Condensed concepts

A nagging question for the whole field of (classical) molecular dynamics simulations of biomolecules is whether they can have an adequate description of water. This is particularly important because almost all biomolecular processes involve subtle interactions of the biomolecule of interest with its aqueous environment. I learnt a lot from reading the article  On the origin of the redshift of the OH stretch in Ice Ih: evidence from the momentum distribution of the protons and the infrared spectral density , by C. J. Burnham, G. F. Reiter, J. Mayers, T. Abdul-Redah, H. Reichert and H. Dosch. They highlight several problems and state: Clearly there is something missing from water models. All of the above difficulties have been consistently tackled by experimentalists, but they remain either unrecognized or unacknowledged by much of the simulation community. Here are the 4 main difficulties they list concerning the differences between the properties of a water monomer and the water m

All the media attention to recent anomalies in the speeds of neutrinos raises some interesting scientific and sociological questions. Should you go to the media before you have results published in a peer reviewed journal? A few things to bear in mind. These deviations from the speed of light are one part in 100 thousand. They require measuring the distance travelled to the same precision, i.e. an accuracy of 20 cm! Relative measurements rather than absolute measurements are usually more reliable. As the Nature News (n.b. not paper) article said Most troubling for OPERA is a separate analysis of a pulse of neutrinos from a nearby supernova known as 1987a. If the speeds seen by OPERA were achievable by all neutrinos, then the pulse from the supernova would have shown up years earlier than the exploding star's flash of light; instead, they arrived within hours of each other. An earlier anomaly in neutrino physics was of the 17 keV neutrino that was "discovered" in 19

Journal of Physical Chemistry Letters has a paper  Origin of the Pseudogap in High-Temperature Cuprate Superconductors  by  Jamil Tahir-Kheli   and William A. Goddard, III I can't say I really follow the details here. The doping dependence of the pseudogap they calculate seems to be a percolation effect. A key issue is whether they can produce the anisotropy in the pseudogap in momentum space. It is not clear they do since everything seems to be done in real space. There is some interesting history here, going back to the early days of high-Tc. Sparks fly over conflicting theories  from Chemical and Engineering News in 1988, discusses conflict between Phil Anderson and Goddard. A clash erupts between scientific subculture  is a  New York Times article from 1989 which  quotes a Dr. Anderson who is presumably Phil Anderson. I thank Seth Olsen for bringing some of these articles to my attention.

Stephen Bartlett gave a colloquium on this topic today. The ground states of quantum antiferromagnets contain substantial amounts of entanglement (although how much is hard to quantify). Hence, one might hope they are a resource that might be used in quantum computation. Stephen described some recent work [see this PRL  and this PRL  ] which considers how this might be done. The focus seems to be on gapped systems which have hidden symmetries and can be described as tensor network states. The prime example is the Haldane spin-1 antiferromagnetic Heisenberg chain which is adiabatically connected to the AKLT model. I was reminded of some work I was involved in a few years ago (described in this PRL ) which showed how one could take any spin singlet state  [not just the ground state!] from a spin-1/2 chain and perform projective Bell measurements (on pairs of spins) along the chain and teleport quantum states with perfect fidelity along the chain. I was wondering what the relationship

There is an Editorial Theoretical Chemistry - Quo Vadis? by Walter Thiel in Angewandte Chemie International Edition. ["Quo Vadis" is latin for "where are you going?"] It is worth reading. It is particularly good that he offers some concrete precautions for experimentalists running computational codes. I thought the following characterisation of theoretical chemistry was disappointingly narrow: Theoreticians are primarily interested in testing the performance and limitations of newly developed computational methods, for example by systematic validation on established benchmarks or through proof-of-principle calculations.  Overall I prefer the articles I highlighted in 5 papers every computational chemistry student should read , together with Hoffmann's 1974 article on theory in chemistry  and Zewail's article on the future of chemical physics . Those articles place a much greater emphasis on theory providing unifying concepts. I thank Seth Olsen for

Most applications for scholarships or admission to graduate school require a personal statement. I found a very useful site at Penn State, Writing Personal Statements online . I read the two sample statements  from applicants for a Marshall Scholarship. Both were very impressive. They illustrate several key ingredients Distinctly personal. It is about you. Only you could write this. Avoid generics "I am really interested in subject X and want to study at University Y because it is a world class university." Personally engaging. A natural outcome is that the reader should want to meet you. Specific connection between applicant and the target institution/program. Mentioning specific courses, faculty, and research projects is key. Polished and well written. This means writing and rewriting and getting feedback on drafts. For those of us reading and reviewing applications I see two important consequences of this material being freely available. First, the bar is higher.

When trying to understand complex molecular materials, the dominant approach in chemistry to is to do DFT-based calculations for the system of interest. However, a case needs to be made for an alternative "physics" approach. Recent Anthony Jacko, Ben Powell and I wrote an article Models of organometallic complexes which makes the case below for effective Hamiltonians. Another approach to modeling the optoelectronic properties of organometallic complexes is to  construct  a model with fewer states but an accurate treatment of the electronic correlations. This contrasts with first principles calculations, which include several basis states for each atom but neglect some electronic correlations. The small number of degrees of freedom in such semi-empirical models allows one to make fewer approximations on the interactions and correlations in the model. It also allows one to identify key trends that describe broad classes of materials. This approach has proven itself incredibl

An important finding of recent cluster DMFT studies  concerns the nature of the metallic state in the Hubbard model at half filling. Near the Mott transition it is found that the scattering rate is  anisotropic over the Fermi surface (a Fermi liquid with momentum space differentiation) just as it is in the doped Hubbard model. Emanuel Gull showed a general phase diagram (U/t vs. doping) in his talk at the Ringberg meeting. (I could not find it in any of his papers, such as this PRB , but he kindly provided a copy). This "momentum space differentiated" phase is intermediate between the pseudogap state and the isotropic Fermi liquid, both as a function of doping and U/t. This (temperature dependent) anisotropy should be observable in angle dependent magnetoresistance (ADMR) measurements on organic charge transfer salts in the kappa-(BEDT-TTF)2X family. These materials are all at half filling. A candidate material is X= Cu[N(CN)2]Br which lies close to the Mott transition.

The popular sit-com The Big Bang Theory  continues to break new ground by introducing prime time TV viewers to the latest developments in condensed matter physics. This  clip  from an episode The Thespian Catalyst  begins with Sheldon attempting to teach a class of Caltech graduate students about topological insulators. Note that the equations on the board are authentic, as usual. Sheldon finds, as many of us do, there is a weak correlation between our perceptions of our teaching performance and our students perceptions of the quality of our performance. The show also discusses important issues about what initiatives we should take to address this issue and to improve the quality of our teaching.

This morning I am giving a seminar at th e  Laboratoire de Chimie Quantique   in S trasbourg. Here are the slides.

Thomas Maier gave a nice talk at the conference. He considered this question [or at least what is the mechanism of superconductivity in the Hubbard model?] via a  Bethe-Salpeter equation (some of the results are described in this PRB  and this PRB ). where Gamma^pp is the irreducible particle-particle vertex and chi_0 is Their calculations are for a cluster DMFT treatment of the doped Hubbard model. They find that the irreducible particle-particle vertex peaks at a wavevector of (pi,pi) as does the spin susceptibility chi(K-K'). Indeed they find that this vertex is to a good approximation related to the spin susceptibility via an RPA type relation. where U(T) is a temperature dependent renormalised Hubbard U. But why does the superconductivity go away as one approaches the Mott insulator? After all, the spin fluctuations are increasing! This is because chi_0 ~ GG [Thomas had a name for this that I did not catch] is decreasing because of the suppresion of quasi-particle weigh

An outstanding theoretical challenge remains (reliably) calculating thermodynamic and transport properties of the one band Hubbard model. This is necessary to answer questions such as: is it the relevant effective Hamiltonian for cuprate superconductors? Emanuel Gull gave a nice talk at the conference about work on cluster DMFT treatment of the doped Hubbard model. This PRB paper  contains a nice comparison of how the results vary with cluster size.  They consider cluster geometries up to 16 sites. At least 8 sites are necessary to cover the important region around wavevector (pi/2,pi/2) where one hopes to find nodes in a pseudogap, superconducting gap, and cold spots on the Fermi surface. The calculations produce four distinct phases: Mott insulator An isotropic Fermi liquid (FL) A FL with momentum space differentiation A momentum selective Mott insulator (a pseudogap state) Of particular interest to me is the existence of the third state which may correspond to the anisotropi

Here are the  slides for the talk, Angle-dependent magnetoresistance as a probe of Fermi surface anisotropies I am giving this afternoon at the conference. Much of the talk is based on this preprint.

David Singh gave a nice talk today about the iron pnictide superconductors. Here are just a few of the points that he emphasized. This is a big family of materials - high Tc is a very robust phenonema. Common features Fe atoms are in a square lattice near divalent Fe tetrahedral coordination (2 Fe per unit cell) The connection of the pnictides to the cuprates is weak, contrary to what some people asserted in the early days [because of the proximity of superconductivity and antiferromagnetism] -doping not essential to superconductivity -Mott physics is not relevant (no Mott insulating state) -magnetic order & superconductivity do co-exist? -multiple orbitals are present [they may be important for avoiding Mott insulator] -many materials are electronically "three-dimensional" rather than two-dimensional [ARPES and dHvA see significant corrugation of the Fermi surface]. Proximity of superconductivity to a magnetically ordered phase should not be viewed as

How long after the experimental discovery of a quantum many-body phenomena does it take to develop a theory that will be eventually accepted as the correct one? Superconductivity was first observed in 1911 and BCS theory arrived in 1957. At the c onference in the castle today, Sasha Lichtenstein pointed out that the Kondo effect was first observed in 1933, Kondo described some of the relevant physics in 1964, but it wasnt until the 1980s that the problem was really solved. Thats 50 years. He pointed out that it is 25 years since the discovery of high-Tc superconductivity in the cuprates and suggested maybe we have 25 more years to get the theory right! On the other hand, Laughlin found the correct theory of the fractional quantum Hall effect within a year of its experimental discovery!

A striking feature of strongly correlated electron materials is the existence of bad metallic behaviour. The resistivity can monotonically increase with temperature to values which are much larger than the Mott-Ioffe-Regel limit, a value corresponding (in a simple Drude model) to a value where the mean-free path is smaller than a lattice constant. Key questions are Does the resistivity ever "saturate" at high temperatures? If so, to what value is the maximum possible resistivity? Could this be related to the large spectral weight spread out over a broad spectral range in the optical conductivity? (see the next figure below). There is a nice summary of the issues in section VIIH of this  RMP by Basov and Timusk . Gunnarsson and collaborators have come up with a simple argument to address these questions [see this nice RMP colloquium ]. At high enough temperatures there is no Drude peak in the optical conductivity. However, the latter must still satisfy the f-sum rule,

I have just finished a paper  Unified description of hydrogen bonding by a two-state effective Hamiltonian. I welcome feedback. Many of the ideas in the paper have been discussed on this blog before over the past year. The paper sits right at the boundary of physics and chemistry and exemplifies the associated tensions. Some physicists may like it because of the simplicity and transparency. Some chemists may consider it glosses over and misses too many details.  Practically all the ideas in the paper have been discussed in some form before. I see the key novelty as synthesis: providing a conceptual and semi-quantitative framework to understand a wide range of experimental and theoretical results. Consequently, I consider the paper may be the most significant one I have ever written... I welcome feedback. I will submit the paper to Physical Review Letters in about a week, after I have received more feedback.

Most molecules and solids exhibit simple isotope effects associated with vibrational modes. In the harmonic limit the vibrational frequency scales with the inverse square root of the mass. Hence, replacing hydrogen with deuterium (D) should reduce the frequency by a factor of 1.414 = sqrt(2). However, significant anharmonicity or non-adiabatic (violations of Born-Oppenheimer?) effects can lead to very different effects.  An important case is that of hydrogen bonding . The graph below shows gamma = the ratio of the O-H stretch stretch frequency to the O-D frequency as a function of the O-H frequency. The latter is a measure of the H-bond strength and is directly correlated with the donor-acceptor distance. The graph is taken from this paper. One sees that as the mode softens [as the H-bond gets stronger] the isotope effect gets smaller. Playing around with the lowest energy eigenvalues for a Morse potential one can reproduce this effect. However, the physics behind the upward turn for l

Who should get their name associated with a particular physical effect? Surely, they should have to be involved in the discovery or in understanding the actual effect. But, it seems this is sometimes not the case. Also, if someone develops a theory for an observation, which later turns out to be the wrong theory, should their name remain associated with the effect? Here are a few examples, up for discussion. The Pauli paramagnetic limit for the upper critical field of a superconductor should be the Clogston -Chandrasekhar limit. Pauli worked out the Pauli paramagnetism which is involved in this effect, but Pauli never said anything about how that might relate to superconductivity. A Fermi liquid should be a Landau fermion liquid. The whole point is not Fermi statistics but the universality that Landau elucidated. The Luttinger liquid  should be a Haldane liquid. Tomonaga and Luttinger introduced the Hamiltonian. Luttinger solved it incorrectly; Mattis and Lieb gave the cor

On Saturday I am heading off to Germany to attend a workshop on Electronic structure of novel materials , organised by the Andersen group at the Max Planck Institute Stuttgart, and to be held in Ringberg Castle. I will give a talk on Interlayer magnetoresistance as a probe of Fermi surface properties in strongly correlated metals. It will be an updated version of this earlier talk.

In basic solid state physics one learns that in metals sign of the Hall voltage is related to the sign of the charge carriers and the Hall coefficient is a measure of the density of the charge carriers, and is essentially temperature independent. However, in strongly correlated metals the situation is more complicated. Today I read a beautiful 1991 paper by N.P. Ong where he derives a simple geometrical interpretation of the transverse conductivity sigma_xy for a two-dimensional metal. It is proportional to the area swept out by the scattering length [Fermi velocity * scattering time] as one traverses the Fermi surface. This result is based on a solution to the Boltzmann equation and so assumes a quasi-particle picture. Ong's result can be used to decipher the relative contributions from the curvature of the Fermi surface the Fermi surface area to circumference ratio variation in the scattering rate at different points on the Fermi surface The latter can be responsible for s

I received a request: "Can you talk about going from a research dependent (when your projects are fed to you) to someone able to write single author papers?"  Here a few thoughts. Get a good mentor. Ask them to help you with this. Be aware of how committed the person paying your salary is to you making this transition. Before and during any project (both those fed to you and ones you come up with) ask yourself, "Why am I doing this? Why is it important? What do I hope to discover? Is it realistic, particularly in the desired time frame? When and why might I abandon the project?" Ask the same questions of your supervisor and/or collaborators. Get in the habit of critically evaluating other peoples research (fellow students and postdocs, papers you read, talks you hear..). What is the basis for your positive and negative evaluations?  Continually work on your writing skills. Having said all that bear in mind that "independence" is not the be al

Writing down the simplest possible effective Hamiltonian for a chemically and structurally complex material is a great challenge. This is particularly true of transition metal compounds because of the presence of multiple d-orbitals. Often crystal field effects split these orbitals and so one needs only consider a subset. Nevertheless, justify a selection and defining the relevant inter and intra-orbital interactions is difficult. Starting from the atomic limit one can consider the following Hamiltonian for a single atom [see this post about Hund's rule ] same orbital, and with opposite spins in the same orbital, maximizing S and then T. This seems a lot simpler and transparent than forms I have seen with creation and annihilation operators.  H ow does one determine U an d J?  Hotta has a helpful review where he discusses these in terms of  Racah (Slater) parameters. He also discusses the overlap matrix elements associated with orbitals on neighbouring atoms. These are needed to d

I just read a nice article Theory in Chemistry by Roald Hoffmann . Although, written in 1974, I consider it just as poignant (or perhaps even more so) today. It should be read in full. But here are a few highlights to motivate you to read the 3 pages. Is not the design and analysis of a beautiful experiment theory? Given the human character, rationalisation poses no problem. Prediction is another matter. By and large, theory has not predicted much chemistry. some exceptions.... I would call a credibility nexus - in which a group of experimentalists, otherwise skeptical of theory, suddenly found itself faced with the success of a simple theory. That set of specialists quickly became concerts, often zealots...   the most important role of theory in chemistry is to provide a framework in which to think, to organize experimental knowledge Hoffmann identifies six examples of "credibility nexus" Huckel's rules for the stability of different conjugated organic molecules Wa