Condensed concepts

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 r

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 unive

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.

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

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 den

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

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

The latest issue of APS News has some useful career advice in an article Ten Mistakes for Physicists to Avoid by James D. Patterson.

In the Guardian, Ian Stewart (one of the most successful authors of maths books for the general public) lists his top 10 choices.  It is interesting that number 10 is Newton's Principia!

Solid state physics text books tell us that Matthiessen's rule is obeyed by simple metals: the temperature dependent resistivity is the sum of a temperature independent term due to elastic scattering off impurities and an impurity independent term which is temperature dependent due to inelastic scattering. I teach this to undergrads, but have struggled to actually find experimental data to show them. Yesterday I came across a 1944 paper by Fairbank which contained the figure below for copper with tin impurities: It looks pretty convincing. However, the text points out that the temperature dependence actually varies significantly with the impurity concentration, in violation of Matthiesens rule! Does anyone know of better data? Any simple explanations for these deviations?

I am currently writing a grant application. This is hard going even for old hands. The most irritating bit is all the messing around with formats and fonts. As to text I find the best strategy is like for most writing: just get something (almost anything!) down on paper and then rewrite and polish. This first step is the hardest.

Last week there was an excellent Op-Ed piece in the New York Times, Research Bought, Then Paid For , by Michael Eisen. It is critical of a Bill before the U.S Congress which would stop the current policy of research results from National Institute for Health funded research being available free to the general public. Apparently publisher commercial journals have lobbied for the bill as they see it a way to increase their revenues. The following paragraph is particularly poignant:   the journals receive billions of dollars in subscription payments derived largely from public funds. The value they say they add lies primarily in peer review, the process through which works are assessed for validity and significance before publication. But while the journals manage that process, it is carried out almost entirely by researchers who volunteer their time.  Scientists are expected to participate in peer review as part of their employment, and thus the publicly funded salaries most of them dra

Advocates of the highly speculative notion of "quantum biology" like to invoke the case of superconductivity as a "proof of principle" that macroscopic quantum effects can play a role in biology. In 1994, Phil Anderson wrote a devastating critique of Roger Penrose's book Shadows of the Mind: A search for the missing science of consciousness . Anderson's review was entitled  Shadows of Doubt , and contains the following relevant paragraph: The review is also reprinted in More and Different . The preamble states the Penrose Fallacy: "all problems too difficult to be solved by the great brain of the author must be identical." (p. 186) BTW: a review of the book by David Mermin just appeared in Physics Today.

There is an interesting preprint,  Wigner-Mott scaling of transport near the two-dimensional metal-insulator transition  by M. M. Radonjic, D. Tanaskovic, V. Dobrosavljevic, K. Haule, and G. Kotliar. They argue that the density dependent metal-insulator transition seen in Silicon MOSFETs and other two dimensional electron gases (2DEGs) in semiconductor heterostructures is not driven by disorder  (which has been claimed for many years) but rather by electronic correlations. Furthermore, the relevant experimental data can be described by a Dynamical Mean-Field Theory (DMFT) treatment of the Wigner-Mott transition in an extended Hubbard model on a lattice. This means that the non-monotonic temperature dependence of the resistivity is associated with the crossover from a Fermi liquid at low temperatures to a bad metal at higher temperatures. I think thermopower measurements may be the most effective way to test this claim (see an earlier  post ).

There is a nice preprint,  Thermoelectric Power of the YbT2Zn20 (T = Fe, Ru, Os, Ir, Rh, and Co) Heavy Fermions  by E. D. Mun, S. Jia, S. L. Bud’ko, and P. C. Canfield The figure below shows the temperature dependence of the thermoelectric power for the title compounds. Note that it non-monotonic, being linear at low temperatures, reaching a maximum magnitude of order k_B/e ~ 80 microV/K at a temperature T_min.  The next figure shows that T_min (left scale) is correlated with the single ion Kondo temperature (horizontal scale) and the temperature at which the resistivity is a maximum (right scale).  The magnitude of the linear temperature dependence at low temperatures is simply related to that for the specific heat (see also this earlier post ) as shown in the Figure below. Aside: the inset on the lower right considers the Kadowaki-Woods ratio but does not make use of recent work  concerning its universality. All of the above features seem to be characteristic of broad classes of

I never reported back on how I fared on my New Year's resolution for 2010  (n.b. not 2011): Spend the first half hour of each day thinking and writing in a notebook about the important science questions I am interested in and want to try and answer. And, specifically coming up with   multiple alternative  hypotheses   and devising ways to distinguish them. I tried hard but found this very difficult, more than I thought. The tyranny of the urgent often takes over and makes even carving out half an hour at the beginning of each day difficult. Maybe I have done this on 2-3 days per week (on average) over the past two years. However, the multiple alternative hypothesis bit is extremely hard, much harder than just carving out the time. I am hard pressed to think of a single example where I have successfully done this, to the level of actually being able to rule out one alternative hypothesis. On the other hand, I do feel the struggling process is sharpening my scientific thinking. I

In 2006 Times Higher Education published a nice review by Phil Anderson of Broken Genius: The Rise and Fall of William Shockley, Creator of the Electronic Age . Here are a few extracts:   Shockley called his method of thinking "try simplest cases". But that is really what many good theoretical physicists do when confronted with a complex problem; they try to find a simple model. Only Shockley elevated it to a mantra. He could see his way through the first few stages of any problem very quickly, but he rarely employed his talents to look further below the surface or to check his models against reality. Those who had this ability - for whom Shockley undoubtedly had a good eye - would almost inevitably go off on their own because Shockley could never allow them to follow their own instincts. He saw them as competition and a threat to his authority. I know, because it happened to me in a small way in 1950, and, like others, I survived and may have been the better for it. ....

I am told one of the most common (and least kept) New Year's resolutions is to "tame the bulge", i.e. diet and exercise. That is not my subject. Rather, it is taming the academic bulge of every expanding papers, reports, filing cabinets, books, and book cases. Of course, those who do everything electronic do not have to worry about this. It is all on their laptop or iPad. I am not there yet. How do I cope? Not well, but there is a simple rule I have been following at both home and work the past few years that seems to be helping. Do not buy any new filing cabinets or book cases. Hence, whenever one buys a new book (or two or three) one has to throw out or give away one (or two or three). Similarily, when one wants to force new files into a filing cabinet one is forced to throw away some old ones. It is amazing actually how easy this is.

In a short essay, [reprinted in More and Different ] Phil Anderson cautions about overplaying the role of mathematics in physical sciences. He states three cautions: I. In my experience, interesting and relevant mathematics is more often stimulated by interesting experimental results or questions than vice versa.   II. Interesting mathematical ideas can misdirect you into scientific dead ends - they can become answers in search of a problem.   III. Complicated or lengthy mathematical procedures are very easy to use as a cover-up for shoddy or dishonest science. He gives the following examples: I. random matrices, general relativity, quantum Hall effect, localisation, Kondo effect II. "particle democracy" = "self-consistent dispersion theory"   quantum critical points! III. Attempts of an unnamed "honored professor" [presumably W. Goddard III's] to calculate superconducting high-Tc using computational quantum chemistry. I agree with Anderson&#