Condensed concepts

Thinking more about my earlier post, Key questions about organometallic materials for LEDs , I realised there is a subtlety that is sometimes overlooked when interpreting experimental data on these materials. The radiative and non-radiative decay rates of the emitting state are never directly measured. Rather, one actually measures the total lifetime tau (or decay rate) of the emitting state and the PLQY (PhotoLuminescence Quantum Yield). This is the ratio of the number of emitted photons to the number of absorbed photons (see the blue and red arrows below). One then uses the following two equations to deduce the radiative and non-radiative decay rates. For just one of many examples, of how this is done, see this paper , by Lawrence Lo and collaborators. However, this analysis assumes that one hundred per cent of the 1MCLT state decays to the 3MLCT state. i.e., that there is NO significant non-radiative decay of this state via other channels (e.g., the MC state shown above).

Tomorrow's lecture is on chemical equilibrium. A few key ideas are: chemical reactions never proceed to completion because of the entropy of mixing the equilibrium constant quantifies how far the reaction proceeds. measuring its temperature dependence allows one to determine the enthalpy change of the reaction. (and consequently also the entropy change). Some cool videos I show are from the Chemistry Comes Alive series produced by the Journal of Chemical Education. These include lots of good ones on thermodynamics and phase transitions.

Learning basic concepts in quantum many-body theory and starting to do actual calculations is not easy. Furthermore, understanding the relationship between its formulation and application in quantum chemistry and solid state physics is even harder. A few years colleagues and I ran a series of summer schools for graduate students in physics and chemistry to help them get started. As usual, I think some of us lecturers actually learnt more than the students. Here are some "basic" problems that I set.

Today Max Lu is giving the weekly Physics Colloquium. No doubt, one thing he will talk about is how his group was able to grow large single crystals of the anatase form of TiO2 (titanium dioxide) with a large percentage of reactive facets. (It is described in this Nature paper ). A key component of that work was that DFT calculations helped guide the chemical synthesis strategy. A really nice exposition of this work and its significance is given by Annabella Selloni in a Nature Materials News and Views . It contains the Figure above.

The figure below, taken from a JACS paper , is a possible schematic for photo-physics of the excited states of Ru(bpy)3 which is a model compound for attempting to understand materials used in phosphorescent organic LEDs. My 5 biggest questions concerning this class of materials are: 1. What is the character of the triplet emitting state? To what extent is it a metal-to-ligand charge transfer state (MLCT) and to what extent is it ligand centred (LC)? 2. What is the non-radiative decay path from the emitting state? What are the relevant vibrational co-ordinates? 3. What is the physical mechanism for the ultra-fast (tens of fsec) transition from the singlet to the triplet MLCT state? Is there are conical intersection associated with this intersystem crossing? 4. Are the excited states delocalised over all the ligands or localised on single ligands? For example, the equation below (from the same JACS) suggests that the singlet state is delocalised and the triplet is localised on a single

The Figure below shows the phase diagram of the Hubbard model on the anisotropic triangular lattice at half filling.as a function of temperature and t/U obtained from cluster DMFT. The figure is taken from this PRB by Liebsch, Ishida, and Merino. As U/t increases there is a first order phase transition from a metallic to and Mott insulating phase. This first order line ends at a critical point. (a) and (b) are for t'/t=0.8 and 1, respectively. Note that the slope of the line at low temperatures depends on the ratio t'/t, reflecting the effect of frustration. The Clausius-Clapeyron equation and the positive slope of the phase boundary implies that for t'=t that the insulating state has a larger entropy than the metallic state, even at low temperatures. The calculated diagram for t'=0.8t is in semi-quantitative agreement with the observed temperature-pressure phase diagram of a range of organic charge transfer salts. The diagram for t'=t is consistent with that obse

This weeks reading from Phillips, Advanced Solid State Physics, is Section 8.4, on the dielectric response function. This is calculated at the level of the Random-Phase-Approximation (RPA) for a Fermi liquid (weakly interacting fermion gas). One finds the density-density response function. The imaginary part is related to the structure factor (via a fluctuation-dissipation relation). This can be thought of as an effective density of states for particle-hole excitations. In three-dimensions these excitations are gapless for all wavevectors. However, one dimension is different. The shaded area in Figure (b) above shows the relevant excitations for on one-dimensional fermion gas. This Figure is taken from a seminal paper by Haldane, who emphasized the distinct difference from higher dimensions. The fact that there is a well defined dispersion for low momenta, shown above means that density fluctuations are well-defined quasi-particles in the one dimensions. This is the basis of bosonisat

In today's lecture I discussed ideal solutions and osmotic pressure. This illustrates the surprising fact that the thermodynamics of dilute solutions is dominated by entropic effects and much of the conceptual formalism of mixing of ideal gases can be carried over, even though the interaction of the solute with the solvent molecules may be highly non-trivial.

In previous years I have struggled to run tutorials/problem solving sessions that students attend and benefit from. However, in a course I am co-teaching with Joel Corney he has developed a structure which I think is quite effective. Students are divided into teams of three. They are then all given the same problem set to complete and hand in before the end of the tutorial in 50 minutes. The three students have different roles: worker, skeptic, and scribe. There are roving tutors (approx. one per 15 students) who are available to answer any questions. The tutors then grade the completed sheet and hand it back the next week. These marks comprise part of the whole course mark. I have been really impressed with how engaged the students are. I enjoy eaves-dropping on them as they explain things to each other and argue about them. I think they are learning a lot more than if I was up the front solving the problems on the whiteboard.

As discussed in many other posts on this blog, organometallic complexes, exhibit rich photophysics and find application in a new generation of plastic LEDs and photovoltaic cells. To what extent do chemical and structural details matter? Anthony Jacko, Ben Powell, and I just completed a paper which considers a simple model effective Hamiltonian which may describe the essential states and their interactions. A key issue for OLED materials is the character of the emitting state, particularly to what extent it is centred on the organic ligands (LC) versus a metal-to-ligand charge transfer (MLCT) state. We identify the key parameters that determine this character.

When you are writing a paper, a grant proposal, a job application, or a talk, think twice before you include a list. I encounter too many generic "lists", whether it is lists of collaborators, research topics, applications, that add little to the substance of the document. So think twice before you include a list!

Organometallic complexes are a key functional component of many organic LED's and photovoltaic cells. Understanding their excited state dynamics is a major challenge. Two key questions: What is the mechanism of the ultrafast (10-100 fsec) intersystem crossing from the singlet to triplet metal-ligand charge transfer state (MLCT) state? What is the non-radiative decay path of the (phosphorescent) triplet state to the ground state? What structural changes are associated with these transitions? A paper in Science last year helps answer the second and third questions for an Fe(II) complex. The results are summarised in the Figure below. This experiment is based on new advances which allow monitoring X-ray Absorption Near Edge Structure (XANES) as a function of the time delay between laser pump and x-ray probe. A key reaction co-ordinate is the Fe-N distance. Increasing it reduces the crystal field splitting which allows excitation of high spin states associated with excitation of the e

Broken symmetry is one of the most important concepts in theoretical physics. It can be illustrated in a very simple way: Consider four cities, each is located at a corner of a square. Find the shortest possible way to join the cities by segments of straight roads. One possible (non-optimum) solution is just lines along three sides of the square. Allow for more than one possible optimum solution. Does your solution maintain the four-fold symmetry of the original square? I use this example (which I first heard from my Ph.D advisor, Jim Sauls, in his first lecture in a graduate class on condensed matter). I now give it in an undergraduate course on thermodynamics of condensed matter. Here is a draft of the lecture for monday. It is one of my favourite because it also discusses space shuttle experiments and shows some cool videos involving broken symmetry in soap films.

I love The Big Bang Theory. Tonight my family and I watched the episode The Cooper-Nowitzi Theorem , (Season 2, Episode 6) which I think is one of the best episodes. It begins with this " inspiring" speech from Sheldon to the incoming class of graduate students.

The above figure (taken from this PRB by Istvan Kezsmarki et al.) compares the frequency dependent conductivity in two Mott insulators, kappa(BEDT-TTF)2X with X = Cu[N(CN)2]Cl and X=Cu2(CN)3. The former has a ground state with Neel antiferromagnetic order and clearly has an energy gap of about 0.1 eV. In contrast, the latter compound may have a spin liquid ground state and has a much smaller energy gap, if any. [The sharp peaks are due to intramolecular vibrational modes and not the electronic degrees of freedom.] Indeed it has been suggested that in the former compound there is a charge gap, but that in the latter compound the optical conductivity has a power law dependence at low frequencies. Note, that the charge gap [the change in the ground state energy when an electron is added or subtracted from the system](a signature of a Mott insulator) is a different physical quantity from the optical gap [the difference in energy between the ground state and the lowest excited single

John Wilkins [who I was fortunate to do a postdoc with] has this useful one page guide on Accepting/Rejecting a Job Offer. I would add that once you get one offer you should write to other places you have applied to and tell them. You should either tell them you are no longer interested or that you are still interested but under a time constraint to decide on your offer. This may stimulate them to proceed faster with a decision about your application. But, do NOT collect offers just for the sake of collecting them.

This weeks reading from Advanced Solid State Physics by Philip Phillips is Chapter 8, Screening and Plasmons. Some key ideas: Thomas-Fermi screening gives a first pass explanation of why the independent fermion approximation for the electron gas in a metal works so well. The estimated screening length is shorter than the inter-particle spacing. Consequently, the effective interaction between the quasi-particles is much weaker and shorter range than the large and long-range bare Coulomb interaction. Key equations are 8.13 and 8.16 Plasma oscillations are collective oscillations of the density. Quanta are plasmons . They arise for a classical plasma (see Ashcroft and Mermin, pp. 19-20). Phillips doesn't make this point clear. Treating the quantum equations of motion for the density at the level of the Random Phase Approximation (RPA) gives their dispersion relation. For elemental metals the plasma frequency corresponds to about 10 eV. For strongly correlated metals such as organic c

Tomorrow's lecture introduces students to the ideas that -critical points are ubiquitous -universality near the critical point The figure is from a 1945 paper

I just read through a section of Excited states and photochemistry of organic molecules by Martin Klessinger and Josef Michl . [You can buy your own copy for US$260! But value for money is extremely high]. The section I read gives a very nice succinct, clear, and concrete summary of the basic phenomenology of radiation-less deactivation of excited states and emission (fluorescence and phosphorescence). I particularly like the way it discusses and shows real data. Key concepts discussed include Kasha's rule, the mirror image rule, intersystem crossing, internal conversion, El Sayed's rules, the "energy gap" law, ... These are basic concepts everyone interested in the photophysics of organic molecules should be familiar with.

A video I like to show students when teaching thermodynamics is The Barrel Crush . It is often used to illustrate how large air pressure is. However, it also nicely illustrates liquid-vapour phase equilibrium. I attach a tutorial problem sheet which allows students to understand it in a more quantitative manner.

Monday's lecture is on the van der Waals equation of state and how it can be used to describe the liquid-vapour transition, including the critical point. The lecture also illustrates how the power of the Maxwell equal area construction, which is not the easiest thing to explain or for students to understand. van der Waals got his Nobel Prize exactly one hundred years ago. Later I am giving a lecture for the Physics Museum at UQ on the significance of his achievements. Of particular significance to me is that it leads naturally to the notion of universality.

Actually, the title is deliberately provocative. Over the years I have noticed in myself and younger colleagues, particularly those teaching a course for the first time, the tendency to get bogged down in endlessly fine-tuning lecture notes, power point presentations, and assignments. Some problems with this are: 1. the time could better spent cutting out material and introducing new methods such as peer-instruction teaching 2. teaching is only part of your job and you need to be carefully not to neglect research, supervision, and "admin" 3. you can always improve it next year So it isn't perfect! Live with it!

How should you respond to referee reports when you re-submit a paper? I have never been the Editor of a journal but I think they really appreciate it if you do the following in your cover letter: Abstain from derogatory comments about the referee(s). Explicitly re-state each objection of the referee before responding to it. (Paraphrases may be suspect, either missing the point for mis-representing it.) Then respond to the objection. Finally, clearly state how and where you have modified the manuscript in response to this criticism.

I just read a very interesting Nature paper, which appeared last month. Quantum spin liquid emerging in two-dimensional correlated Dirac fermions , by Z. Y. Meng, T. C. Lang, S. Wessel, F. F. Assaad & A. Muramatsu The authors perform Quantum Monte Carlo simulations on the Hubbard model at half-filling on the honeycomb lattice. [This is the relevant lattice for graphene]. As U/t increases there is a phase transition from a semi-metal (SM) (which has gapless excitations at corners of the Brillouin zone, Dirac fermions) to a Mott insulating phase. But, they also find that there is a spin liquid (SL) phase with a spin gap before entering a phase with antiferromagnetic order (AFMI). The latter what one expects from a strong coupling expansion, i.e U >>t), which is described by an unfrustrated Heisenberg model. This is summarised in the figure below. A few random observations: The spin gap is very small Delta s ~ t/40~J/40. The single-particle charge gap Delta sp ( K ) is quite s

This week we are discussion sections 7.5 and 7.6 of Advanced Solid State Physics by Philip Phillips. He gives a nice discussion of poor mans scaling of the Kondo model. One important feature emerges from this analysis is the existence of a strong-coupling fixed point to which is associated a non-trivial energy scale, the Kondo temperature, T K. This means that all physical quantities should be universal functions of the ratio T/TK where T is the temperature. Below is a plot of the measured conductance through a quantum dot. It can be seen that all values lie on a single universal curve, regardless of the value of epsilon (the impurity energy relevative to the Fermi energy) and Gamma (the hybridisation energy), parameters in the underlying Anderson model. The data is taken from this landmark PRL, From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor

Today I gave a lecture on the phase diagrams of carbon and superconductors. I showed a couple of cool videos: This is what happens when you don't properly vent a storage tank. The superconducting hula hoop. One student had a question I did not have a good answer to: How does BCS theory explain that the Gibbs free energy of the superconducting state is lower than the metallic state?

A nice accessible article which discusses the basics of the Kondo effect and how it occurs in quantum dots, carbon nanotubes, and "quantum corrals" is this 2001 Physics World article by Leo Kouwenhoven and Leonid Glazman.

A while back Ben Powell asked "What do we really know in condensed matter theory now that we did not know ten years ago?". Recently, a former student was asked in an interview, "What is the most significant achievement in the theory of strongly correlated electrons in the past decade?". He later asked me how I would have answered this question. We were both encouraged that we had the same answer.... The marriage of dynamical mean-field theory (DMFT) and density functional theory (DFT) based electronic structure calculations. This has given a qualitatively correct (and often quantitative) description of iso-structural phase transitions in cerium and plutonium and of the ground state of transition metal oxides. A nice overview is in this recent preprint by Dieter Vollhardt. A more detailed description is in Reviews of Modern Physics by Gabi Kotliar and collaborators.

Here is tomorrow's lecture for PHYS2020: Thermodynamics and Condensed Matter Physics. I am finding it a challenge to come up with good questions for clickers. Any suggestions welcome.

At an undergraduate tutorial last week I notice how many students were getting into all sorts of difficulties in solving problems because they would do the algebra just by quickly scribbling on a scrap of paper. There is no substitute for working on lined pieces of paper and carefully writing out each line of algebra. This is a difficult discipline which even very smart people need to master.

I am really happy with making the transition from a PC to a MacBook Pro. I mention here two bugs I recently had to solve in the slim chance that my solutions may be of use to others. I installed a new wireless router at home (D-Link) and had a lot of trouble getting the Mac to connect. Various online forums testified to many others having similar problems. (I always find this encouraging). But, they said things like you have to put a $ before the password. None of the suggestions worked. It turned out that when AirPort asks for the "WPA password" for the wireless network it wants the Key not the password. A second issue was I had some VOB videos I wanted to insert in Powerpoint. On the PC I could do this with a hyperlink. It did not work on the Mac. Instead, what works even better is to download the freeware HandBrake which can convert the .VOB files to .mp4 format, and then Powerpoint can imbed them directly in the presentation.

As I emphasized in a previous post , getting a "good" ground state energy with a variational wave function is not necessarily and indication that the wave function itself is very accurate. Computational quantum chemistry (for some good reasons) is fixated on calculating energies. However, I would like to see some concrete criteria and indications or anecdotes concerning the reliability (or lack thereof) of the variational energy. One example that comes to mind is the idea of UHF (unrestricted Hartree-Fock) which allows one to consider breaking spin rotational symmetry. States are then no longer purely spin singlet or triplet. One improves the variational energy but has a wave function which is qualitatively wrong.

Apparently human resource experts say that the interviewee is not objective about how the interview went. Most think it went worse than it did. Most are very hard on themselves. So don't despair after an interview. My experience from being on many interview panels is that people are rarely "sunk" from one poor answer. Furthermore, it is the "vibe" that matters not all the specifics. While on the subject, positive feedback does not necessarily translate into a forthcoming offer. Furthermore, even a verbal (or email) indication of a forthcoming offer is not the same as an official written offer. Sometimes wheels do fall off the wagon....

This weeks reading from Philip Phillips' book, Advanced Solid State Physics was Chapter 7, Quenching of Local Moments: The Kondo Problem. First, the Kondo problem is not just of interest and importance because it exhibits some highly profound many-body physics which is of relevance to not just magnetic impurities in metals. It is the first known example of asymptotic freedom, where an interaction actually becomes stronger at lower energy scales. Phenomenology. In most metals resistivity decreases with decreasing temperature. However, in the presence of magnetic impurities the resistivity actually increases below some temperature. Kondo sought to explain this. He found that a perturbation theoretical calculation actually led to a resistivity that diverged logarithmically at low temperatures. However, it was found experimentally, that the resistivity saturated. So did the magnetic susceptibility and the specific heat coefficient. Furthermore, the Sommerfeld-Wilson ratio for the imp

Understanding and describing the pseudogap state in the cuprate superconductors continues to be a major unsolved problem. There are several physically distinct models for this state of matter (fluctuating d-wave superconductor, density wave state, nodal metal, ...). A key problem to explain are the "arcs" seen in ARPES experiments. A nice comparison of the different models has been given by Mike Norman and collaborators in this PRB paper . Mike Smith and I have just finished a paper where we consider the charge and thermal transport of the different pseudogap models. One thing we encountered was that defining the charge current operator is a rather confusing and ambiguous problem. This has significant effects on the results, particularly the doping and disorder dependence of the conductivity and Lorenz ratio. Consequently, it may be possible to rule out some of the models using transport measurements.

Physics Today has a nice obituary for Conyers Herring , written by Phil Anderson, Ted Geballe, and Walter Harrison. Herring founded the Theoretical Physics department at Bell Labs (and presumably hired a young Phil Anderson). The obituary testifies to Herring's basic contributions to band theory (orthogonalized plane wave theory) and magnetism (exchange interactions between itinerant electrons) and to his scientific leadership and mentoring. Herring was particularly known for the critical review articles he wrote. It is worth reading this tribute from Eugene Garfield, founder of ISI. Forty years ago, Physics Today published Herring's article, Distill or Drown: the need for reviews. I look forward to reading it.

Tomorrow I am giving my first lecture using clickers! Hopefully, it will all work o.k. I have included two questions in the lecture on phase transitions to test student understanding. I found 7 things you should know about clickers helpful. A useful resource on the use of clickers has been prepared by the Carl Wieman Science Education Initiative at University of British Columbia.

Rajiv Singh has a really nice Physics article , which gives a very clear commentary on a recent PRL by Anders Sandvik, which looks at numerical evidence for deconfined quantum criticality in a Heisenberg model which exhibits a quantum phase transition between Neel order and Valence Bond Solid order. Anders' paper seems to raise important questions about the field theory descriptions of these transitions.

Finding unifying principles and concepts to describe large classes of complex molecular materials is no easy task. Seth Olsen has made significant progress in this direction by giving a rigorous quantum chemical justification of a heuristic "colour resonance" theory for methine dyes proposed by Platt almost 60 years ago. Seth has a paper that just appeared in Journal of Chemical Theory and Computation and discusses it on his blog . A key component of Platt's theory is assigning a "basicity" to the molecular fragments which form the left and right part of the dye. This quantity should be an intrinsic property of the fragment and independent (or at least very weakly dependent on) what other fragment it is combined with the form the methine dye. The figure below is taken from the supplementary information from Seth's paper. It shows the basicities one deduces for the different fragments (including different protonation states) that can make up fluorescent pr