Friday, 12 April 2013

Superconductors - Resistance is futile

This post is part of a pub physicists quest to find a new theory for superconductivity. In the previous post I listed some of the well known properties of superconductivity. They are re-listed here;
  • Zero resistance
  • Meissner effect
  • Discontinuity in the Specific heat capacity
  • Type I and Type II behaviour, ideally with some values for the magnetic field strengths
  • The isotope effect
  • The Josephson effect
The most famous of these is probably the Meissner effect, though this is only because of the levitating magnet experiment. For me though the one that really appeals is the zero resistance.

Just think about that, no resistance whatsoever. As mentioned previously, although we can't know for sure that the resistance really is zero, we are fairly confident that it is. All experimentation points to this conclusion.

Now anyone who has done some science at school would have come across Ohms law which can be stated as follows

V = IR or I = V/R

The current (I) passing between two points is directly proportional to the potential difference (V) across the two points. This gives us the resistance (R). All wires have resistance. It is estimated that 6 % of the electricity produced in the USA is lost just transmitting it to the end user.

Imagine if we could transmit electricity with no loss! None, not even a little bit, absolutely no loss. It can be done with superconductors. That's one thing that zero resistance gives us, zero loss. That would be something, because if nothing else it means we could generate electricity anywhere on the planet and move it to the end user anywhere else on the planet without loss.

Anyway, back to it.

Bose with Einstein
One of the great theories of superconductivity, the BCS theory (named after the authors) explains that the electrons in a material pair up, creating Cooper pairs. These are what are known as Bosons. I think this is one of the first great clues, the BCS guys thought this also. Here is why...

The universe can be considered to be made up from two elementary particles, these are your boson and your fermion. Bosons are named after Satyendra Nath Bose. Fermions are named after Enrico Fermi.

The most famous boson is undoubtedly the Higgs boson, which has now taken its place in the Standard Model along with the other four force carrying gauge bosons, the photon, gluon, the W and Z particles.

Here is the thing that makes bosons important to superconductivity. There are other particles besides those just mentioned that are also bosons. Check this out.

Single electrons are NOT bosons 

they are fermions, and behave according to Fermi Dirac statistics (more on this later). They adhere to the Pauli exclusion principle (doesn't that sound cool).

Two electrons can pair up to become a boson

In superconductivity these are known as Cooper pairs. For me this is massive.

In the Standard model fermions are sometimes described as the constituents of matter, while bosons are the force carriers. I can help thinking this is important. If we use this analogy then is it correct to say that a single electron, a constituent of matter, joins up with another electron to create an electron pair that is a boson, a force carrier! We have switched from one type of elementary particle to another.

I'll come back to this in a later post, but I just want to make a note here that an electron pair (bosons - force carrier) can interact with regular electrons (fermions).

OK. So lets take a little look at bosons. They behave according to Bose Einstein statistics, which is a description of how indistinguishable particles may occupy available energy states. Just think of it as how we may stick a load of white tennis balls on shelves.

Back in the day London (we will come to the London penetration depth in a later post) thought that B-E stats may help explain superconductivity. The B - E condensate.

Two bosons with identical properties can be in the same place at the same time (two fermions most certainly cannot). There is NO limit to the number of bosons that can occupy the same quantum state. You can swap two bosons of the same type and the over all system does not alter, we say that the wave function of the system is unchanged. This is like saying you can put an unlimited amount of tennis balls on the one shelf. Can't help thinking I have that wrong.

Another thing I think I may have wrong is this... A photon is a combination of an E field and a B field described by Maxwell's equations. The E and B fields are a 90 degrees to each other and are perpendicular to the direction of motion.

An electron also as an E field and a B field. This time though the E field is perpendicular to the electron and the B field circulates with a standard N/S. Does it really? Going to have to think about this because I think the behaviour of the magnetic field is different in the electron because of gravity/mass, not charge. More on this later.

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I write this listening to Pink, http://www.youtube.com/watch?v=q-XLvUpvjZo. Thanks for that.

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