Condensed concepts

Last week in Ljubljana, I had a nice discussion with Denis Arčon about this paper concerning fullerenes, A3C60 where A = alkali metal. Optimized unconventional superconductivity in a molecular Jahn-Teller metal Ruth H. Zadik, Yasuhiro Takabayashi, Gyöngyi Klupp, Ross H. Colman, Alexey Y. Ganin, Anton Potočnik, Peter Jeglič, Denis Arčon, Péter Matus, Katalin Kamarás, Yuichi Kasahara, Yoshihiro Iwasa, Andrew N. Fitch, Yasuo Ohishi, Gaston Garbarino, Kenichi Kato, Matthew J. Rosseinsky and Kosmas Prassides This is a rich system and is summarised in the (temperature vs. volume) phase diagram below. Superconductivity appears in proximity to a Mott (Jahn-Teller) insulator. The JT metal is a bad metal. The novel signature here is that because the electrons are almost localised on individual molecules there is Jahn-Teller effect. This is seen in the Fano line shape of the associated vibrational spectra. Aside: I have often wondered about a good theoretical description of the F

Not all materials are equal. Over the years I have noticed that there are certain materials that are rich, complex, and controversial. Common problems (opportunities) are that it is extremely hard to control their chemical composition , they may have many competing ground states, tendency to inhomogeneity and instability, structural phase transitions, sensitivity to impurities (especially oxygen and water), and surface and bulk properties can be significantly different. One never knows quite which material system is being measured, regardless of what authors and enthusiasts may claim. Consequently, these materials can be an abundant source of spurious experimental results leading to endless debates about their validity and possible exotic theoretical interpretation. Pessimist's view : the material is a minefield for both experimentalists and theorists and with time the "exciting" results will disappear. They are a scientific nightmare. Be skeptical. Avoid. Optimis

A magnetic field can couple to the electrons by two distinct mechanisms: by the Zeeman effect associated with the spin of the electrons and via the orbital motion of the electrons. In the absence of spin-orbit coupling the Zeeman effect is isotropic in the direction of the magnetic field and leads to Paul paramagnetism. The orbital motion, leads to Landau diamagnetism, and free electrons with a parabolic dispersion (and mass m) in three dimensions the magnitude is one-third (and opposite in sign) to that of Pauli susceptibility. What happens for a parabolic band with effective mass m*? The Pauli susceptibility is enhanced by m*/m and the Landau susceptibility is reduced by m/m*. Thus in semiconductors (where m* can be much less than m) the latter can become dominant. In a simple Fermi liquid enhancing the interactions will make the spin susceptibility even more dominant over the orbital susceptibility. What happens in the presence of a band structure? This problem was "

Tomorrow I am giving a seminar on the absence of quantum limits to the shear viscosity in the Theoretical Physics department at the Stefan Institute in Ljubljana, Slovenia. Here is the current version of the  slides . The main results are in  this paper. This is Lake Bled, a popular tourist destination outside the city.

Superconductivity in strongly correlated systems such as cuprates, organic charge transfer salts, and the Hubbard model presents the following interesting puzzle or challenge. On the experimental side the superconducting phase can extend from a region of strong correlation (close proximity to the Mott insulator) to one of weak correlation (a Fermi liquid metal with a small mass enhancement). On the theoretical side, one can obtain the d-wave superconducting state from a weak coupling approach (renormalisation group or random phase approximation) or a strong coupling approach such as an RVB variational wave function. Aside: This also relates to the  challenge/curse of intermediate coupling . Given that in the two extremes the superconducting state emerges as an instability from two very different metallic states, the questions are: What signatures or properties does the superconducting state (or "mechanism") have of these two distinct regimes (strong vs. weak coupling)

Superconducting organic charge transfer salts exhibit many signatures of strong electron correlations: Mott insulator, bad metal, renormalised Fermi liquid, ... Several times recently I have been asked about the Hall coefficient. There really is little experimental data. More is needed. But, here is a sample of the data for the metallic phase. Generally, increasing pressure reduces correlations and moves away from the Mott insulator. Almost all of these materials are at half filling and at high pressures there is well defined Fermi surface, clearly seen in angle dependent magnetoresistance and quantum oscillation experiments. The figure below is taken from this paper . At low temperatures the Hall coefficient is weakly temperature dependent and has a value consistent with the charge carrier density, i.e., what one expects in a Fermi liquid. However, about 30 K, which is roughly the coherence temperature, corresponding to the crossover to a bad metal, R_H decreases significantly, a

The Aspen Center for Physics is a unique and wonderful institution offering relaxed and stimulating workshops in the midst of great scenery. It has been the setting for many famous collaborations and papers. Maybe it is an apocryphal story, but I heard that the theoretical chemists got jealous and so started the Telluride Science Research Center . This (northern) summer I was privileged to spend time at both, and so I offer some friendly comparisons. Both are excellent and so if you have opportunity to attend either, I would encourage you to. Participation.  This is highly selective and mostly restricted to faculty, with a few postdocs. Workshops are small, with typically only about twenty participants. For Telluride you have to be invited and for Aspen you apply and are then selected. Duration. For Telluride most workshops run for 5 days. For Aspen they run for 3-4 weeks and participants must come for a minimum of two weeks. Apparently, in the good old days people used to st

Consider scientific productivity as a problem in economics. One has a limited amount of resources (time, money, energy, political capital) and one wants to maximise the scientific output. Here I want to stress that the real output is scientific understanding . This is not the same as numbers of papers, grants, citations, conferences, newspaper articles, ... The limited amount of resources is relevant at all scales: individual, research group, fields of research, departments, institutions, funding agencies, ... As time passes one needs to face the problem of diminishing returns with increased resources. Consider the following diverse set of situations. Adding extra parameters to a theoretical model. Continuing to work on developing a theory without advances. Calculating higher order corrections to a theory in the hope of getting better agreement with experiment. Applying for an extra grant. Taking on another student. In quantum chemistry using a larger basis set or a h

There is a nice preprint Strong Correlations, Strong Coupling and s-wave Superconductivity in Hole-doped BaFe2As2 Single Crystals  F. Hardy, A. E. Böhmer, L. de' Medici, M. Capone, G. Giovannetti, R. Eder, L. Wang, M. He, T. Wolf, P. Schweiss, R. Heid, A. Herbig, P. Adelmann, R. A. Fisher, C. Meingast The figures below summarise some of the key physics. The top is the phase diagram. The bottom shows the specific heat coefficient gamma as a function of alkali metal content (Cs to Rb to K, and then fractional K content (doping x). Note that a. The black curve shows values calculated from density functional theory (DFT) based calculations. The blue points are experimental data, which are as much as an order of magnitude larger, reflecting strong correlations. b. As one goes K to Rb to Cs the correlations are enhanced, somehow reflecting the "negative pressure" associated with the increasing ion size. c. The experimental trend is captured nicely by calculation

On sunday I went to the Science Street Fair hosted by the Aspen Science Center. It featured booths from a diverse range of organisations, many offering hands on activities for children. I was on the look out for new ideas for demonstrations to do with kids. A new one for my dry ice repertoire is the smoke ring device featured in the video below. There were public performances by Doctor Kaboom and Mr. Freeze from Fermilab . One challenge of such performances is to go beyond "wow" and "gee whiz" to trying to teach something about how science works . Dr. Kaboom tries to do this by testing a hypothesis about why the catapult was invented ( video ). However, I thought it was a little drawn out and was not sure if the point got through. Mr. Freeze has a host of demonstrations based on liquid nitrogen. The one with the exploding cardboard box is pretty cool ( video ). He also has a nice demonstration to show how the volume of a gas is about one thousand ti

I am giving a talk tomorrow at the Superconductivity workshop at the Aspen Center for Physics. Here is the current version of the slides . I will only cover the first half of the slides in the talk. The rest are from a longer version. Often it is claimed that the overdoped cuprates are Fermi liquids. However, work with Jure Kokalj and Nigel Hussey, has shown that a wide range of experimental results can be described in terms of an electronic self energy that includes a marginal Fermi liquid component which has the same angular dependence as the pseudogap, i.e. there are cold spots near the nodes of the superconducting state. What is particularly interesting to me is that this shows that even in the overdoped region one sees precursors of the distinct signatures of the strange metal and the pseudogap regions, that occur at optimal and underdoping, respectively. The talk is largely based on this PRL and this PRB.

The New York Times has an obituary for Ahmed Zewail  who died this week. He received the Nobel Prize in Chemistry for work that used ultrafast lasers to probe the dynamics of chemical reactions and the associated potential energy surfaces. This is all standard today. However, before Zewail, many reaction mechanisms and the associated surfaces were just theoretical constructs and conjectures. I often use the picture below from one of his papers, which I posted about years ago. I also posted about a nice article about the future of chemical physics  and a Nature column about the importance of basic science and how to cultivate it.  His wisdom needs to be heeded. The NYT obituary points out how after the Nobel, Zewail took on an admirable challenge that was greater than anything he had tackled in science: the promotion of scientific research and education in the Arab world, and particularly in his native Egypt. I really hope he will have a significant legacy there. In this vein, M

There is an interesting preprint Broken rotational symmetry on the Fermi surface of a high-Tc superconductor  B. J. Ramshaw, N. Harrison, S. E. Sebastian, S. Ghannadzadeh, K. A. Modic, D. A. Bonn, W. N. Hardy, Ruixing Liang, P. A. Goddard They measure the interlayer magnetoresistance as function of magnetic field direction (see below) and from this deduce that the C4 symmetry of the crystal is broken to C2 in the charge density wave phase that occurs in the pseudogap region. They then compare their experimental results to a calculation that uses a Fermi surface (that is reconstructed due to the CDW), a coherent three-dimensional Fermi surface, and a Boltzmann equation. One might be concerned about the use of a three-dimensional Fermi surface because a. the CDW correlation length between the layers is small b. the interlayer charge transport is not necessarily coherent. However, based on work I did long ago with Perez Moses and Malcolm Kennett [see for example this paper ]

For the next two weeks I am at the Aspen Center for Physics participating in a workshop on Superconductivity. A blog  for the meeting captures its flavour, spanning a diverse range of systems and debates. I was not here for the first two weeks. Here are two related experimental results for the underdoped cuprates that have generated a lot of discussion. 1. A charge density wave (CDW) phase. This has been observed directly with X-rays. The figure below is taken from this paper. 2. A jump in the charge carrier density versus doping. Hall resistance measurements at high magnetic fields imply that for small doping the charge density scales with the doping p [p=0 corresponds to the Mott insulator that occurs at half filling] and at higher dopings, 1+p. This is summarised in the figure below from this paper. A few comments. 1. Is the CDW phase relevant to understanding the pseudogap, superconductivity, and the strange metal phase? There is debate about this. On the one ha

Solid state physicists love model effective Hamiltonians such as Hubbard, Heisenberg, Anderson, and Holstein because they are simple but have rich properties, can explain diverse phenomena, and present a significant intellectual challenge. However, it is worth considering key assumptions. The first is imbedded in the model and the second in approximate solutions. Computational quantum chemistry does raise some questions that physicists rarely seem to think about. They are hard and scary. 1. Rigid orbitals. Each lattice site is associated with some sort of atomic or molecular orbital. A beauty of the models is one does not have to know exactly what this orbital is. Now consider different energy eigenstates of the model. These only differ in orbital occupations and the different coefficients in superposition of Slater determinants (or creation and annihilation operators). The localised orbitals do not change. Similarly, when one changes lattice or vibrational co-ordinates in a Ho