Condensed concepts

Ben Powell alerted me to a stimulating post and comments about "Slow science" on the Quantum Pontiff blog. It is worth thinking about. Here are a few random thoughts: This gets back to a point I made in a few earlier "career advice" posts. Good reliable influential science is hard. Consequently, it is slow. I think we all need to do more "slow" science. We would produce higher quality work AND enjoy ourselves more. Don't blame the "system". Focus on your "circle of influence" (e.g, what you CAN change: how you choose to spend your time, how you review grant proposals, and papers) rather than your "circle of concern" (i.e., what you care about but can't change, e.g., the way universities hire, promote, etc., funding agencies make decisions). In spite of all the flaws of the "system" and the bean counters I think it is still clear that really significant work is rewarded . I agree with John Preskill (and Clin

“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk. ” John von Neumann (via Enrico Fermi and Freeman Dyson ) I believe that any significant physical effect/discovery should be able to be seen by the naked eye in the experimental (or computational) data and should not require curve fitting. For a helpful discussion, see Dangerous Curves. The first principle is that you must not fool yourself--and you are the easiest person to fool Richard Feynman, Caltech 1974 Commencement address

Reality is stratified and science is hierarchial: from physics to chemistry to biochemistry to biology to psychology. Generally, as one goes up the strata the complexity of the system under study increases and the relevant length and time scales become greater. At each strata or level of hierarchy, science seeks to illuminate what are the principles that describe the phenomena under study. Sometimes principles can be reduced to and understood in terms of principles from the strata below. For example, genetics can be understood in terms of molecular biology. Rules of chemical bonding can be understood in terms of quantum physics. However, it should be stressed that there are very few specific cases where phenomena at one strata have been predicted solely from a knowledge of the laws underlying strata below. In almost all cases, one observes (n.b., not deduces) phenomena at one level, develops concepts to understand them at that level, and then a posteriori tries to understand them

As we struggle to understand the pseudogap state in the cuprate superconductors any successful theory must be able to describe at least qualitatively a few key features: the d-wave symmetry the existence of Fermi arcs which increase in length with doping well-defined quasi-particles near the nodes incoherent excitations near the anti-nodes Can a one-band Hubbard model capture such features? Furthermore, if it can, is there a "simple" physical picture of the underlying physics? I believe that affirmative answers to both questions are given in a very nice preprint by Ferrero, Cornaglia, De Leo, Parcollet, Kotliar, and Georges. Some of the results were published earlier in PRL, which contains the nice figure below of the spectral function at the chemical potential at different doping away from half filling. This work builds on the successes of Kotliar and Georges at developing Cluster Dynamical Mean-Field Theory (DMFT), rotationally invariant slave boson theory, and orbital-s

I almost never take up an offer by conference organisers to publish a paper in their proceedings. I think such proceedings have passed their use by date because: * They usually appear 6 to 18 months after the conference. By then most of the papers have already been published elsewhere * Almost all conference papers seem to be cut-and-paste versions of papers that the authors have already published or about to publish elsewhere. * Most proceedings are published by mediocre journals. * One of the main reasons some people publish in them is to pad their publication lists and keep bean counters happy. * The only conference papers I tend to read are review articles based on plenary talks by leading scientists. But, most of these I get off the arXiv. Given all of the above I think conference proceedings are just a waste of time for the organisers, referees, and authors. We should all exercise more self-control and abstain.

In order to understand the role and implications of emergence it is helpful to define different forms of reductionism in science. It is also important to make a distinction between reductionism as a practice in science and reductionism as a philosophical outlook. As a method, reductionism has been extremely powerful. Examples of successes include the understanding obtained by reducing genetics to molecular biology, atomic spectra to quantum mechanics, and planetary motion to Newtonian mechanics. A reductionist approach gave a unifying description of a diverse range of phenomena, and elucidated "cause and effect", i.e., if one component or variable of the system is changed what is the resulting change in other components or properties. In terms of popular books, advocates of the primacy of reductionism include Steven Weinberg, Stephen Hawking, and Richard Dawkins. They also appear to presuppose that because reductionism is a fruitful strategy for certain scientific problems

What is a spin liquid? There are several alternative definitions. The definition that I think is the most illuminating, because it brings out their truely exotic nature, is the following. A spin liquid is a quantum state in which there is no long-range magnetic order and no breaking of spatial symmetries (rotation or translation). One can write down many such states. A concrete example is the ground state of the one-dimensional antiferromagnetic Heisenberg model with nearest-neighbour interactions. However, despite an exhaustive search since Anderson's 1987 RVB paper, it seems extremely difficult to find a physically realistic Hamiltonian in two dimensions which has such a ground state. As far as I am aware we are still seeking a counter-example to the following conjecture : Consider an spin-1/2 Heisenberg model on a two-dimensional lattice with short range antiferromagnetic exchange (both pairwise and ring exchange are allowed) interactions. The Hamiltonian is invariant under SU

This is the provocative title of a very nice paper by Laughlin and Pines in PNAS back in 2000. They point out that in principle Schrodinger's equation from quantum mechanics and Coulomb's law of electrostatics is ‘ The Theory of Everything ’ since these equations determine all of chemistry and all the properties of all matter that we encounter everyday. Yet, due to limited computational resources even the most powerful supercomputer can only solve these equations and make predictions for systems containing at most ten particles. However, even if we had a supercomputer that could treat Avogadro's number (i.e., 10^23) of particles that would not help. Such a computer would require more atoms than there are in the universe. First, doing the calculations would be just like doing an experiment. It would be a ‘black box’ that would give little insight into the origin of the phenomena. Morever, such calculations on finite systems cannot predict phenomena such as broken sy

"The main thing is to keep the main thing the main thing" Lee Iacocca , former CEO of Chrysler, who in the 80's turned the company around. [He is about to loose his pension ....] Anyway, each year I have to do several staff appraisals. It is easy to get distracted by the onerous paperwork and lists of publications, grants, future plans... Here are some questions I want to focus on this year. What did you enjoy the most about the past year? What did you enjoy the least about the past year? What specific scientific questions did your research answer in the last year? What specific scientific questions do you want your research to answer in the next year? The worst enemy of the excellent is the good. What should you say no to in the next year? How can I better help you reach your goals this year?

A recent preprint from Ni, Thaler, Kracher, Yan, Budko, and Canfield (Ames Lab, Iowa State) reports the above phase diagram for members of the 122 family (based on the parent compound BaFe2As2). When doped with transition metals the antiferromagnetic transition is suppressed and superconductivity appears below the lower dome. Near the antiferromagnetic transition there is also a structural transition from a tetragonal to an orthorhombic crystal structure.

I am giving the Chemistry seminar at UQ this week. Here are the slides

A book I really like and strongly recommend is A Different Universe: Reinventing Physics from the Bottom Down by Bob Laughlin. He received the Nobel Prize in Physics in 1998 for the theoretical description of the fractional quantum Hall effect, and was a co-founder of I2CAM . Laughlin has highly original ways of looking at science and is a very gifted writer. Laughlin is passionate advocate for emergent phenomena being the most interesting and challenging aspect of science. Just to illustrate some of the insights.... Laughlin points out that emergent phenomena can present significant paradoxes. Laughlin considers two paradoxes associated with the Integer Quantum Hall effect. First, there is “perfection due to imperfection”: the precision of the quantisation of the Hall resistance improves as the sample quality decreases , i.e., the number of impurities that scatter the electrons increases. Second, the Quantum Hall effect provides a very precise means to determine properties

Here is a rough summary of a few things I think I learnt (or was reminded of) this week about superconducting organic charge transfer salts. Please post corrections and clarifications. Where there is interest I will post more details... A long-standing mystery in the Bechgaard salts has been the presence of rapid oscillations associated with an unexpected Fermi surface reconstruction. Could this be a many-body effect as in the cuprates? (DMe-ET)2PF6 has superconductivity next to a charge ordered insulator. Near the Mott transition critical point the low temperature NMR relaxation rate 1/T1 T should scale with |P-Pc|^delta, where delta =2 is the same critical exponent as for the conductivity. This is because at half filling the number of localised spins is related to the number of doublons. Kagawa et al., PRB 78, 184402 (2008) have a very elegant way of using NMR and the DM interaction to determine the staggered magnetisation (something is normally only observable via neutron scatter

Here is a rough summary of a few things I think I learnt this week. More to come later... Please post corrections and clarifications. A lot of attention in both STM and ARPES studies on the cuprates is being given to questions of particle-hole symmetry. This is because in a superconducting d-wave gap, the Bogoliubov quasi-particles have perfect particle-hole symmetry. In contrast, other possible nodal states such as the staggered flux phase (d-density wave, DDW) do not have this property. The evidence from both STM and ARPES is that the physical origin of the gap near the nodes is quite different from the gap at the anti-nodes. They have different temperature and doping dependence. The consensus also seems to be that the gap near the nodes is from fluctuating superconductivity. Some of the issues are nicely summarised in a Science Perspective by Andy Millis. Electronic Raman Scattering (ERS) is a sensitive probe of the d-wave gap and pseudogap. The B1g polarisation ERS is dominated b

Hearing some talks about properties of the metallic state of the iron pnictide superconductors underscored to me that one sees certain common features in a wide range of strongly correlated electron materials. These properties are distinctly different from electronic properties of elemental metals. These unusual properties arise from the fact that a low energy scale emerges which defines a temperature scale T0 (often in the range 10-100 K) above which quasi-particles do not exist and we have a bad metal . Signatures of this crossover from a Fermi liquid at low temperature to a bad metal are: the resistivity, Hall coefficient, and thermopower can have a non-monotonic temperature dependence with increasing temperature the resistivity can smoothly increase to values much larger than the Mott-Ioffe-Regel limit (h2 a/e ~ 1 mohm-cm) at temperatures of order T0 the thermopower can reach values as large as kB/e ~ 50 microV/K above temperatures of order T0 the Drude peak in the frequency dep

Here are the slides (plus extras) I will show when I am discussion leader for the session on organic superconductors tonight.

Before going to a conference and experiencing information overload it is worth thinking through what one is hoping to learn. One thing I am looking forward to at the GRC on superconductivity is getting up to speed on the new iron pnictide superconductors . Some of the questions I have are: Is there a universal phase diagram? What is the superconducting pairing symmetry? What are the experimental signatures of strong electronic correlations? Is there a pseudogap? Is the quality/purity of the samples high enough we can be confident that experimentalists are measuring what they claim on what they claim? What is the minimal quantum many-body Hamiltonian that can describe these materials? How many bands are necessary? Is there an variational wave function that captures the essential physics of the competition between the different ground states? What are the outstanding unresolved questions? A nice introduction to some of these issues is this brief overview by Mike Norman.

Given the success described in the prevous post, an important question I have been wondering about the last couple of years is whether angle-dependent magnetoresistance (ADMR) can be used to detect and quantify the anisotropy of a pseudogap? I believe the answer is yes, based on recent calculations by Michael Smith, described in this preprint . Michael and I derived an expression for the interlayer magnetoresistance as a function of the direction of the tilted field, including the effects of anisotropies in all Fermi surface quantities including the pseudogap. We found a pseudogap can have significant effects on ADMR. As the temperature decreases the interlayer conductivity is dominated by the parts of the Fermi surface near the nodes of the pseudogap. This reduces the amplitude of variation in the magnetoresistance as the direction of the component of the field parallel to the layers changes. As the magnitude of the pseudogap increases the anisotropy becomes dominated by the anisotrop

A few years ago Malcolm Kennett and I developed a theoretical formalism that enabled the extraction of information about Fermi surface properties of layered metals from an analysis of the dependence of interlayer magnetoresistance on the direction of the magnetic field. We then contacted Nigel Hussey to get feedback on our paper before we submitted it. It turned out Nigel and his experimental group in Bristol were pursuing similar ideas to extract new information about the temperature and anisotropy (around the intralayer Fermi surface) of the scattering rate in overdoped cuprate superconductors. The figure below, from our Nature Physics paper , shows the dependence of the interlayer resistance on theta, the angle between the field and the normal to the layers of the metal. Solid lines are experimental data for an overdoped cuprate superconductor in a magnetic field of 45 tesla and at temperatures varying from 4 K to 55 K. The dashed line are the results of our theoretical calculation

Molecular orbital theory is a wonderful theory which has provided many qualitative insights into the electronic structure, optical and magnetic properties, and reactivity of organic molecules. Schematics such as that below can be extremely useful. However, it is important to appreciate its limitations. In its simplest version it completely neglects interactions between electrons. Bear in mind molecular orbitals are just a theoretical construct. They do not actually exist . One can certainly calculate theoretically molecular orbital energies. However, these energies (e.g., of the HOMO and LUMO) can not be measured. What one can measure (and also calculate theoretically) are the energy of quantum states that do exist and obtain quantities such as ionisation energy, I electron affinity, A electrochemical oxidation potential electrochemical reduction potential energy of the lowest lying singlet excited state, E(S1) energy of the lowest lying triplet excited state, E(T1) Molecular orbit

As mentioned in a previous post organic charge transfer salts have revealed rich new physics associated with strong electronic correlations. The family kappa-(BEDT-TTF)2X has the phase diagram below as a function of temperature and pressure. There is a first-order phase transition between a Mott insulator and a metal (which becomes superconducting below about 12 K. The first-order transition line ends a critical point at about 40 K. In 2005, Kagawa, Kawamoto, and Kanoda published a beautiful paper in Nature which did a scaling analysis of the conductivity near the critical point. From the figure below they could the extract critical exponents show (delta,beta,gamma)=(2,1,1). These values did not correspond to any known universality class. This is in distinct contrast to the critical exponents found for the corresponding metal-insulator transition for vanadium sesquioxide (V2O3) doped with chromium. In that case the exponents were those for the three dimensional Ising transition (liqu

I gave my last lecture today. This is always a good feeling. Again I went over the 20 key ideas that I hoped they learnt in the course. The most important one, which we have to keep repeating is that in an non-isolated system whose state is defined by pressure and temperature, the Gibbs free energy G can never increase . Consequently, in the equilibrium state G must take the smallest possible value. On my previous post on the 20 key concepts, Will Polik wrote a helpul comment: Related to concept 10 (free energy), I think that a key concept in the practical application of thermodynamics is the idea that "the entropy of the universe tends toward a maximum" is equivalent to "the Gibbs free energy of the system (at constant T and P) tends toward a minimum" and the corresponding statement about Helmholtz free energy. This allows one to use just the state properties of the system to determine the direction of change and equilibrium conditions, rather than having to worr

Normally magnetic fields destroy superconductivity not help create it! However, in 2001 Uji and collaborators discovered that while the organic charge transfer salt (BETS)2FeCl4 had an insulating ground state applying a magnetic field parallel to the layers could create a metal, and for sufficiently high magnetic fields, superconductivity! This can be explained in terms of the exchange interaction between the magnetic Fe3+ ions and the pi electrons in the BETS molecules. When this exchange interaction is cancelled by the applied field (the Jaccarino-Peter effect, first proposed in the 1960's) the electron spins effectively see zero magnetic field. I was very happy that in our paper Olivier Cepas, Jaime Merino, and I were able to predict the magnetic field range in which one should observe magnetic-field induced superconductivity for a specific material and this was subsequently observed . One can tune between Mott insulating, metallic, and superconducting states by varying the ma