in one state or another depends on temperature.
Typical values of penetration length
Taking into account the definition given above, taking the values corresponding to the constants and giving the electron density in the superconducting state ns a typical value of about 1023 electrons per cm3 (which will be lower as the temperature approaches the critical ) a penetration length LL ~ 1700 Å is obtained, which corresponds to a penetration between hundreds and thousands of atomic layers, which corresponds quite well with the experimental values.