Condensed concepts

Superconducting organic charge transfer salts are diverse. One class that has attracted considerable attention are the kappa-ET and dmit families that can be described by a Hubbard model on the anisotropic triangular lattice at half filling. Superconductivity emerges out of the parent Mott insulating state. The half filling arises because the molecules occur in pairs [dimers] within the crystal structure. Each dimer corresponds to a site in the lattice for the Hubbard model. In a second class of materials the molecules are not dimerised and the resulting electronic bands are one-quarter filled with holes. Each site in the relevant lattice is a single molecule. The superconductivity emerges out of a charge-ordered [Wigner-Mott] insulator. The simplest possible effective Hamiltonian is an extended Hubbard model at one-quarter filling on a square lattice . In a 2001 PRL Jaime Merino and I showed how superconductivity could occur in these materials as a result of charge fluctuations ass

Robert Mulliken was one of the founders of quantum chemistry. In 1965 he gave a conference talk Molecular Scientists and Molecular Science: Some Reminiscences . In it he made a commonly quoted statement highlighted below. I reproduce it in context. . ...I would have liked first to say something about Molecular Quantum Mechanics (MQM) problems.  .... The general idea [of Lowdin's conferences] was that with old-fashioned chemical concepts, which at first seemed to have their counterparts in MQM, the more accurate the calculations became the more the concepts tended to vanish into thin air . So we have to ask, should we try to keep these concepts-do they still have a place-or should they be relegated to chemical history. Among such concepts are electronegativity....., hybridization, population analysis, charges on atoms, even the idea of orbitals, .... Roald Hoffmann has argued these concepts do have a role. I would certainly agree. Computations should support, elucidate, and cl

Maybe I am slow, but when I read the introductory sentence below in an ABC [Australian version of NPR in the USA] news article I began to worry about both the convoluted state of  education policy and the quality of journalism in Australia:   Education Minister Christopher Pyne has denied he is planning to renege on a promise not to restore limits on university places I think this simply means, "The Education Minister may limit the number of students that can enrol."

Tomorrow I am giving a seminar, "Essential state models for fluorescent protein chromophores and methine dyes," in the Chemistry department at Parma University, Italy. Here is  the current version of the slides . My host is Anna Painelli . Over the past few years she and her collaborators have done some very nice work showing that the optical properties of a diverse range of complex chromophores can be described by "essential state models" that are effective Hamiltonians acting on a just a few valence bond states. These models include dominant molecular vibrations and the effect of the solvent. For example, an earlier post mentioned their work on crystal violet. This work nicely complements work done by Seth Olsen giving a rigorous quantum chemical justification for such essential state models, as in this J. Chem. Phys. paper.

In some of my interactions with undergraduates who wish to make a career in science I observe unrealistic expectations about what is required to survive, let alone succeed. Here are three lies they have been told and some have believed. 1. You are special. If you grew up in the Western world you are part of Gen Y and it is likely you have been continually told you are wonderful and you can be anything you want to be. Furthermore, if you are moderately bright and enthusiastic about science you may have received a lot of affirmation from high school teachers, career counselors, some peers, and/or undergraduate advisors. This is particularly true if you attend an average or mediocre institution that desperately wants to recruit students to go to graduate school. The problem is that once you get to a respectable graduate school you will discover that you are just average. Why does this matter? Don't expect or demand special treatment. You are going to have to work much harder t

I have really enjoyed the Hydrogen Bonding conference this week. There are about 120 people which is a good size. The diversity of the topics covered is a testimony to just how ubiquitous, important, and challenging hydrogen bonds are. The participants ranged from old timers who have probably been to all twenty conferences to many newcomers like me who tthis was their first time. People were quite friendly and any contested discussion was quite cordial. I also enjoyed the lack of hype or sef-promotion. I got a lot of positive feedback for my simple model, showing that the field is quite open to new people and new approaches, particularly from physicists. Here is a somewhat random commentary. If you want more details, ask. Double proton transfer in porphycenes. This proceeds via a concerted mechanism and quantum tunneling is clearly present. Jacek Waluk's group has some beautiful results. Water. [The basic questions never go away!] Ali Hassanalli gave a nice talk about

It is the conservatives vs. the radicals, the right vs. the left. A colleague recently suggested to me that this is a good metaphor or analogue for describing and understanding the divisions in the physics community working on the theory of correlated electron materials. In the USA political divisions have led to a "gridlock" that is stopping the country moving forward. Both conservatives and liberals have a rigid ideology that prevents them from seeing the merits of their opponents concerns and from being willing to compromise. Conservatives believe one should never raise taxes. Liberals believe one should never cut social welfare programs. Both "cherry pick" economic data to support their point of view. Historically, political radicals believe that capitalism is a flawed and unstable system that must be replaced by some new, but unknown, system. The world is more complex than political ideology concedes. Both radicals and conservatives have extreme beli

Previously I have written about that tables are wonderful in papers. This is because science is all about comparisons. However, I think tables should not be shown [banned?] in seminars and conference talks. Flashing a detailed table of data on the screen for a minute is useless. The audience does not have nearly enough time to absorb and process the table, even when you verbally explain the main points. This will increase the tendency of the audience to tune out. I suspect computational chemists are particularly bad at this. They like to show all these quantities they have calculated with different levels of theory and different basis sets. If you want to highlight a trend [or lack of one] you need to graphically represent the data. The audience can then quickly understand and assess the result. I can think of a couple of exceptions from my own talks. Then I have merely a the table as an "existence proof". For example, "The parameters describing the spectral

Here is the current version of the slides for my talk  I am giving tomorrow at the  Horizons in Hydrogen Bond Research conference. The first half of the talk is based on this paper. I worked hard to cut down the number of slides, since the talk is only fifteen minutes, and the last one before morning coffee. I have lots of backup slides. I also included a slide suggesting that the model and approach might be readily extended to apply to topics considered in other talks at the conference. Hopefully this will generate more discussions. Aside: the lecture room is like nothing I have seen before. It is in an historical building and is long and narrow with low rafters from the roof. On each set of rafters as you go towards the back of the room there is another screen, leading to about 6 different screens. Hence, there is no point in using a laser pointer on the front screen. Only the people in the front 4 rows will be looking at it. You have to use your mouse cursor as a pointer. This

If it's tuesday, this must be Belgium . Somehow I can't get that out of my head, partly because I have been travelling a lot. I first saw the movie in 1969, strangely in Princeton, while on an 3 month overseas trip with my parents. My father was visiting Walter Kauzmann, who knew all about hydrogen bonding. I think we thought the movie was pretty funny. I was only 8 years old. But I watched it again a few years ago and did not think it was that funny anymore. But, I digress... This week I am in Antwerp, Belgium attending the 20th International Conference on Hydrogen Bond Research . Why am I here? It is part of the process of trying to break into a new field. The program and attendees are diverse ranging from theoretical physicists like me to quantum chemists to experimental physical chemists to biochemists. The challenge for me will be filtering through all the chemical detail to figure out what is really important and what is not. I am looking forward to learning more abou

Iridates such as Sr2IrO4 have attracted considerable attention because they are 5d systems that exhibit a strong interplay between spin-orbit coupling and strong electronic correlations. [See this earlier post ]. Sr2IrO4 is a focus because it has been argued that it is a J=1/2 Mott insulator, just like La2CuO4, the parent compound for cuprate superconductors. A current holy grail is to dope this material in the hope of producing high-Tc superconductivity. Many are trying. No one is succeeding. There is actually a whole series of layered compounds, the Ruddlesden-Popper perovskites that differ, not just in their stoichiometry, but also their crystal structure, and consequently how the Iridium ions are coupled together. Sr_n+1Ir_nO_3n+1, where n is the number of SrIrO3 perovskite layers sandwiched between extra SrO layers. Resonant-Inelastic-X-ray-Scattering ( RIXS) experiments show that spin excitations in the Mott insulating phase of Sr2IrO4 appear to be well described by a

Annual Reviews in Condensed Matter Physics has two inspirational articles Why I Haven’t Retired by Ted Geballe [aged 93!] Sixty Years of Condensed Matter Physics: An Everlasting Adventure by Philippe Nozières [aged 81] Here are a few random Nozieres quotes to motivate you to read his whole article: equations without a phenomenological background remain a formal game. Only simple qualitative arguments can unveil the underlying physics.  A dialogue between experiment and theory is a difficult venture, which requires a lot of patience on both sides to find a common language. When it succeeds it is incredibly rewarding. I often made proposals to experimentalists, who always had the same initial reaction: “one more crazy theorist’s idea!” But my experimentalist friends are smart and sometimes they accepted the challenge, with spectacular results. I am very grateful to them. A corollary of that view is that theorists should not live in ghettos, but be immersed in experimentalist

A common problem in the practical implementation of quantum many-body theory [whether for quantum chemistry, solid state physics, or nuclear physics] goes like this. One starts with a Hamiltonian and observables that are written in terms of second quantised operators. Real calculations of observables requires diagonalising the Hamiltonian matrix. It must then be written as a symmetric real matrix in some basis of many-body states. To do this means manipulating large numbers of creation and annihilation operators. This  can quickly become cumbersome, particularly for fermions. It is easy to loose track of signs when calculating matrix elements. It would be nice to be able to do this in an automated way, e.g., using Mathematica. Sriram Shastry and John Wright have developed a Mathematica program DiracQ that will do all this. It can be downloaded for free and is described in detail in a preprint.  The latter contains some highly non-trivial examples, e.g., finding the conserved quant

On Tuesday I am giving a Condensed Matter Seminar  at Rutgers. Here is the current version of the  slides  for my talk. The main results in the talk are in a recent  PRL , written with Jure Kokalj. The organic charge transfer salts and the relevant Hubbard model are discussed extensively in  a review , written with Ben Powell.

One of the exciting things about condensed matter physics is that we are continually discovering exotic new phenomena. Many are unanticipated and understanding them presents a rich intellectual challenge. That is the nature of emergence. Due to chemical complexity and the richness of quantum many-body physics it seems the frontier is endless. Superfluid 3He, heavy fermions, sliding charge density waves, weak localisation, giant magnetoresistance, organic superconductors, quantum Hall effects, quantum point contacts, cuprate superconductors, non-Fermi liquids, buckyball superconductors, Luttinger liquids, colossal magnetoresistance, spin liquids, pseudogap, composite fermions, strontium ruthenate, topological order, quantum dots, sodium cobaltates, solid state quantum computing, fluctuating gauge fields, spinons, topological insulators, iron pnictide superconductors, ultracold atomic gases, quantum criticality, spin-charge separation, anomalous Hall effect, Majorana fermions, ....

Until last week I had several misconceptions about unconventional [i.e., non s-wave] superconductivity due to purely electronic interactions. I thought weak coupling approaches tend to give a clear "pairing mechanism" and the symmetry of the Cooper pairs is related to the type of fluctuations or collective mode responsible for the pairing For example, d-wave singlet pairing tends to go with antiferromagnetic spin fluctuations and p-wave triplet tends to go with ferromagnetic spin fluctuations. There is a very nice paper Band structure effects on the superconductivity in Hubbard models by Weejee Cho, Ronny Thomale, Srinivas Raghu, and Steve Kivelson They consider a weak-coupling renormalisation group (RG) treatment of a Hubbard model with specific band structures that are varied by changing tight-binding parameters. The relevant Feynman diagrams are below Calling this "spin fluctuation exchange" is not clear as there is no well defined collective mode t

This month many bright and ambitious young people will begin science Ph.D's in the USA. What might they anticipate? Exactly thirty years ago I was one of sixteen young men in the incoming Physics class at Princeton. Here is a photo of fourteen of us outside Jadwin Hall. Thanks to Stephen Naculich and Bill Somsky for providing this copy. Also, here is a picture of me in the front of Jadwin this week. Here are a few random observations about my class and where we ended up. I am not sure I have all the history correct so others should feel free to correct me. There were no women in the class. We came from the USA, Canada, Greece, Italy, Australia, China, and India. Our future appeared to be bright and exciting. Prospective advisors included two Nobel laureates [Phil Anderson and Val Fitch] and three future Nobel laureates [Joe Taylor, David Gross, and Dan Tsui]. Other faculty included a young Ed Witten, Bob Austin, Ian Affleck, David Wilkinson, James Peebles, Bob D

Largely due to the work of Sriram Shastry I have recently become aware that particle-hole asymmetry in strongly correlated electron systems is an important issue (and challenge). This was flagged in an earlier post. There are a number of experimental anomalies that suggest the asymmetry is much larger than that associated with band structure effects. These include: - highly asymmetric ARPES line shapes in the cuprates -the slope of the I-V characteristics for some STM spectra - a thermoelectric power that is large and changes sign with temperature in some cuprates Theoretically it has been a puzzle that theoretical calculations for doped Mott insulators often give self energies that have a large particle-hole asymmetry. See for example Figure 3 in this PRL , Figure 13 of this PRB , and the figure below. It is very different from the perfect particle-hole symmetry implicit in Fermi liquid theory and marginal Fermi liquid theory. Also the quadratic frequency dependence only app