Lorentz force in BCS theory

In summary, the BCS theory is able to derive the London equations and the Meißner-Ochsenfeld effect.
  • #1
tom.stoer
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BCS theory is able to derive the London equations and the Meißner-Ochsenfeld effect.

Experimentally the Meißner-Ochsenfeld effect can be demonstrated via levitating superconducting rings. So we have the usual Lorentz force acting on the Cooper pairs carrying the current. However in order to lift the ring the force has to act on the ring i.e. on the lattice as a whole. But there is no interaction between Cooper pairs and the lattice due to the energy gap seperating the BCS ground state from the 1st excited state.

So my question is how the force can act on the ring w/o having any interaction between the Cooper pairs and the lattice?

Let me speculate that due to the disperison relation of accustic phonons

##\omega(k) = c_S\,k##

there is a coupling of two effective d.o.f., namely the ground state of the Cooper pairs and the lattice, which allows for a collective mode at k=0 w/o energy gap for the phonons. This would correspond to a movement of the lattice as a whole.

EDIT: any ideas regarding this critical paper? http://iopscience.iop.org/1402-4896/85/3/035704/
 
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  • #2
I don't know the precise answer to your question. However, it is well known that the simple BCS treatment isn't precise enough to describe completely the interaction of the cooper pairs and the magnetic field.
There are Goldstone boson like excitations which become massive due to the Anderson-Higgs mechanism.
Nambu has first given a description which is gauge invariant and also contains these long range modes.
 
  • #3
thanks!

DrDu said:
There are Goldstone boson like excitations which become massive due to the Anderson-Higgs mechanism.
Nambu has first given a description which is gauge invariant and also contains these long range modes.
This seems to be exactly what I wanted to indicate by
tom.stoer said:
... there is a coupling of two effective d.o.f., ... which allows for a collective mode at k=0 w/o energy gap for the phonons. This would correspond to a movement of the lattice as a whole.
 
  • #4
I just came back from vacations and found time to look up some reference which I found quite lucid:
Cremer, S., M. Sapir, and D. Lurié. "Collective modes, coupling constants and dynamical-symmetry rearrangement in superconductivity." Il Nuovo Cimento B Series 11 6.2 (1971): 179-205.
It is an easier read than Nambu's original article. I found it quite interesting as it also showed how to treat bound states in QFT, something which is missing in most books on QFT.
The most interesting point in the whole treatment is the following: Why aren't there any Goldstone bosons in the reduced BCS hamiltonian? Because the reduced hamiltonian corresponds to a nonlocal long-range interaction which allows to circumvent the Goldstone theorem!
When treating the full Hamiltonian, there are indeed long range interactions, but the reason that there are also no Goldstone bosons is now the Higgs mechanism!
 
  • #5
I thought a little bit more about your question and I think the collective modes calculated e.g. by Nambu
are not the ones relevant as they are also gapped.
In fact, a careful examination of even the BCS hamiltonian shows that is has some ungapped modes which the following guys call the "thin spectrum":
van Wezel, Jasper, and Jeroen van den Brink. "Spontaneous symmetry breaking and decoherence in superconductors." Physical Review B 77.6 (2008): 064523.
 

1. What is the Lorentz force in BCS theory?

The Lorentz force in BCS theory is a phenomenon where a charged particle experiences a force when placed in a magnetic field. This force is perpendicular to both the magnetic field and the velocity of the particle, and is a result of the interaction between the magnetic field and the electric charge of the particle.

2. How does the Lorentz force affect superconductors in BCS theory?

In superconductors, the Lorentz force causes the electrons to move in circular paths, rather than in a straight line. This circular motion of the electrons helps to maintain the superconducting state, as it counteracts the effects of the impurities and defects in the material that would otherwise disrupt the flow of electrons.

3. Can the Lorentz force be used to explain the Meissner effect in superconductors?

Yes, the Lorentz force is responsible for the Meissner effect in superconductors. When a superconductor is placed in a magnetic field, the circulating electrons create their own magnetic field which cancels out the external magnetic field. This results in the expulsion of the magnetic field from the interior of the superconductor, known as the Meissner effect.

4. Why is the Lorentz force important in BCS theory?

The Lorentz force is important in BCS theory because it helps to explain and predict the behavior of superconductors in the presence of a magnetic field. It also plays a crucial role in maintaining the superconducting state and understanding the properties of superconductors.

5. How does temperature affect the Lorentz force in BCS theory?

As the temperature increases, the strength of the Lorentz force decreases in BCS theory. This is because the superconducting state becomes weaker at higher temperatures, resulting in a weaker counteracting force against the external magnetic field. As a result, the superconductor may lose its ability to expel the magnetic field and transition back to a normal state.

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