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Hi, Billy!
Today we explore an exotic area of science, the Bermuda Triangle of Physics: superconductivity.
As soon as I mentioned superconductors, I am sure you thought about Carl Accounts or Jerry Overcooked, but even though I am sure Carl visited Bermuda very often and Jerry loves triangles, maybe with some pickles, this is not the case. I am talking about the phase transition that occurs when certain materials are cooled down below a characteristic critical temperature and an abrupt drop to zero electrical resistance and the expulsion of the magnetic flux density take place. I said superconductivity is an exotic phenomenon because these are its two main properties, but actually, they don’t happen whenever the conditions for superconductivity are satisfied. In fact, there exist different types of superconductivity, each of which is really peculiar. Moreover, this phenomenon is not fully understood yet and an air of mystery surrounds it; there are still details that need further investigation, especially as regards the so-called “High Temperature Superconductors”. Finally, superconductivity is extremely interesting also because it can be studied with different methods, that confirm already known results and give new information, for example the simple electromagnetic approach, the quantistic one, the Ginzburg-Landau theory and the Bardeen-Cooper-Schrieffer formulation. They are different not only in terms of analytical tools, but also they consider various points of view, someones macroscopical, some others microscopical.
An exhaustive explanation of superconductivity would require a quite difficult analytical approach, that exceeds our full comprehension. Since “little but good” is always our motto, Billy, we will rather choose a more qualitative profile, in order to understand its main physical concepts. Our final goal is to depict how two of the most exotic and surprising superconducting phenomena work: magnetic levitation and suspension. Despite the fact that superconductivity might appear as a purely abstract topic, actually some of its effects have a very practical use, for example magnetic levitation is responsible for the Japanese MAGLev trains.

Let’s now describe the main features of superconductivity.
As we already said, superconductivity is an intrinsic property of materials. Some examples of superconducting materials are pure elements like iron, aluminum, lead, mercury, but also some alloys, such as the cuprate YBa2Cu3O7 and Bi2Sr2Ca2Cu3O10. A superconductor does not always exhibit a superconducting behavior, but such a phenomenon manifests itself only under some specific conditions. Firstly, the temperature must be lower than a certain value, typical of each material. The problem is that usually this value is located in the cryogenic range. The critical temperature of the pure elements we mentioned before is about 10 K, which corresponds to -263 °C, quite distant from the temperature of your ordinary domestic freezer, Billy. The cuprate materials, on the contrary, are High Temperature Superconductors, whose critical temperature is about 100 K (-173 °C). This is still far below room temperature, but at the same time much easier to reproduce. In fact, a simple bath of liquid nitrogen ensures a temperature equal to 77 K, that thus enables the phase transition to superconductivity. Then, you can see, Billy, that working with superconductors requires a remarkable technological effort: sometimes, the energy required to guarantee superconductivity is much higher than the one actually generated exploiting its effects, so that costs become larger than advantages. Recent researches are then intended to find out new compositions that act like superconductors with a critical temperature as high as possible.
The other requirements that must be fulfilled in order to give rise to superconductivity concern the entity of the applied magnetic field and of the injected transport current, indispensable ingredients of the phenomenon. There exists a maximum limit for each of them, otherwise the existing conditions of the carriers responsible for superconductivity do not subsist anymore and the sample behaves like a normal conductor. The region in which superconductivity is allowed is represented in the figure below, in yellow.

Indeed, the most important role in this phenomenon is played by some special carriers that we can call superelectrons. Superelectrons are Cooper pairs, that consist of a couple of normal electrons, bounded to each other thanks to some kind of energy. This is one of the highlights of the BCS theory, that we will not explore further. It is sufficient that only one parameter out of the 3 we mentioned above overcomes the corresponding threshold, so that the energy acting on the pairs (thermal or kinetic) is larger than the one that keeps the 2 electrons united and the couples split up. Here, the thermodynamic nature of the phenomenon emerges. The phase transition that takes place once the temperature is below Tc (critical temperature), then, is not abrupt and sudden, but quite gradual. As temperature decreases, more and more normal electrons combine, creating Cooper pairs. In other words, at T=Tc the formation of the first couple occurs and at T=0 K there are no single electrons: the transition to the superconducting state is complete.
Of course, Billy, only superelectrons are endowed with “superproperties”. These are a zero electrical resistance and the expulsion of the magnetic flux density.
Let’s focus on the first peculiarity. The electrical resistance is a measure of the difficulty of an electric current to pass through a conductor. The higher the resistance, the larger the effort, the bigger the loss. In fact, the resistance subtracts useful energy, making the conductance less performant. This lost energy is converted into heat, according to the so called Joule effect. Sometimes, the Joule effect and the resulting heat is the real purpose of a device, like in a hair dryer or a toaster (for Jerry Overcooked’s happiness), but most of the times it is only a side effect that we aim at removing. In our case, we model the resistance on the base of the scattering mechanism, as collisions between electrons and ions that interrupt the continuous flow of current. However, if the frequency of the applied field is such that its period is much shorter than the time between two consecutive collisions, a superelectron rapidly changes its trajectory due to an inversion of the field polarization and the probability to collide against other particles gets smaller. Its mean free path (= the distance covered by the superelectron between two consecutive collisions) becomes ideally infinite and dissipation and resistance are ideally null. In reality, resistance is not perfectly trivial, there is always a little residual component of losses due not only to normal electrons that have not coupled into Cooper pairs yet, but also to the superelectrons themselves, that can be neglected, though. Billy, this characteristic represents a huge advantage in terms of quickness and efficiency. However, superconductors in a normal state have a resistance much higher than natural normal metals. This emphasizes the importance of the cooling system and the field source control, in addition to the composition of the material. Any defects could jeopardize the performance of the sample.

Let’s now pass to the second property. The expulsion of the magnetic flux density is known as Meissner effect. Don’t worry Billy, we will perform an experiment in order to clarify this concept. More specifically, we will compare the results of 2 experiments:
1. Zero Field Cooling: let’s consider a superconducting sphere. Firstly, we reduce the temperature below Tc, then we apply a magnetic field.
2. Field Cooling: the procedure is similar to the previous one, but the chronological order of the sequence is inverted. Firstly, we apply an external field and then we decrease the temperature.

A perfect conductor is a non-superconducting normal material that in a proper spectral range exhibits the lossless condition. In the figure, the circle represents the sphere and the curves the field lines. We can observe that the ZFC operating mode returns exactly the same results both for the normal and the superconducting samples. On the contrary, the FC configuration gives two different outcomes: while the normal conductor admits a finite static magnetic flux inside it, the superconducting sphere repels the field lines. Nevertheless, the penetration of the magnetic field is not completely contrasted, the sphere allows it in a thin superficial layer. The field confined in this coat gives rise to supercurrents, that in turn generate a magnetic field opposite to the external one. The final result consists in a compensation of the two fields inside the sphere, that produces a null total field, ending with the Meissner effect.

Dear Billy, this is only a very general and first smattering of superconductivity. In the next episodes, we will survey the different kinds of superconductors with the corresponding peculiarities and finally the levitation and suspension phenomena, where the Meissner effect plays an essential role.

Next part HERE!

Pubblicato da Giulia Maffeis

Crede che esistano due cose infinite: l'universo e il suo amore per la fisica, ma riguardo la prima nutre ancora dei dubbi.