Tempo di lettura stimato: 8 minuti

You can find the first part here!
You can find the second part here!

Welcome back Billy! Have you fallen asleep serenely after the bedtime story of the last time? I hope so, also because you now need to be full of energy and enthusiasm to face the continuation of our travel through the mysteries and the secrets of superconductivity. The exploration is becoming tougher and tougher, in fact, we need to introduce some more technicalities, but always within a qualitative framework. You already had some hints about the evolution of our dissertation by reading the story. Some names and discoveries were already known, while you heard some others for the first time. Today, we will deepen our knowledge about type II superconductors, that, as you can remember, were introduced for the first time by Alexei Abrikosov. In particular, we will focus on their interaction with the Meissner effect, so that we are closer and closer to our final goal: a true understanding of magnetic levitation and its free-suspension counterpart.

As we already told, any sufficiently big superconductor immersed in a small enough magnetic field will create non-dissipative supercurrents confined in a thin skin on its surface. They induce a magnetic field that counterbalances and cancels out the externally applied field in the material. Therefore, a superconducting sample can expel the external magnetic field to produce a null magnetic flux density in its interior (perfect diamagnetism), provided that the field is kept in a specific range of strength. This behaviour is known as the Meissner effect.
After the bedtime story, Billy, we are now aware that there exist two kinds of superconductors: type I superconductors, endowed with a normal and a superconducting state, and type II superconductors, which comprehend a third intermediate phase, called vortex state. Most pure elements are type I superconductors, while most alloys and all HTS belong to the type II family.
So far, we have always referred to type I superconductors, that exhibit Meissner effect up to a thermodynamic critical field Hc, at which superconductivity is destroyed and the field fully penetrates into the sample. Above this value, the material is in the normal state.
On the contrary, type II superconductors are characterized by two critical surfaces, that share the same critical temperature, but have two different critical fields and critical current densities. In this case, the Meissner effect is only observed for magnetic fields below a lower critical field Hc1 and superconductivity is destroyed for fields above an upper critical field Hc2 (Hc1 < Hc2). For magnetic fields between these two values, the material is not perfectly diamagnetic and it is said to be in a mixed or vortex state. Indeed, the field is allowed to enter the material, not uniformly, but in discrete arrays of entities known as vortices.

Vortices represent the most peculiar objects in superconductivity. The vortex state is denoted also as mixed state because this third intermediate phase consists of the coexistence of both normal and superconducting state. In fact, we can figure out vortices as cylinders made of normal material, immersed in a superconducting ambient, usually displayed in a hexagonal arrangement, known as Abrikosov vortex lattice. In other words, they are normal cores cylinders surrounded by circulating supercurrents. The crossing of Hc1 determines the entrance of the first vortex in the sample, from its sides. The larger the applied magnetic field (still below Hc2), the more vortices enter the material, the more densely packed they are. As mentioned above, they tend to acquire a hexagonal arrangement, so that their reciprocal distance is maximized, due to the repulsive interactions among them.

Then, at the upper threshold between mixed and normal state, vortices are so near to each other that the superconducting space that separates them can be neglected, and the sample is entirely normal. Vortices are discrete entities as a consequence of the fluxoid quantization, but, my dear Billy, this is another story. The most important aspect for us is that they are made of normal material, that means that they are not subject to the two main properties of superconductors: they are provided with a certain resistance and they do allow the penetration of an applied field.

Now, Billy, it’s time to go a step further. Type II superconductors admit two subclasses: reversible and irreversible superconductors.
Reversible superconductors are flawless, homogeneous samples where vortices feel the influence of two competitive forces: the Lorentz-like force and the drag one. The former is due to the fact that an external magnetic field is applied to the material and it tries to remove vortices out of the superconductor, pushing them back towards its sides. The latter derives from the normal nature of vortices. It is possible to prove that for a constant driving current and constant applied field, dissipation is constant and vortices move across the sample at constant speed. Consequently, in light of the first principle of dynamics, in addition to Lorentz-like force, there must be also some other drag force opposing the flow of vortices, that is the cause of power dissipation. Such drag force is a manifestation of resistance. This means that a reversible type II superconductor is globally devoid of the first property typical of superconductors and they behave like normal conductors. Thus, we can say Billy that reversible superconductors are useless.
Now, Billy, you will say: “So much effort for nothing! Everything has been worthless!”, but don’t be demoralized, the best is yet to come. Our secret weapon are irreversible superconductors.
Irreversible superconductors are inhomogeneous materials, that consist of type II superconductors provided with defects, for instance impurities, vacancies and dislocations. Such defects act like pinning centres, that are the origin of irreversibility, indeed. In fact, depending on the entity of the applied field and of the current density, they represent energetically favourable sites for vortices: as soon as a vortex enters the material and meets a pinning centre, it gets trapped in its position. Therefore, every vortex feels the influence of two opposing forces, once again: one is the Lorentz-like force we mentioned before, that tries to remove vortices, the other is the pinning force, that keeps them blocked in a certain place. It is possible to show that power dissipation (then resistance) is mainly due to the movements of vortices. Then, as long as vortices remain fixed, resistance is negligible. We have finally depicted the material we will use for our experiment: magnetic levitation.

We can conclude that pinning is intimately connected to the superconducting behaviour of a material. Dissipation, thus the transition from superconducting to normal state, arises whenever either of these two events takes place: depinning, when a vortex is separated from the defect and becomes able to move, or depairing, when the Cooper pair that constitutes the superelectron breaks, generating two single normal electrons.
Now, only the last piece of the puzzle is missing: the hysteretical behaviour of magnetization in a superconductor. Don’t worry Billy, no one is getting crazy! We have presented all the ingredients we need to finally describe and understand magnetic levitation. We will see how an irreversible type II superconductor, vortices and the Meissner effect interact in order to reproduce one of the most enchanting physical phenomena. In the meantime.. sayonara Billy!

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.