Fermi Surface Nesting: Explained

[nbo10]

What is fermi surface nesting? I don't have a hard reference, but I've heard this term thrown around quite a bit lately when talking about SDW, CDW, and SC.

 

[ZapperZ]

What is fermi surface nesting? I don't have a hard reference, but I've heard this term thrown around quite a bit lately when talking about SDW, CDW, and SC.

Fermi surface nesting is large segments of a Fermi surface that can be connected to another large segment of another Fermi surface via the reciprocal lattice vector. Because of this, these Fermi surface segments tend to be straight "lines".

Zz.

 

[sam_bell]

Can anyone elaborate on the connection between fermi surface nesting and SDW, CDW, etc. ? This has me kind-of puzzled too.

 

[M@2]

Can anyone elaborate on the connection between fermi surface nesting and SDW, CDW, etc. ? This has me kind-of puzzled too.

Fermi surface nesting and SDW, CDW interests physisists mainly of existence of phase transition to gap state in some direction.

Till now mainly plain waves are researched (CDW, SDW, PHONON). If the amplitude of wave is greate and wave connect electron orbitals at Fermi level, than electron levels repel each other and there must be energy gap. It is energetically favorable when such pairs of electron levels would be in greate number. For plane waves it means that it is desireable to have opposite parts of Fermi surface be parallel.

It is not obligatory to use plane waves to get phase transition and gap in electron spectrum. We can use wave packet of plane waves to adjust to unparallel parts of Fermi surface.

Such methods are well known in open resonators (lasers) to give multimode regimes. The same methods can be used in metal physics for SDW, CDW, phonon waves...

If the fermi surface is well adjusted to wave packet (SDW, CDW,...), than we can get phase transition in metal.

See for example:
http://www.pi1.uni-stuttgart.de/glossar/SDW_e.php

A typical example of a one-dimensional metal which undergoes a SDW transition is the Bechgaard salt (TMTSF)2PF6.

 

[genneth]

Generally, the Fermi liquid is very unstable because it has such a large density of states near the Fermi level --- it is usually energetically favourable to open up a gap, so that you end up putting some electrons into lower energy states. Nested Fermi surfaces are extra unstable because many interactions in a lattice can make a electron pick up a "free" momentum transfer equal to the reciprocal lattice vector; if so, you end up with a degenerate perturbation situation where all points on the Fermi surface pick up "partners" from this momentum transfer, and degenerate perturbation theory gives a linear change, so you inevitably open up a gap, which is energy collectively favourable! States which can arise this way are things like CDW or SDW states, and because of the above two reasons, tend to be very stable and thus easily seen experimentally.

 

[vkroom]

Generally, the Fermi liquid is very unstable because it has such a large density of states near the Fermi level.

Are you sure? Fermi liquid theory works so well because of its stability to perturbations. For generic momenta even four fermion interactions are irrelevant. Only the Cooper channel makes four fermion interactions marginal and hence we get superconductors. This is one of the very few instabilities of a Fermi liquid.

Nesting is another such instability. Density waves result from effective period doubling of the crystal lattice, which is a response of the Fermi liquid to avert the nesting instability.

Regarding references for CDW/SDW Wikipedia lists good references. I would recommend Gruner's articles.

 

[genneth]

Are you sure? Fermi liquid theory works so well because of its stability to perturbations. For generic momenta even four fermion interactions are irrelevant. Only the Cooper channel makes four fermion interactions marginal and hence we get superconductors. This is one of the very few instabilities of a Fermi liquid.

Nesting is another such instability. Density waves result from effective period doubling of the crystal lattice, which is a response of the Fermi liquid to avert the nesting instability.

From an RG point of view, the state has a lot of potential marginal instabilities --- which are the ones that really give rise to a phase transition since you have a good chance of hitting "infinite" coupling with only finite renormalisation.

My statement about unstable is purely with respect to energetics --- you can get a lot of energy out by making a gap. Remember that actually opening a gap is quite frequent --- Pierls instability, superconductivity, density waves, J-T distortions, quantum hall states, Mott-ness related transitions, etc.. Even a bit of weak disorder is enough (though admitted that only depresses the DoS, but the point stands).

From that point of view, it's actually surprising that the FL is stable at all, which is of course your point --- but I think the OP might have benefited from understanding that there's a lot of "room for improvement" in the FL state.

At a more technical level, it's not quite true that the "only" marginal instabilities are the ones you mentioned. Those are the ones we know! There is a vast sea of possibilities to do with moving the Fermi surface. People usually skate over it, but Fermi surface movement is a marginal perturbation (or worse, i.e. more relevant). However, practical calculations on this matter are *very* hard, and so we usually look at more symmetric states, i.e. circular/spherical Fermi surfaces or simply nested ones. The feeling I get from the gurus on this matter seems to be that serious work involving hard maths (algebraic geometry and the like) would be needed to start making dents on this issue...

 

[vkroom]

The feeling I get from the gurus on this matter seems to be that serious work involving hard maths (algebraic geometry and the like) would be needed to start making dents on this issue...

I've been thinking on similar lines for sometime. I was trying to use some differential geometric ideas to construct local field theories. Do you think there's some reference out there that I may be able to look into regarding these matters or, would it be possible to mention some people who are worrying about these issues?

Coming to the point regarding the Fermi surface deformations. Isn't there a Quantum Boltzmann equation formalism which deals with these kinds of hydrodynamic / sound modes of the Fermi surface?

Also in the RG sense given a Fermi surface without nesting, I thought that there are very few marginal perturbations as outlined in the papers of Shankar and Polchinski. Are you suggesting something more that I'm unaware of?