Can strongly correlated electrons save the planet II?

Several earlier posts discussed the thermoelectric effect in strongly correlated electron materials. The Seebeck coefficient S is a quantitative measure of the effect. At low temperatures it can be orders of magnitude larger than in elemental metals. 

The figure above illustrates how thermoelectric couples can be used to either perform refrigeration or generate electrical power from waste heat. It is taken from a nice Perspective in Science Smaller is Cooler by Brian Sales which reviews state of the art materials in 2002.

The thermoelectric figure of merit, ZT is a dimensionless ratio which is a good measure of how useful a material will be in thermoelectric applications.

sigma is the conductivity and kappa the thermal conductivity.

Currently used materials such as Bi2Te3 [also a topological insulator!] have values of ZT ~1. If materials can be found with ZT~4 then thermoelectric refrigerators will be competitive with traditional compressor refrigerators, which are less reliable and environmentally dirtier.

So how good are strongly correlated electron materials?

There is a nice review by Paschen on heavy fermions.

It is important to note that the thermal conductivity is the sum of electronic and phonon contributions. If one neglects the latter (for the moment) and uses the Wiedemann-Franz ratio then ZT ~ S^2 where S is in units of k_B/e. This is indeed its magnitude near the coherence temperature in strongly correlated electron materials. Hence, ZT ~ 1 (but not larger) seems possible.

BUT, this argument neglects the thermal conductivity due to phonons which is much larger that the electronic contribution in this temperature regime. So one needs to find a way to reduce this. This leads to the idea of a Phonon Glass Electron Crystal.

Candidate strongly correlated materials may be skutterudites which exhibit heavy fermion behaviour (e.g. SmPt4Ge12).

Giving up on theoretical physics?

No I am not! But it seems some of our colleagues are.

Alan Lightman has a rather disappointing article The accidental universe: science's crisis of faith in the last issue of Harper's from 2011.

[It was reprinted this week as the lead article in a weekly section of the Australian Financial Review, Review: Your Guide to the world of issues, ideas, and opinion. I thank an economist friend from church for bringing it to my attention, ``Is this really what you theoretical physicists believe?"]

Here are a few choice from Lightman's article quotes I found debatable:

Dramatic developments in cosmological findings and thought have led some of the world’s premier physicists to propose that our universe is only one of an enormous number of universes with wildly varying properties, and that some of the most basic features of our particular universe are indeed mere accidents—a random throw of the cosmic dice. In which case, there is no hope of ever explaining our universe’s features in terms of fundamental causes and principles...
Theoretical physics is the deepest and purest branch of science. It is the outpost of science closest to philosophy, and religion....  

Theoretical physicists are Platonists. Until the past few years, they agreed that the entire universe, the one universe, is generated from a few mathematical truths and principles of symmetry, perhaps throwing in a handful of parameters like the mass of the electron. It seemed that we were closing in on a vision of our universe in which everything could be calculated, predicted, and understood.... 

We are living in a universe uncalculable by science.... 

The most striking example of fine-tuning, and one that practically demands the multiverse to explain it, is the unexpected detection of what scientists call dark energy.

Perhaps rather than giving up on theoretical physics better options may be to

• give up on Platonism, 
• give up on reductionism, 
• give up on unbridled philosophical speculation
• be a little humbler and be open to the idea that there may be some new physics to be discovered in the particle physics Desert which covers 12 orders of magnitude in energy!

Low Tc but strong Cooper pair binding

The plot below is an important one which I have been meaning to blog about for a while. It shows the strength of the diamagnetic signal [increasing from blue to purple to red]

from an underdoped cuprate superconductor as a function of magnetic field H and temperature T.

The figure is taken from a paper from Ong's group, discussed in an earlier post.
The superconducting transition temperature Tc is 12 K.  However, a magnetic field of about 45 tesla is required to destroy the diamagnetic signal which is associated with Cooper pairing. Furthermore, this "upper critical field" H_c2 is weakly temperature dependent. This large field scale reflects the large binding energy of the Cooper pairs. This can be seen by converting H_c2 to a coherence length (~30 A) and then an energy gap (~20 meV ~ 200 K) via a Pippard type formula [see this earlier Science paper by Ong et al.].  The energy gap is comparable to the pseudogap seen in ARPES and much smaller than k_B Tc.

I cannot get excited about atomic BEC's

There is an interesting article Ultracold Bose gases deviate from the textbook picture in the Search and Discovery section of the July 2011 Physics Today. [My issue just arrived by snail mail today!].
It discusses how recent experiments have quantified deviations from the non-interacting boson theory of Einstein, which is taught to undergraduates.
It seems that these deviations can be described by Hartree-Fock theory. One might argue Hartree-Fock is also rather "text book".

For all the hype, somehow I cannot get excited about atomic BECs. To me, there seems a distinct contrast to solid state systems such as strongly correlated electron materials which exhibit properties (high-Tc superconductivity, spin liquids, heavy fermions, pseudogap, non-Fermi liquid metals,...) which are such a long way from anything remotely "text book"-ish and whose explanation requires the development of new physical concepts, approximation schemes, and numerical methods.

But, perhaps I am missing something.

Probing fluctuating superconductivity

An important paper for understanding the pseudogap state of the cuprates is Diamagnetism and Cooper pairing above Tc in cuprates by Lu Li, Yayu Wang, Seiki Komiya, Shimpei Ono, Yoichi Ando, G. D. Gu, and N. P. Ong.
Physics has a helpful commentary by Kivelson and Fradkin.

Diamagnetic response of the superconducting state is orders of magnitude larger than other states of matter. [Due to the Meissner effect superconductors are sometimes said to be perfect diamagnets]. A state with no long range superconducting order but large fluctuations can produce a significant diamagnetic response. The authors find that for a wide range of underdoped cuprates that there is significant diamagnetism for a wide temperature regime above Tc. Moreover, this signal co-exists with a large Nernst signal.

This is important because it tends to rule out a proposed alternative explanation for the large Nernst signal that it could be produced by quasi-particles in small hole pockets associated with a density wave state.

A key signature of superconducting fluctuations is a non-linear dependence of the magnetisation on the magnitude of the magnetic field. For small fields it must be linear in field, but there must be some field scale, of the order of the upper critical mean-field H_c2 above which there is no diamagnetic response. This means there is some field scale H_min at which the magnetisation is a minimum. The non-linearity of the field dependence is seen in the Figure below. (The different curves correspond to different temperatures).

The Nernst signal shows a similar non-linear field dependence (see this PRB). The authors argue that if it is due to quasi-particles it should be linear in field up to a much higher field scale, e.g. comparable to the band width.

Aside: Are there any measurements of non-linear diamagnetism on organic charge transfer salts?

Strongly correlated electron systems in high magnetic fields III

Metamagnetism occurs when the magnetic susceptibility increases with increasing magnetic field. This generally does not occur in weakly interacting systems. For example, if the susceptibility is enhanced by magnetic fluctuations, these are generally decreased by a magnetic field. However, DMFT calculations show this can occur for intermediate coupling. This is discussed in detail in the following paper:

Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behavior by J. Bauer

In a Fermi liquid picture the susceptibility can either increase due to an increase in the effective mass or increase due to the quasi-particle interaction F0a (the Landau Fermi liquid parameter which determines the Sommerfeld-Wilson ratio).

Possibly the most promising candidate material for some of this physics is CeRu2Si2. The susceptibility increasses by a factor of more than 8, whereas the specific heat coefficient gamma only increases by a factor of 1.6.

Other candidate heavy fermion materials include YbT₂Zn₂₀ (T : Co, Rh, Ir) which is the same family described in an earlier post because it has particularly interesting thermopower.

Do conical intersections really matter?

Conical intersections [where the potential energy surfaces of two electronic states touch] are ubiquitous in photochemistry. Their most important role is that they can explain why some photochemical reactions proceed so fast (i.e, on the scale of 10's of femtoseconds). However, an important outstanding question is:

Does the Berry's phase [geometric phase] associated with the conical intersection [CI] have important observable consequences?

There is a nice 2005 Perspective in Science by David Clary which discusses this for the specific case of the simplest possible chemical reaction  H2 + H to H + H2. It seems that [contrary to what was claimed in the 90's] molecular scattering experiments associated with the ground state surface below are not sensitive to the geometric phase due to cancellations of terms associated with different angular momentum channels. However, showing this cancellation is rather subtle!

Aside 1 : the CI here arises due to the degeneracy of the E irreducible representation associated with the C_3 symmetry of the transition state which occurs when the three H atoms form an equilateral triangle.

Aside 2: For more background see the nice Physics Today article by Berry, Anticipations of the Geometric Phase.

I thank Seth Olsen and Ben Powell for discussions stimulating this post.