Peierls Instability is a one-dimensional feature. Then, it is rarely found in real materials, only in so-called quasi-one-dimensional conductors. 3D version of PI is a charge-density-wave. CDW is found to be adjacent to SC state in some cuprates and organic superconductors. SC state assisted by SDW is a topic of deliberate debates and one of possible mechanisms of non-conventional superconductivity (means non-BCS). All new superconductors including pnictides (but excluding fullerides and MgB2) are non-BCS.

Dear Andrey, thanks a lot for your explanation.I did not see someone like you that pnictides have a non-BCS mechanism. 

Murat,

the reason is electron interection with some other degrees of freedom (in the case of BCS phonons) wich makes electron system not closed and produce it's motion in it's (electron system) ground state. It may lead (as Andrey said) alternativly to SC or some type of Peierls distortion (CDW, SDW and so on).

Peierls distortion may be static or dynamic, depending on it's power.

Regards,

Eugene.

P.S. In the case of molecules this phenomena is called Jhan-Teller effect.

Dear Kislyakov,

thanks a lot for reminding Jahn-Teller effect. According to your contributions, I derived that not only molecular distortions but individual atom distortions in a lattice may lead Superconductivity too.

Best wishes.

Murat

Dear Murat,

atom distortions in a lattice are special cases of Jahn-Teller effect and their dynamical version may be the cause of superconductivity.

Regards.

Eugene.

Dear Sir, let me find an article concerning above mechanism that you mentioned. Some sentences about the driving mechanism (SC) can be crucial.

Best wishes.

Such articles don't exist. Be a pionear, Murat!

Best wishes,

Eugene.

Thank you for encouraging Sir, I am working on it :)

Kindly regards.

I think that the effect Peierls Instability are competing with superconductivity. In many cases, if it is possible to suppress the CDW, the observed superconductivity. In fact, PI related to the resonance between the characteristic vibrations of the electron and phonon systems. Whereas superconductivity is provided by the pairing of electrons. If you suddenly get the resonance, leading to the CDW, the electrons are localized and the pairing between them becomes impossible.

Dr. Titov,

I did not understand your second sentence. 

I think you notice the results of PI.

Thank you for your valuable contribution. Please excuse me for missing the point.

Best wishes. 

Alexander,

all this can be described only takeing into account nonlinearity.

Regards,

Eugene.

Free electron is a wave modulated periodic lattice. Phonon is also a wave, modulated by the same lattice. At the coincidence of their wave vectors inevitable resonance. It leads to an increase of the dielectric constant. In the one-dimensional case, it becomes infinite, two-dimensional increases to a finite value, in three-dimensional increase slightly.

This leads to softnening of lattice and it's instability and causes its reconstruction so that the dielectric constant is not shows discontinuous.

For this it is necessary to exclude the resonance between the free electrons and phonons. And this is possible only through the elimination of free electrons. Therefore, the lattice is rearranged so that at the Fermi level was a gap.

Get a gap at the Fermi level without changing the degree of oxidation possible only by one way. It is necessary that at the Fermi level was the boundary of the Brillouin zone. For this purpose it is necessary to increase the period of the lattice, as in reciprocal space it will cause an increase in the Brillouin zone size.

Actually, this transition is known as Peierls Instability .

Eugene,

resonance is spicifically nonlinear phenomenon.

Alexander,

You correctly described static Peierls (or Jahn-Teller) effect, leading to static lattice distortion. But Murat is interested in dynamic effect, leading to superconductivity.

Regards,

Eugene.

Eugene,

dynamic effect on distortion? Apparently refers to incommensurate CDW? It's the same, only the superstructure period is very large compared with the period of the main lattice. In dozens of times. Then the full period be determined by diffraction is not possible and it is necessary to break into sublattices with parameters measurable.

So great parameter means the weakness of the interactions in such a large scale. This leads to the possibility of charge transfer by this complex periodic structure. This so-called Frohlich conductivity. There really is a strong non-ohmic due to the fact that the period of the CDW is too large to be scattered by phonons. However, today reliably ascertained that the conductivity does not lead to superconductivity.

Where is this ascertained, Alexander?

Thank You in advance,

Eugene.

Dear all,

I am gratefull for your valuable discussion.

I read that Fröhlich and Kun Huang made similar calculations by taking interaction terms into account from different ways. Attached articles prove your sentences in more detail. I tought they will help someone to understand general points of the topic.

They helped me a lot ,thank you.

Regards.

A prototypical system undergoing the Peierls transition is a 1D metal consisting of an equally-spaced chain of atoms (as well as a number of strongly anisotropic quasi-1D materials made of weakly-interacting chains).

When the electron-phonon interaction overwhelms the repulsive electrostatic

term in the system Hamiltonian, such interaction becomes attractive and

an abrupt change in the screening of the ion cores by the surrounding electron gas occurs. This causes a renormalization and softening of the phonon frequencies, with the formation of a CDW  by a charge modulation accompanying a

periodic lattice distortion with identical wave length. This corresponds to the opening of a gap at the Fermi level from the coupling of a 2kF wave-vector with the

underlying lattice.

All of that is well described within the Froehlich model.

This model suggests that there can be states with current flow if the energy gap is displaced with the electrons and remains attached to the Fermi surface. In a tight binding model by Allender et al, if the lattice wave

moves with the electrons with velocity v , the order parameter for the transition becomes v-dependent in the argument of the exponential function. In the Galilean frame in motion with v, the system is again unstable with regard to a distortion which opens an energy gap at the new Fermi surface with the wave vector Q = 2kF . If v is

small, that is, if the electronic translational kinetic energy is small

compared to the Peierls gap  in the static reference frame, the current in the sample becomes J = −nev (extra-current density)

with n=number of electrons per unit volume in the band affected by the

CDW. At low velocities, the energy gap reduces the elastic scattering of individual electrons because there is no state available for relaxing energy: this causes the motion to be with no dissipation, making the compound  superconducting (in principle). Conversely, when this kinetic energy grows greater than the gap, electrons can be scattered back to the next higher band and the current decreases rapidly to zero.

In real systems, translational invariance, which leads to Froehlich superconductivity for ideal pure materials, gets  broken by a variety of 'pinning' phenomena (impurities, lattice

defects, etc.), and prevent superconductivity from

occurring, even though the application

of an electric field of sufficient strength can overcome the pinning of the CDW phase and favor nonlinear collective motion.

A nice review of the topic is the one by Monceau (2012).

Dear Parmentier, thanks a lot for your detailed explanation. I will read it again till I understand exactly.

Can you predict a colleration between the role of gap and the Tc in superconductivity? 

Best wishes.

Hi again,

sorry for replying this late - my accesses to this account are rare.

That's a nontrivial question to answer indeed. CDW and SC are competing ordered ground states and in recent times those experimentally  studying cuprates found that the SCW state could be sorta pre-SC (http://www.nature.com/nphys/journal/v8/n12/full/nphys2456.html). But doubt any reliable theoretical arrangement has been made so far.

For sure the Froehlich model shares similarities with BCS theory (and recently an even more tentative link has been proposed between Josephson tunneling in SC junctions and soliton nucleation and tunneling in CDW materials: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.036404), but the point is that in fact strong pinning phenomena in quasi 1D metals mostly prevent them from experimentally exhibiting collective charge motion.