# BCS/Cooper Pairing in Electrons during Superconducting

Why do electrons with negative charges pair together during superconducting? Since electrons have negative charges, shouldn't they repel each other instead of pairing up? As far as I understand, during superconducting, the superconductor is cooled down, which deforms the lattice of the superconductor and forms an area of greater positive charge. The electrons then pair together and then pass through the positive area with no resistance. If electrons can pair up, then why does it only occur at low temperatures and not at room temperature, for example?

• The attractive force holding the electrons together in a Cooper pair is very weak; so weak that thermal fluctuations easily disrupt the pairing. At low temperatures these thermal fluctuations are small enough that this disruption doesn't occur. – wgrenard Oct 25 '15 at 6:41
• Your understanding of what creates the attractive force seems off. As an electron travels, it leaves in its wake an area of increased positive charge because the electron attracts the positive ions toward itself. Other electrons are attracted to this positive wake, hence the time dependent attractive force. – DanielSank Oct 25 '15 at 6:54
• Also note that pairing happens in reciprocal space. In the real space electrons in a Cooper pairs are always moving with opposing speeds. – rpsml Oct 27 '15 at 11:25
• Ok thanks guys for your inputs! Understand better now! :-) – Russell Ng Oct 28 '15 at 12:30

Explaining Cooper pairs classically

I have used the following reasoning and modeling to help explain this subject more classically. It may not be totally accurate and some of the assertions made may be unproven, but it works for me.

We know from classical physics, that when a charged particle is in motion, whether its translational motion or rotational motion (spin), a magnetic field is generated that is orthogonally oriented to the motion of said charged particle. The magnetic field generated by the charged particle in motion is stronger and effective at a longer distance that the electric (Coulomb) field of the charged particle itself. We can see this by comparing the magnetic field permeability of free space ($$u_0$$) to the electrical field permittivity of free space ($$e_0$$). $$e_0 = 8.85 x 10^{-12} Coulombs^2/Nm^2$$ $$u_0 = 1.26 x 10^{-6} N/m^2$$

So, the magnetic field is $$10^6$$, or a million times stronger at a distance in free space than the electric field. This is why, at the macro level, electric motors are actually magnetic motors, as strictly electrostatic motors would be too weak to be useful. This is also why, at the nano scale level, the electrons magnetically “pair up” despite the like charge Coulomb repulsion between them. It is an interplay between electrical and magnetic forces; the basis for electromagnetism.

As a side note, I tried to figure out why a charged particle in motion causes a magnetic field and why the magnetic field is so much stronger. It gets into heavily abstract areas of quantum electromagnetic and chromatics and how the charged particle in motion perturbs the quantum vacuum, and Higgs field. I may understand this; some day:)

Electrons "pair up" to at normal temperatures due to the magnetic field of their opposite spins. a +1/2 spin electron is strongly attracted magnetically to an opposite - 1/2 spin electron and they "pair up" almost instantly in the settled quantum orbital shell. This is the reason for chemical reactions and why we always observe hydrogen as $$H_2$$ molecule at standard pressure and temperature and not alone as H atom. Whereas a Helium atom and atoms of other noble gases are loners since they already have all their electrons “paired up”. As electrons "pair up" they drag their corresponding nucleus with them due to the Coulomb force attraction to the nucleus (protons in nucleus positively charged). The magnetic field attraction force between the opposite spin electrons is stronger, and significantly more so, than their coulomb force “like charge” repulsion so they “pair up” to neutralize the magnetic field.

In the case of water, $$H_2O$$, there are 2 un-paired electrons in the outermost shell of the oxygen atom. When we say Hydrogen "chemically reacts" with Oxygen to form water, the electrons in the $$H_2$$ molecule each pair up with the said 2 unpaired electrons of the oxygen atom to achieve a lower overall energy potential and in the process, emitting photons as an exothermic reaction.

All the above scenario is for standard pressure and temperature (STP). The paired electrons still maintain their ½ spin in opposite directions and thus are still fermions. The net magnetic field of the paired electrons is neutralized and effectively zero. The question that comes up is what prevents the electron pair itself from spinning as a unified couplet and generating its own net magnetic field? This is what a Cooper pair would be. The answer is the constant interference and bombardment of photons and neighboring electrons from neighboring atoms and molecules that are in constant motion; vibrating, colliding, bouncing, on each other from their kinetic energies at STP. There is perpetual and un-isolated decoherence happening at the nanoscale level at STP so the couper pairs never have a chance to establish their own spin.

What happens when we reduce the temperature considerably close to absolute zero? Temperature is defined as a measure of the average kinetic energy of the atoms or molecules within a defined volume. The atoms or molecules should have zero translational, rotational, and vibrational motion (kinetic energy) at absolute zero.

In a metal or super-conductor crystal lattice, the atoms or molecules slow down their vibrations considerably. The allows for considerable coherence times where the un-paired electrons in the outermost shell are relatively easily attracted to the un-paired electrons of neighboring atoms. Very little voltage is needed for the electrons to flow from atom to atom as they seek an atom with holes to pair up with. However at very near absolute zero or higher depending on the material, the electrons “pair-up” to form a couplet that also has a magnetic spin as a whole since there is more coherence time to do so. This is a Cooper pair and is no longer a pair of fermions that have matched opposite + and - ½ spins but becomes a boson with its own spin of 0 or 1. These cooper pairs are strongly attracted magnetically to opposite spin cooper pairs and we have a flow of cooper pairs form one atom to another through the lattice with very little or no resistance to current flow.

In fact the increasing coherence times allow the atoms and molecules themselves to exhibit quantum mechanical properties as an aggregate. This constitutes another state of matter known as Bose-Einstein condensate.