A unified picture of iron and cuprate superconductors

Oh, how I love simplicity and physical insight!

There is a beautiful Physics Viewpoint Untangling the Orbitals in Iron-Based Superconductors by Daniel Podolsky.

It describes a Phys. Rev. X paper by Jiangping Hu and Ningning Hao.
They show that a key to understanding the electronic structure of the iron pnictide and chalcogenide superconductors is the S4 symmetry of the lattice of Fe ions.

They are able to explain why the iron chalcogenides do not have holelike Fermi surface pockets whereas the iron pnictides do.

Furthermore, by means of a simple gauge transformation associated with the S4 symmetry they map the s-wave superconducting order parameter to the d-wave order parameter associated with the C_4v symmetry of the Cu ions in the cuprates.

Strong correlations lead to local physics at relatively low temperatures

Antoines Georges has a nice article Thinking locally: Reflections on Dynamical Mean-Field Theory from a high-temperature/high-energy perspective.
The article is a short review dedicated to Dieter Vollhardt on his 60th birthday.

He discusses recent work which compares DMFT to high temperature series expansions for the Hubbard model. They agree for temperatures above about t, the hopping integral. This supports intuition that with increasing temperature physics becomes more local and so DMFT should be more reliable.

He also mentions cold atom experiments which are getting towards low enough temperatures that they could potentially be used to test DMFT predictions.

Born-Oppenheimer in nuclear physics

How do single nucleons and associated excitations couple to collective degrees of freedom such as rotations and shape deformations?
Is there a Born-Oppenheimer approximation in nuclear physics?
What is the origin of non-spherical nuclei and the associated symmetry breaking?
Is the notion of a Jahn-Teller effect and conical intersections relevant?

There issues go back to classic ideas in theoretical nuclear physics for which Aage Bohr, Mottelson, and Rainwater were awarded the Nobel Prize in Physics in 1975. This is discussed in an earlier post.
There is also a classic paper by Hill and Wheeler which does include a discussion of conical intersections [I thank Seth Olsen for bringing it to my attention].

The relevant physics is elegantly discussed in a nice review article The Nuclear Collective Motion by Witold Nazarewicz. Here is an extract

He then goes on to discuss how the deformations of nuclei can be understood in terms of the Jahn-Teller effect.

The figure below is a microscopic calculation from a density functional method of the energy as a function of the nuclear deformation of different Nd isotopes. As the mass number A=N+Z increases there is a transition from a spherical nuclei to an axially deformed one.

This figure is taken from a recent RMP Quantum phase transitions in the shape of atomic nuclei. 

Things I am still looking for discussions are 

1. using diabatic states

2. roles of conical intersections, particularly in dynamics

3. breakdown of Born-Oppenheimer.

Are reaction speed and efficiency linked?

There is an interesting JACS communication
Backbone Modification of Retinal Induces Protein-like Excited State Dynamics in Solution from a group at Oxford.
Here is some of the abstract:

The drastically different reactivity of the retinal chromophore in solution compared to the protein environment is poorly understood. Here, we show that the addition of a methyl group to the C=C backbone of all-trans retinal protonated Schiff base accelerates the electronic decay in solution making it comparable to the proton pump bacteriorhodopsin.
Contrary to the notion that reaction speed and efficiency are linked, we observe a concomitant 50% reduction in the isomerization yield.

The results are of particular interest because most previous attempts to modify the chromophore and/or solvent have not led to much change in the photo-isomerisation rate.

A point I am not clear on, concerns the significance of the statement:
  "Contrary to the notion that reaction speed and efficiency are linked, we     observe a concomitant 50% reduction in the isomerization yield."

The authors point out that "a common feature of highly efficient light-induced biological processes" is "the correlation between ultra-fast dynamics and high reaction efficiency."
One some level this is not surprising: if one process is much faster than all the other competing processes then that process will have a high quantum yield. However, if we change a variable and increase the speed of a process we should not necessarily expect the quantum yield to increase dramatically since the speed of other competing processes may also increase.
Or am I missing something?

I thank Seth Olsen for bringing this paper to my attention.

Changing face of Australian universities

In the past week I saw two articles highlighting changes in Australian universities. The Weekend Australian ran a piece Mass education changes face of universities by Julie Hare.
[There is also a video summary but it lacks some of the important statistics and graphs in the article.]

While the total population of Australia has increased by a factor of less than than three since the 1960's the university student population has increased by a factor of 26!

But, increasingly, graduates work in areas unrelated to their studies. Only half of law graduates will work as lawyers. Just 2 per cent of teaching graduates in NSW each year are directly offered a position in the state school system. About 4750 students are enrolled in journalism schools, but with 100 entry-level positions in mainstream media, many will struggle to get off the starting block. 

Corkindale says: "Does the community, including school-leavers and their parents, need to be made more aware that going to study at a university for a lot of students is, it seems, for 'education's sake', not training for a particular job, profession or career?" 

And should universities and government be more upfront about career prospects, particularly in narrow vocational fields? Or is it a case of caveat emptor?

This illustrates to me that degrees such as Arts and Science should be more valued. You might as well do something interesting and which will develop basic thinking, writing, and analytical skills.

The Sydney Morning Herald published Lonely students play varsity blues by Adele Horin, which points out how isolated and relationally disengaged many students are.
For science, this highlights to me the importance of running tutorials which force students to work together in small groups and the value of student clubs such as the legendary student physics club PAIN at UQ.

Effect of a solvent on excited state dynamics

Last two days I have read through a nice paper Modeling the Nonradiative Decay Rate of Electronically Excited Thioflavin T
by Yuval Erez, Yu-Hui Liu, Nadav Amdursky, and Dan Huppert

The relevant molecule [chromophore] is shown below. It is of particular interest because its fluorescence intensity increases significantly when bound to amyloid fibrils which are associated with Parkinson's, type II diabetes, and Alzheimer's disease.
The key photophysics is associated with twisting about the central carbon-carbon bond.

The experimental results that need to be explained are
-the non-radiative life time increased linearly with the solvent viscosity over 3 orders of magnitude
-the fluorescence intensity decreases with time on the scales of tens of picoseconds

The calculated [via TDFT = Time-Dependent Density Functional Theory] dependence of the ground and excited state energies as a function of the twist angle is shown below.

As the twist angle increases from zero to 90 degrees the transition dipole moment between the ground and excited states decreases by 2 orders of magnitude.

Much the above can be qualitatively understood in terms of a two-site Hubbard model where the two sites correspond to two orbitals localised on the two opposite sides of the molecule.

Excitation from S0 to S1 at 30 degrees then leads to downward movement on the S1 potential energy surface towards the minimum at 90 degrees [referred to as the TICT =Twisted Intra-molecular Charge Transfer] state.
Hence, with increasing time the fluorescence intensity decreases due to decreasing oscillator strength for the S1-S0 transition. However, the twisting motion of the large rings is opposed by friction (viscosity) arising from the solvent.

The paper applies a theory due to van der Meer, Zhang, and Glasbeek that I discussed in an earlier post, to give a quantitative description of the experiment. It is assumed that the viscosity is sufficiently large that the twisting motion is classical and over-damped and so can be described by a Smoluchowski diffusion equation. This is solved to given emission line shapes as a function of time. For times larger than 3 picosecond a diffusion constant of D=0.1/psec gives results consistent with experiment. This value is nicely consistent with that predicted by combining the Einstein relation [fluctuation-dissipation relation]
D= k_B T/friction
with a Stokes formula relating the viscosity to the friction for a rotating disc with the size of a phenyl ring.

A few open issues

• it would be nice to see a plot showing the calculated relationship between the non-radiative lifetime and the solvent viscosity with a comparison of the correlations seen experimentally.

• describing the short time dynamics (greater than 3 psec) requires a larger diffusion constant (smaller friction) consistent with the idea of a frequency dependent friction due to the finite relaxation time of the solvent.

• I assume the classical dissipative dynamics is justified because the timescales of interest are much larger than the relevant thermal time ~ hbar/k_B T ~ 20 fsec.

• A very broad "line shape function characteristic of the Frank-Condon factor" is used. The width is 3300 cm-1. It is not clear what the physical origin of this large width is.

• The line shape function is taken to be a log normal distribution. This form is often used to empirically describe emission lines, going back to a 1969 paper by Siano and Metzler. However, as far as I am aware, there is still no clear theoretical justification for this form.

Assessment creep

It is interesting to see how much undergraduate teaching has changed in just the past decade. Here is a case study for just one course I have been involved in.

In 2001 when I came to UQ I first helped teach a second year undergraduate course Thermodynamics and Condensed Matter Physics. Back then any use of Powerpoint or online resources was a novelty. There was no Blackboard or YouTube. Videos were shown by taking a videocassette to a central projection unit on campus and booking for them to show the video in the lecture at the requested time.
Students expected lecture notes and these were photocopied and handed out.
The course comprised 3 lectures and 1 tutorial per week.
All the assessment was exams: one mid semester and a final.
There were 20+ students enrolled.

What about now?
There are 2 lectures and 1 tutorial per week. In addition students do 3 labs lasting 3 hours.
The assessment has expanded substantially. Students now complete
   23 online reading quizzes
   10 problems sets
   12 tutorial problem sets, done during the tutorial in teams of 3 students
   3 lab reports
   mid-semester exam
   final exam

There are now 50+ students enrolled.
There are no lecture notes. Powerpoint slides are uploaded onto Blackboard after the lectures.
Faculty only grade the online quizzes and the exams.
But setting all this assessment is a significant expansion in workload.
Part time tutors and lab demonstators do the rest of the grading.

Times they are a changing...

Opening the book on water clusters

What is the structure of small clusters of water molecules?

The latest issue of Science has a fascinating article Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy. The associated Perspective by Saykally and Wales is particularly helpful.

In particular, for six molecules there are three alternative structures which are very close in energy, denoted the prism, cage, and book, in the figure above.
Quantum chemistry calculations give different energetic orderings depending on the level of theory used. Furthermore, the zero point motion of the atoms is important.

The high resolution spectroscopy in the paper suggests that the cage structure is the most stable, but only by an energy of about 1 kJ/mol (~10 meV). Contrary to what one may expect, not all the bond lengths are equal.

The value and cost of student reading quizzes

Following the example of some of my colleagues this semester I have started doing pre-lecture reading quizzes for my second year undergraduate course on Thermodynamics and Condensed Matter. Here is how it works.

A reading on the subject of the lecture (usually a Section from the textbook by Schroeder) is assigned.
A brief quiz of 2-4 questions is placed on Blackboard. These can be multiple choice and/or brief essay. The aim is to "force/encourage" students to engage with the text, think about the material, and be better prepared for the lecture. Reading the quiz results before the lecture provides some useful feedback on students levels of understanding and misconceptions. The occasional question, "What don't you understand in the reading?" provides useful feedback to the lecturer who can try and address these in the actual lecture.

The marks/grades for the quiz contribute a small amount to the formative assessment. This seems to be enough to motivate the majority of students to take the quizzes. However, it seems that about 30-50% of the class don't bother. A similar fraction don't bother to come to the lecture, which is serious problem that needs to be addressed.

Overall, I think this is a successful and worthwhile exercise. It is encouraging to see some of the students really do put the effort in and you see how they are wrestling with the material. I have been encouraged by the depth of some of the questions I have gotten in lectures which I think reflect this.

Although, valuable we should be mindful of two significant costs associated with this exercise.

First, it all takes time: designing the questions, uploading them on Blackboard, downloading the responses, assigning grades, reading the responses, and figuring out how to modify the lecture.
Blackboard will mark multiple choice quizzes automatically. For the essay questions, a graduate student, Chao Feng, has written nice software that allows one to look at all the responses in a convenient format. Nevertheless, it still take time.
A minimum of several hours a week is required. To do it really effectively one may need to devote one day a week. I don't know where I or others would find the time...

Second, are we actually hurting the students. I wonder whether this is just another exercise in babysitting students and fear-driven learning. Every year we see to be giving more and more small items of assessment to motivate students to engage with the course and learn something. But, they aren't in high school anymore. Hopefully, sometime in their life they are going to grow up and learn to be responsible, independent, and quasi-disciplined adults who do things because they actually want to or at least because they realise there is some benefit from doing it...

The tragic comedy of academia

Last night my wife and I went to watch the movie Footnote. It chronicles the tensions and competition between a father and son who do research in the same obscure field of Talmudic studies. The movie was made in Israel, is in Hebrew with English subtitles, and received an awarded for best script at the Cannes film festival.

The movie captures some of the silly ways of academia: pedantry, exclusion, ambition, stubborn idealism, ...
I found some of it quite humorous but some of it was a bit too close to the truth to be funny.

Is meso the new nano?

There is an interesting article Emergent Physics the Mesoscale: Report from the special Kavli session at the 2012 APS March meeting by Sam Bader on The Back Page of the May edition of the American Physical Society News.

It sounds like there was a fascinating and contrasting series of talks by Bob Laughlin, Bill Phillips, Angela Belcher, Bill Bialek, and George Whitesides. Apparently Phillips "gave short shrift of the concept of emergence, discarding it mercilessly."

I would be interested to see copies of the talks. Has anyone seen them online?

Overall, this latest focus on the "meso" seems to be driven by hopes of a new burst of funding like what happened with nanotechnology in 2000. [See this brief piece in Science] In the end I think that initiative was a big disappointment scientifically. I feel the whole field was hijacked by people who just relabelled whatever they were doing as nanoscience or nanotechnology. To me it should have been all about control and manipulation at the nanoscale, e.g., single molecule electronics.

The two-site Hubbard model and photochemistry

At the cake meeting I gave an informal talk on how a two-site Hubbard-Holstein model can illuminate some basic and important concepts in the photo-isomerisation of simple molecules such as ethylene. A previous post discusses how the two-site Hubbard models illustrates many basic concepts in quantum chemistry and many-body theory.

Here are a few of the key references and ideas I drew upon in my talk.

A PRA from 2000 (and largely uncited) by Aalberts et al.
Quantum coherent dynamics of molecules: A simple scenario for ultrafast photoisomerization

1. It points out that photoisomerisation only occurs if there are "steric" interactions. i.e. the sigma bonds (not included in the Hubbard model) do not favour a planar arrangement for the molecule. Thus, the ground state is only planar due to the delocalisation energy associated with the pi electrons included in the Hubbard model.

2. This then leads to a twist angle (phi) dependence of the energies of three singlet states similar to that shown below from ab initio calculations in
Photoinduced dynamics of the valence states of ethene: A six-dimensional potential-energy surface of three electronic states with several conical intersection
by Robert P. Krawczyk, Alexandra Viel, Uwe Manthe, and Wolfgang Domcke

Note that the potential energies surfaces of the S1 (V) and S2 (Z) states touch when the molecule is twisted (phi=90 degrees).

This paper also gives a complete parameterisation of an effective 3x3 matrix Hamiltonian for these three low-lying singlet states. The paper never mentions it but this can be compared to the corresponding Hamiltonian for the two-site Hubbard-Holstein model to extract parameters.

3. How does one get a conical intersection between the S0 and S1 (N and V) states?
One must introduce an asymmetry between the energies of the pi orbitals localised on the two carbon atoms. This can be done by pyramidalization, where the hydrogen atoms are moved out of plane (HOOP=hydrogen out of plane) so that the sp2 hybridisation of the sigma orbital is distorted towards the sp3 hybridisation (pyramid) characteristic of methane. The graph below shows the ab initio calculation of the eigenenergies for a twisted geometry (phi=90 degrees) as a  function of the pyramidalisation angle.

In the Hubbard Holstein model the co-ordinate on the horizontal axis is q=q1-q2, the difference in the on-site vibrational mode co-ordinate between the two sites.

Some of the above connections are aided by the classic paper
Neutral and Charged Biradicals, Zwitterions, Funnels in S1, and Proton Translocation: Their Role in Photochemistry, Photophysics, and Vision
Vlasta Bonačić-Koutecký, Jaroslav Koutecký, and Josef Michl

and a 1985 Journal of Chemical Education paper
Electronic structure in pi systems. Part I. Huckel theory with electron repulsion 
Marye Anne Fox and F. A. Matsen

The former does not mention the Hubbard model, but the latter does.

The value of single author papers

There can be significant career value is writing a single author paper, particularly for graduate students and postdocs. It clearly shows that one has become independent, and is not completely dependent on senior people for ideas, guidance, techniques, ...
Hence, one is ready for a faculty position.

I try to encourage my postdocs, particularly senior ones to do this, occasionally suggesting my name should not be on a paper because I have not made a significant contribution.

Unfortunately, there are some senior people who will not allow or will strongly discourage this. They believe that if they pay the salary or provide the lab that entitles their name to be on every paper produced by someone in their group (even sometimes associated junior faculty). Hence, negotiating single authorship can be a difficult and sensitive subject. Thus, it can also be potential career killer...

For experimentalists single author papers may be difficult, except for review articles. For theorists it should be relatively straight-forward.

Common structural motifs for conical intersections

Finding conical intersections between potential energy surfaces is key to understanding photochemistry, particular for ultrafast non-adiabatic reactions. An earlier post pointed out how often these conical intersections occur at a molecular geometry where there is a local triangular symmetry. This leads naturally to an effective Hamiltonian which has a C_3 (or higher) symmetry and the degenerate eigenstates are in the two-dimensional E representation.

However, there is more to the story...

There is a nice recent review Electronically excited states and photodynamics: a continuing challenge by Plasser, Barabatti, Aquino, and Lischka.
They present a Table of common motifs for "primitive conical intersections".

These do not have the "hidden" triangular symmetry discussed above.

The authors also suggest there are three distinct excited state pathways, summarised schematically in the diagram below. They respectively occur in the molecules shown:

How fast are chemical reactions?

Calculating the rate of a chemical reaction in a condensed phase environment is a highly non-trivial problem. It is easy to make a hand-waving argument that the rate is proportional to an Arrhenius factor associated with the activation energy. But, getting the prefactor is a rather subtle problem. There is a seminal 1990 review Reaction rate theory: 50 years after Kramers by Hanggi, Talkner, and Borkovec. One of the main results is the Kramers turnover described below.

For "strong" friction the rate is controlled by "spatial diffusion" and given by

where gamma is the friction which can depend on frequency (i.e. be non-Markovian). This rate decreases monotonically with increasing friction.

For "weak" friction the rate is controlled by "energy diffusion" and increases monotonically with increasing friction.

Interpolating between the two regimes is difficult. But, the important point is there should be a Kramers turnover in the prefactor. The dependence on friction is shown below

Observing this Kramers' turnover has been a bit of a "holy grail". One way one can tune the friction is by varying the viscosity (or diffusion constant) of the fluid environment by varying its density via pressure. The data below shows the rate of photoisomerisation of trans-stillbene as a function of the diffusion constant. 

It appears to show the turnover but there are quite a few questions about the details.... It seems the activation energy varies with pressure and the barrier frequency (omega_b) varies with temperature (see this 1995 paper).

A somewhat accessible discussion of all of this in a 1990 Physics Today article, Chemical Dynamics in Solution by Fleming and Wolynes.

Effective weekly group meetings

I believe every research group should have one timetabled meeting each week. If not, people tend to get disconnected and drift. Students can get isolated and lose motivation. Attendance should be compulsory.

Effective meetings are enjoyable and productive. People learn new things, particularly what is relevant to their own research. Furthermore, informal interactions associated with these meetings can lead to breakthroughs, both minor and major.

What should be the format of the meeting? A balance between structure and informality seems to be key. Talks on the whiteboard are preferable to power point presentations. Here are a few ideas on meeting content:

• A group members talks about what they are currently working on. This provides feedback and accountability in a friendly environment. People learn more about what other group members are working on. Hopefully this leads to other conversations.
• A group member talks about an important paper by someone else. It can be an old "classic" paper or a recent one. Everyone gets educated. Students learn what might be important or not. Everything in Nature and Science is not important or reliable.
• Everyone in the group brings a paper they have recently read to the meeting. They then have limited time (e.g. 7 minutes) to convince everyone else they should read the paper. This encourages people to keep up with the literature and be reflective about what they are reading.
• A group member gives a practice of a seminar or conference talk they are due to give soon. The group provides constructive feedback. This can significantly enhance the quality of presentations group members give. [I remember when I was a postdoc, another postdoc told me he was more scared of giving the practice talk than the conference talk!]
• The dice meeting. [I have not done this but heard of it in German research groups]. A paper from the literature will be discussed. Everyone in the group reads it and prepares a talk on it. But, at the meeting a dice (or two) is rolled. Whoever's number shows up gives the talk.
• Questions should be encouraged. Sometimes a prize (e.g., a bottle of wine) can be awarded for the person who asks the most questions.
• Serving food (e.g. a cake) is a good thing.

I welcome other suggestions that readers have found particularly effective and useful.

Characteristics of optimal doping in cuprates

In the cuprate superconductors there is a value of the doping at which the superconducting transition temperature is a maximum (optimal doping). Coincidentally (?) this also seems to the doping at which the metallic phase is most non-Fermi liquid like. Some theories (especially due to Varma) try and connect these two phenomena via a quantum critical point below the superconducting dome. An earlier post discusses how the entropy is maximal and the thermopower changes sign near optimal doping.

A cluster DMFT (Dynamical Mean-Field Theory) calculation by Kristian Haule reproduces the correlation between high-Tc and anomalous metallic properties. The figure below shows the Matsubara frequency dependence of the imaginary part of the self energy (at wave vector (0,pi) = anti-nodal region) (top) and the anomalous self energy (related to the superconducting pairing) for different dopings.

In a simple Fermi liquid the slope of the upper curve at low frequencies is related to the quasi-particle weight.
Haule concludes the quasi-particles are most incoherent and the scattering rate the largest around optimal doping.

Students love video demonstrations

Today I gave a lecture on first-order phase transitions to undergraduates. Again I find the students love the videos I show.
 I mostly use videos from the Video Encyclopedia of Physics Demonstrations, which I got my dept. to buy a decade ago. However, now you can find virtually anything you need on YouTube! For example, here is a nice one of regelation of ice which demonstrates that the solid-liquid phase boundary has a negative slope.