Strange Peculiar Effects Occur at Low Temperatures, Levitation Manifested by Magnetic Fields and Superfluids.

Image Credit:-wikimedia

Introduction

When we start to cool atoms to very low temperatures close to absolute zero, we start to see some weird things occur. In fact a lot of these peculiar phenomena are leading to very practical uses. When gases are cooled we observe Bose-Einstein condensates where all the atoms are in the same quantum macroscopic state. Helium-4 exhibits superfluidity when cooled below a critical temperature, here the fluid can flow without any resistance but has a maximum speed it can flow without destroying the superfluid. When some solids are cooled to critical temperatures we see superconductive behaviour, where electric can flow without any resistance and energy loss. Also these have an expulsion of the magnetic flux outside the material which leads to levitation effects with external magnetic fields; this is called the Meissener effect.

I've written an article about the Bose-Einstein Condensate (BEC) which you can read HERE. I plan to write an article about Super conductivity in the future so watch out for that, I will explain some basic theory for now.

This article will focus largely on the Superfluidity in Helium-4 and the Meissner effect in Superconductors.

Superfluidity

Image Credit:-wikimedia

There is superfluid Helium-4 in the cup, it climbs up the sides and drops down. It will continue to do this as long as Helium remains in the superfluid phase, and empty the cup.

A superfluid is related the BEC, it is also a condensate which means a number of particles exist in the same quantum state (described by the same equation). Helium-4 can do this because it is a Boson, only particles that are Bosons can exist in the same Quantum state. The opposite of a boson is a fermion, which has a half-spin and two electrons cannot exist in the same energetic state. If you want to know more about particles you can check out some of @lemouths articles.

The critical temperature that Helium-4 reaches the S.F phase is about 4 degrees Kelvin. You maybe asking the question why doesn't the Helium turn to solid when cooled to below the critical temperature (Tc) like usual liquids. Well the low mass of the Helium atoms leads to large zero-point energies which overcomes the tendency to crystallise into a solid. The superfluid has some remarkable properties, it can flow through narrow channels with zero shear-viscosity, and without any friction at all or loss in energy. It's similar behaviour to superconductivity, in some respects a superconductor has a superfluid flow of electrons. Another interesting feature is the existence of quantized vortices in the SF, the vortices have energy which take specific quantised energies depending on atomic mass.

Physicist Lev Landau made extensive research in this area and developed most of today's SF-dynamics. He devised a two fluid description of the hydrodynamics, there is the normal fluid part and a super fluid part. There two components of the overall fluid are interpenetrating and the densities depend heavily on the temperature. The density of the normal component vanishes at very low temperatures, while the superfluid density approaches the total density of the fluid. As a result the SF density is different from the density of particles in the condensate, for Helium-4 it's only about 10 % or of the total number of particles. However at the transition temperature associated to the normal state, the situation is opposite such that the SF density goes to zero as the temperature nears the lambda point, but the normal density approaches the density of the fluid.

The physical properties of the normal component is related to elementary excitations of the superfluid, which are at the heart of the SF quantum description. The excitations associated to superfluidity are low energy and low momentum, the Helium-4 particles have energy and momentum related to quantum state. The small energy excitations are called phonons which are vibrational in nature and manifest as sounds waves in the fluid.

Image Credit:- Extracted from University Notes

At very low momentum and energy these two quantities are related by the linear equation:

where e is energy, p is momentum and s is the speed of sound. This equation describes the linear behaviour and gradient you see at low momentum on the graph. The gradient is the speed of sound in the fluid.

You can see as the momentum is increased the linear behaviour changes into quadratic behaviour with a minimum and a maximum, which is described by the equation:

where m∗ is the mass, p0 is the momentum at the minimum, and Δ is called the energy gap. Excitations around the minimum close to p0 are the rotons, which are considered to be short wavelength phonon excitations, it's these excitations that lead to the SF behaviour. The theory states for an excitation to occur that leads to the rotons the SF must flow with velocity faster than E(p)/p (energy over momentum), but will not flow faster than it's critical velocity which is actually the speed of sounds in the fluid (the gradient of the graph).

Even after years of research in this field a full understanding is not complete, there is a lot of theory believe me, this is just the tip of the iceberg, but I thought you might appreciate some more in-depth physics this time. It is not easy to understand the physics of what process occur in quantum systems, so I don't except people to fully comprehend and it's also a "basic" explanation; if you are interested in reading further please see the book:

Quantum Theory of Many-Particle Systems by Alexander Fettah.

As you have seen, the SF occurs at very low temperatures, we are nowhere near producing high-temperature superfluids, there is more effort going into high-temperature superconductors. There seems to be more attractive uses for superconductors than superfluids, super conductors can transport electric without losing energy. Superfluids carry to fluid without losing energy due to friction, it has a zero viscosity so can be used as a lubricant reducing energy loss through friction. This is attractive to some areas, but the there seems to be more concern about producing high-temp super conductors due to it's technological benefits. Who knows some scientists could discover amazing benefits of superfluids.....

Meissner Effect

Image Credit:-wikimedia

Here you can see the magnetic field flux lines through some object. Above the critical temperature on the left, the field flux behaves normally and penetrates the material. However when cooled below it's crtical temperature (Tc) it expels the magnetic field outside the object, so no magnetic field flux exists inside the body. This is an illustration of the Meissner effect.

As we are starting to discover, some weird stuff happens to some materials when we start to cool them, the Meissner effect is just another example. When a superconductor is in an external magnetic field and then cooled to it's critical temperature, the material cancels all of it's interior magnetic field. A super conductor will conserve it magnetic field flux, so when the interior field is decreased the external field must increase, and this is what we see in the Meissner effect. When a superconductor has a negligible magnetic field it is in the Meissner state, which is destroyed when a large external magnetic field is applied.

The breaking down of the Meissner state lead to the description of two different types of superconductors; type-I and type-II. For a type-I superconductor, the superconductive properties are quickly destroyed when an external magetic field is larger than a critical value. A type-II superconductor has two critical values of applied external magnetic fields, at the first critical value there is penetration of the magnetic field into the material but still has zero resitance to electric flow, at the second critical value the superconductor is destroyed.

When the applied external field is weak the superconductor expels the mag-field, it does this by producing electrical currents near the surface that have a vortex-like nature. These currents at the surface produce a magnetic field that opposes the applied field inside the superconductor and they cancel, due to the conservation of magnetic flux the field exits nearly entirely outside the material. There is a small depth as to which the field can penetrate the material depending on the physical characteristics or it.

This behaviour of having a zero magnetic field in the material leads it to be superdiamagnetic. This means it has a magnetic susceptibility very close to -1, which means it can easily generate magnetisation in the atoms which opposes external fields. This is not to be confused with diamagnetic behaviour in normal material where the electron spin is modified by external fields, here the opposing field is generated by the vortex surface current.

Image Credit:-wikimedia

A magnet levitating above a cooled superconductor, showing the Meissner effect.

Practical uses of the Meissener effect are not vast, but it's still not fully understood. Theory of superconductors and condensates are one of the same and progress must be made to have a fully functioning complete mathematical description. But believe me when I say, when this physics is fully understood technology will take leaps and bounds and we will quickly find ourselves in a new tech-era.

What is interesting and pretty cool with the Meissner effect is it's ability to "levitate" the superconductor with an external magnetic field, this works both ways above and below the magnets. A cool video you must watch can be seen HERE on youtube, it's the levitation of a SC on a mobius strip (infinity sign). An interesting point to make is the motion you see can theoretically continue forever if there was no air resistance and the superconductor keeps it's properties. Also what ever orientation you place the superconductor in the magnetic field it will remain locked to this orientation due to the conservation of magnetic flux.

Conlusion

Low temperature physics is a world of wonders, it's one of the most researched topics mainly looking for the holy grail of superconductivity at room temperature. We see weird and wonderful effects occur as a result of cooling atoms to their lowest states. Bosonic Helium-4 becomes superfluid at about 4 Kelvin and can climb walls defying gravity, it has many similarities to how electrons flow in superconductors. Uses for superfluidity are not in great demand, maybe because we don't fully understand, but research is helping to develop theories for superconductors. When superconductor reach their critical temperature, they is an abrupt expulsion of the magnetic field outside the conductor. Vortex-like electric currents are produced near the surface which act to cancel the external field that penetrates the material, the result is a zero mag-field inside the conductor. As the flux decreases inside in increase outside, as a result of conservation of magnetic flux.

I hope you liked the information in this article today, it's hard to explain in an easy way trying to include key physical points, but I hope i did it justice. If you have any comments please leave them, i love feedback and want to see what others think. Until next time.....

@physics.benjamin

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References:

Meissner Effect
Superfluids
Superconductors
Lev Landau

Books:

Quantum Theory of Many-Particle Systems by Alexander Fettah
Bose-Einsein Condensation by Lev Pitaeveskii

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