Going beyond the data?

In a 2007 Nature paper Engel et al. reported the data below showing the amplitude of an optical signal versus time.

The lower curve is the Fourier transform [using a new numerical method they developed explicitly for this paper] of the upper data.
They interpreted this data as evidence for quantum coherence between the excited states of different chromophores in a photosynthetic protein, since an oscillatory signal is a signature of quantum interference (Rabi oscillations). Engel et al. went on to claim that this coherence enabled the biomolecule to function in a highly efficient manner because:

…the system is essentially performing a single quantum computation, sensing many states simultaneously and selecting the correct answer, as indicated by the efficiency of the energy transfer. In the presence of quantum coherence transfer, such an operation is analogous to Grover's algorithm, …such a scheme can provide efficiency beyond that of a classical search algorithm.

This Nature paper greatly excited many in the quantum information community and has led to a host of theoretical papers about "quantum biology". The paper has already been cited hundreds of times.

But is this enthusiasm and hyperactivity justified? Given the noisy data and the absence of any concrete measurements of entanglement (e.g., violation of Bell inequalities) are the conclusions and claims really justified? I do not think so, as I have expressed several times in previous blog posts.

There is an interesting new preprint A critical view on transport and entanglement in models of photosynthesis by Tiersch, Popescu, and Briegel which has the abstract:

Quantum effects in biological light-harvesting molecules, such as quantum coherence of excitonic states and entanglement have recently gained much attention. We observe a certain discrepancy between the original experimental work and several theoretical treatments of coherent excitation transport in light-harvesting molecules. Contrary to what is generally stated, we argue that entanglement in such molecules is generally not equivalent to the presence of coherence but mostly introduced by initial assumptions underlying the models, and that entanglement, as opposite to coherence, seems to play no role in the transport efficiency.

Preparing good talks is hard work

Almost anyone can cobble together some powerpoint slides.
But, actually preparing a good talk is very hard work.
This is on my mind because this week I am working on a colloquium I am giving this friday.
Why is it hard work, even for the experienced?
Because you have to decide what material to leave out!

A dubious argument for quantum biology

Over the past decade there has been an amazing set of experiments performed which involve seeing quantum interference associated with the wave nature of very large molecules. The figure below is taken from a nice review article by Markus Arndt and Klaus Hornberger. It shows some of molecules, including as many as one hundred atoms and of the order of one thousands of elementary particles (protons, neutrons, and electrons).

The figure below shows some of the interference fringes seen.

Occasionally I hear these incredible experiments used as a "proof of principle" to justify the possible role of significant quantum effects in biology. However, I think this a fanciful view because of the following significant constraints in the experiments:

• They involve single molecules
• They are performed in vacuum.
• The quantum interference is associated with the centre of mass degree of freedom. By, definition this does not couple to all the internal degrees of freedom.

This is a very long way from a biological cell where the molecules are packed close to one another and interact strongly with their surrounding environment of water.

I cannot deny this

This week the UQ Physics Colloquium was given by John Cook on Communicating Climate Science and Countering Disinformation. He is a UQ physics graduate and now writes an influential blog Skeptical Science which aims to present peer-reviewed climate science in an accessible fashion that answers climate change skeptics. He has also developed a popular Phone application which answers 10 common used arguments of climate change skeptics. He recently published a book Climate Change Denial.

Here is my summary of some of the main points.

97 out 100 climate scientists believe that humans are causing carbon dioxide levels to rise.
Why?  There are many different lines of evidence.
In contrast, only 58% of the general public believe this. This is because the mainstream media gives the impression of a 50/50 debate.

Several references were made to a book Merchants of Doubt"  by Naomi Oreskes and Erik Conway which documents how vested financial interests have funded disinformation campaigns to undermine public debate about issues on which the scientific evidence is clear.

John summarised a paper Denialism: what is it and how should scientists respond?
which argued that there are 5 characteristics common to other denials as well. e.g., dangers of cigarette smoking, HIV causes AIDS, young earth creationism,
[I think this also applies to some proponents of quantum biology!]

1. Cherry picking of data
e.g. glacier mass balance. there are a few glaciers that are indeed growing. But the vast majority are shrinking.
Human carbon dioxide emission is only a small fraction of total emission from the planet. This ignores that natural processes balance out absorption and emission.

2. Promoting the views of fake experts
e.g. The petition project - 31,000 "scientists" have signed it.

3. Impossible expectations
Always demanding more evidence and complete certainty.

4. Logical fallacies
Climate changed has happened before

5. Conspiracy theories
e.g. climategate. But, 8 independent investigations have found no evidence of conspiracy

In contrast, to denialism genuine skepticism considers all the evidence and weighs it. I would add a sixth common feature of denialsm: a lack of humility to acknowledge that their lack of relevant scientific expertise, experience, and knowledge may just possibly mean that their opinion is not valid.

John answered one question I have had for a while. Why do weather fluctuations increase with increasing global temperatures?
This is due to the water cycle because higher temperatures lead to more evaporation, more drought, more water in atmosphere.

There is one complex and subtle issue which was not addressed and I do not understand. That is the views of and role played by distinguished physicists such as Freeman Dyson, Bob Austin, William Happer, and Bob Laughlin. They are not climate scientists but on some level are "skeptics". Indeed, some of them unsuccessfully petitioned the American Physical Society to change its policy on climate change. Why do they believe what they do? Perhaps it is just a mixture of physics hubris and political sympathies...

Overall, I thought this was a great colloquium. It generated a lot of good questions and discussions.

How much money should I ask for?

As little as possible! What?
Occasionally when I review grant proposals I am dismayed by the large amount of money that some people, especially junior people, ask for. I wonder who, if anyone, is advising them to do this. A few things to consider when you prepare your proposed budget:

• The greater the requested budget the greater the scrutiny of the application.
• If your budget is 2 or 3 times the budget of competing applications the funding agency will almost always think that it is better to fund 2 or 3 groups rather than just one.
• Getting some money is always better than getting none, especially if you are starting out.
• The kudos of actually getting the grant is fairly weakly dependent of how much money you actually get.
• The maximum possible allowed budget is not a good guide as to how much you should ask for. A better guide is the average size of grants previously given to applicants of comparable stature and experience to you.

And if you do get the grant, but the budget is trimmed substantially, don't whine. There are plenty of unsuccessful applicants who would happily take the money.

Singing superlatives of superconductivity

I recently gave two lectures on superconductivity to a fourth year undergraduate Condensed Matter Physics course. In hindsight, there are few points that I did not discuss but should have included:

• the relevance of BCS theory and Cooper pairing to nuclear physics and neutron stars
• how the Meissner effect can be viewed as a photon obtaining mass and that this idea is key to electro-weak theory and to the Higgs boson

These issues are nicely discussed in an article Superconductivity's Smorgasbord of Insights: A Movable Feast by Adrian Cho which appeared in Science last month to celebrate the Centenary of Kamerlingh Onnes discovery. It contains the figure below.

The complex nature of the self energy

I am trying to understand under exactly what conditions it is (or is not) meaningful to use a self energy to describe and understand experiments on a strongly correlated metal which may be (at least in some sense) a non-Fermi liquid. This is particularly motivated by a recent paper on the overdoped cuprates.

Below are some statements which I am trying to ascertain the truth of and relationship between them. I believe
1. and 2. are always true.
3. and 4. are equivalent but are not always true.
5. is true.
I am not sure about 6.

1. The one-electron Greens function G(k,E) is an analytic function of energy E.

2. One can always define a self energy by Dyson's equation

where G0 is the non-interacting Greens function. This self energy will be an analytical function of E.

3. If E is treated as a complex variable G(k,E) has isolated simple poles in the complex plane. These poles correspond to quasiparticles. One can then write down a Boltzmann transport equation for these quasiparticles.

4. The self energy can be written as a convergent perturbation expansion. This ensures adiabatic continuity and the existence of quasi-particles.

5. If G(k,E) has a non-integer power law dependence on E there will be a branch cut in the complex plane. This means a description in terms of quasi-particle poles is inadequate.
[This is what happens in one dimension with Luttinger liquids].

6. Branch cuts in the plane may mess up the Kramers-Kronig relation which relates the real and imaginary parts of the self energy.

So, I welcome thoughts about the above claims.
Is there somewhere that this is all written down and discussed clearly?
I have gleaned the above from my subconscious memory of a diverse range of sources.

The figure is from Piers Coleman.

Don't you love automated email!

Undergraduate lecture on broken symmetry

Broken symmetry is one of the most important concepts in physics from the second half of the twentieth century. Hence, surely all undergraduate physics majors should learn it. Here are the slides from a lecture I gave last week to PHYS2020 Thermodynamics and Condensed Matter. In the lecture and (in a tutorial) I get the students to try and solve the problem below.  

I then illustrate the solution (and the associated equal angles) with bee hives and some videos of soap films.

This version is taken from the book Introduction to statistical physics by Herson Huang. 

I first encountered the problem in my second year of graduate school when Jim Sauls (later to become my advisor) in the very first lecture of a graduate condensed matter course asked students to solve it "cold" [right there in the lecture and hand in a solution] without the suggested form of the solution given above. 

I would be interested if someone knows the associated history of this problem.

The most precise measurement of Planck's constant

Compared to some fields (e.g. biology, high energy physics, philosophy, history, movies, historical theology) I think most Wikipedia articles on condensed matter physics and theoretical chemistry are sporadic in quality. It would be wonderful if someone took the initiative and time to improve them. I keep trying to encourage students to do this but not succeeding. But, that is another story....
The actual purpose of this post is just to highlight some of the actual content of a really nice entry on the Magnetic flux quantum, [h/2e] which states:

The magnetic flux quantum may be measured with great precision by exploiting the Josephson effect. In fact, when coupled with the measurement of the von Klitzing constant R_K = h/e², this provides the most precise values of Planck's constant h obtained to date. This is remarkable since h is generally associated with the behavior of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both collective phenomena associated with thermodynamically large numbers of particles.

This point is also stressed and discussed at length in Bob Laughlin's book A Different Universe which this blog contains many quotes from.

Writing effective talk abstracts

This is not easy. It is worth the effort. You want to convince people to attend your talk: it will be interesting, important and understandable.

Things to do:

• tailor your abstract to your audience (e.g. their backgrounds and interests)
• explain why the topic is interesting
• use words sparingly
• find a balance between being generic and too technical
• include some key scientific ideas you will discuss
• include a brief statement of your main results
• include a few relevant references the really keen may want to look at
• re-write it several times (especially if you are in-experienced)

Things to avoid

• superfluous phrases such as "In this talk I will..." and "I will end with some conclusions".
• using acronyms: nLAs, DFT, LDA+DMFT, NMR, ENDOR etc. 
• hype

But, it is always easier to tell people what to do rather than actually do it yourself! So I offer up for critique my latest abstract: for the UQ Physics Colloquium next friday.

Quantifying the limited role of quantum dynamics in biomolecular function

Quantum effects such as coherence, interference, tunnelling, and entanglement are well established at the level of atoms and small molecules in a vacuum. However, could quantum "weirdness" occur in large biomolecules which are in thermal equilibrium with water at room temperature? I will show how it is possible to give a quantitative description of quantum decoherence for the excited states of optically active biomolecules in a native environment [1].

A key to a quantum description of biomolecules are the multiple time, energy, and length

scales associated with the dielectric relaxation of proteins and water. In most cases appears that quantum coherence requires time scales less than 1 picosecond and distances less than 10 nm.

This work provides a framework to critical evaluate the claims of some physicists (and New Age pop psychology gurus) that quantum effects are important in biology. Such speculations have increased in the past few years stimulated by some experimental results concerning photosynthetic systems.

I contend that most claims of "quantum biology" are based on wishful thinking and involve

(i) debatable data analysis with an excessive reliance on curve fitting, 

(ii) a misunderstanding of what biological evolution implies about efficiency, and/or 

(iii) speculations which go far beyond what the experimental data may imply.

Nevertheless, there is a lot of interesting physics involved in understanding the role of quantum decoherence in biomolecular function at sub-nanosecond timescales.

One key challenge is for specific class of processes defining an effective Hamiltonian. This must find a balance between the level of detail normally used in physics, chemistry, and biology. I will briefly illustrate this with recent work on Green Fluorescent Proteins [2]. A second challenge is solving the quantum dynamics in realistic parameter regimes where there is no simple separation of time scales. 

[1] J. Gilmore and R.H. McKenzie, J. Phys. Chem. A 112, 2162 (2008).

[2] S. Olsen and R.H. McKenzie, J. Chem. Phys. 130, 184302 (2009).

Lecture on superfluids

Last week I gave half a lecture on the phase diagram of helium and superfluidity to a second year undergraduate class on Thermodynamics and Condensed Matter Physics. The lecture includes:

• a discussion of the differences between the phase diagrams of 3He and 4He
• a list of the 4 Nobel Prizes awarded for work in superfluidity [Landau, Kapitsa, Osheroff, Richardson, and Lee, Leggett] (I did not include BECs but should have]
• a video of the superfluid transition
• a discussion of an amazing experiment on the space shuttle which determined the critical exponent for the specific heat at the superfluid (lambda) transition to five significant figures.

Measures of (static) electronic correlations in molecules

I particularly like the Figure below taken from a paper The radical character of the acenes: A density matrix renormalization group study by Johannes Hachmann, Jonathan Dorando, Michael Avilés, and Garnet Chan.

HUNO = highest occupied natural orbital          
LUNO = lowest occupied natural orbital

Note how as the acene gets longer the spread in orbital occupation number increases.

In a nice review article Schmidt and Gordon state:

The presence of occupation numbers between 0.1 and 1.9 indicates considerable multireference character. 

(Multi-reference character means how many Slater determinants are required to describe the state.)

It seems to me that the spread in the above distribution gives a measure of the number orbitals M one needs to include in the active space of a Complete Active Space (CAS) calculation. In a Hartree-Fock calculation the occupations are all 2 or 0. The number of natural orbital occupations that deviate significantly from 2 or 0 is a good measure of M. It may be possible to relate this to various quantum entanglement measures.

Readers with backgrounds in solid state physics may note the similarity to the above picture to how  in Fermi liquids one can quantify the strong electronic correlations in terms of the discontinuity in orbital occupation number at the Fermi surface (discussed in an earlier post).

What should motivate us?

I just received by snail mail the December 2010 issue of Physics Today.  The whole issue is devoted to Subrahmanyan Chandrasekhar, marking the centenary of his birth. There is a fascinating and challenging article Some memories of Chandra by Robert Wald and four other scientists, including Roger Penrose. Wald states:

Of all the scientists I have met, Chandra had the highest standards for both intellectual rigor and personal integrity. He applied those standards most uncompromisingly to himself, but he also did not tolerate failings by others in such matters. He was particularly intolerant of scientists motivated primarily by the hope of receiving recognition from others rather than by a deep, inner conviction that their work was of importance and interest, whatever anyone else might think. He was equally intolerant of scientists who rested on their laurels or were otherwise lazy or sloppy, rather than applying their full intellectual efforts toward their work.

The Hidden Fermi liquid theory

This week I have been re-reading Phil Anderson's paper,  The `strange metal' is a Fermi liquid with edge singularities. Here is a brief summary of some of the main things I gleaned from the paper. The question is:
What is the nature of the excitations (and one-electron Greens function) of the Hubbard model in the infinite-U limit and for large dopings (perhaps x greater than 0.3) above which superconductivity occurs?
Anderson claims:

• the strong interactions lead to a significant particle-hole asymmetry [which should be visible in tunneling spectra] 
• excitations exhibit anomalous forward scattering
• the quasi-particle weight Z vanishes on the Fermi surface

• there is  a formal similarity of this problem with that of Fermi-edge singularities in the X-ray spectra of metals, where the one-electron Greens function has a power law decay associated with the phase shift from an infinite potential.

• A simple argument (exploiting the Friedel sum rule) gives the main quantitative prediction of the theory a value for the doping (x) dependence of the exponent

• a power-law frequency dependence of the optical conductivity
• this theory may have some similarities to one of Norman and Chubukov.
• Quasiparticles emerge in the superconducting and pseudogap states: "But above T* and above the gap energy the quasiparticles experience power-law decay: essentially, the line of quasiparticle poles turns into a cut in the complex  plane."

Superconductivity for the general public

In honour of the 100th anniversary of the discovery of superconductivity Julien Bobroff and collaborators developed a really cool site meant for the general public. It contains many videos and discussions of basic science.

Two particular videos are of interest, one a general introduction to the subject and the other historical details about the original discovery.

I also really liked the video below.

My favourite quote about thermodynamics

A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.

Albert Einstein

Thermodynamics is a great source of both profound and humorous quotes. Many are collected at Wikiquote and on a site due to Franco Nori.

Some morbid but fascinating discussion about the mental health and suicides of many famous pioneers of thermodynamics and statistical mechanics are on a somewhat strange site Encyclopedia of Human Thermodynamics.

Lecture on Fermi liquid theory

Last week I gave a single lecture on Fermi liquids to the honours year undergraduate course PHYS4030 Condensed Matter Physics.
The slides do not include the expression for the quasi-particle lifetime or the rough argument  (based on phase space considerations) used to justify its form. This is because I do that on the whiteboard.
Perhaps such an important topic justifies more than one lecture...

Increasing undergraduate student engagement

My wife brought to my attention a New York Times article Improving the Science of Teaching Science which discusses a recent Science paper Improved Learning in a Large-Enrollment Physics Class. Science Now has this summary:

Any physics professor who thinks that lecturing to first-year students is the best way to teach them about electromagnetic waves can stop reading this item. For everybody else, however, listen up: A new study shows that students learn much better through an active, iterative process that involves working through their misconceptions with fellow students and getting immediate feedback from the instructor.

The research, appearing online today in Science, was conducted by a team at the University of British Columbia (UBC), Vancouver, in Canada, led by physics Nobelist Carl Wieman. First at the University of Colorado, Boulder, and now at an eponymous science education initiative at UBC, Wieman has devoted the past decade to improving undergraduate science instruction, using methods that draw upon the latest research in cognitive science, neuroscience, and learning theory.

In this study, Wieman trained a postdoc, Louis Deslauriers, and a graduate student, Ellen Schelew, in an educational approach, called “deliberate practice,” that asks students to think like scientists and puzzle out problems during class. For 1 week, Deslauriers and Schelew took over one section of an introductory physics course for engineering majors, which met three times for 1 hour. A tenured physics professor continued to teach another large section using the standard lecture format.

A psychologist James Stigler criticised some of the methodology but stated: “As a psychologist, I’m ashamed that it is physicists who are leading this effort, and not learning scientists.”

Et cetera Et cetera

For a while I have been uneasy about the use of "etc." in papers, talk slides, grant applications, etc.

I see too many sentences like
"this research has important implications for chemistry, physics, materials science, etc."
or
"quantum theory can describe atoms, molecules, etc."

Somehow, it communicates to me laziness on the part of the author. Intuitively, I think I object when it is not completely clear or universally agreed upon what the "etc." actually is.

I found it helpful to read the Wikipedia page for Et cetera which states

The phrase et cetera is often used to delete the logical continuation of some sort of series of descriptions. For example, in the following expression...

We will need a lot of bread: wheat, granary, wholemeal, etc.

... the "etc." stands for "and other types of bread".

So, if you have actually not thought out what you would list instead of "etc." or if others may disagree with your list, it would be better not to use "etc.".

But this is part of my agenda that we should ban the indiscriminate use of lists, nLAs etc.

Are there quasi-particles in the overdoped cuprates?

A key question concerning the metallic state of cuprate superconductors is: to what extent they can be described by something like a Fermi liquid with quasi-particle excitations? As the doping increases away from the Mott insulating state this is more likely to be possible. If it is possible one should be able to define an electronic self energy for the metallic state. Many experiments have been interpreted in these terms. But there are fundamental questions, particularly stressed by Phil Anderson (and embodied in his Hidden Fermi liquid theory) about whether this is really possible, even in the overdoped region.

Jure Kokalj and I have just finished a paper Consistent description of the metallic phase of overdoped cuprate superconductors as an anisotropic marginal Fermi liquid

We consider a model electronic self energy, motivated by Angle-Dependent Magneto-Resistance (ADMR) experiments, and consisting of two terms:

The first term has the frequency and temperature dependence of a Fermi liquid (FL) and is isotropic on the Fermi surface.

The second term has the same frequency and temperature dependence as that of a Marginal Fermi liquid, [but in contrast to the original form proposed by Varma et al.] is anisotropic over the Fermi surface, and vanishes in the same directions as the superconducting gap and the pseudogap observed in underdoped cuprates. 

This model self energy gives a consistent description of results from ADMR, specific heat, de Haas van Alphen, and ARPES experiments. In particular, we have reconciled a strongly doping dependent anomalous scattering rate observed in ADMR with an almost doping independent specific heat. This was a question originally posed to us by Nigel Hussey and which I discussed in an earlier post, A key property of cuprate superconductors.

Although the scattering can be dominated by the anisotropic Marginal Fermi liquid term the quasi-particle renormalization is dominated by the FL term.

We also show that several predictions of the Hidden Fermi liquid (HFL) theory (proposed by Anderson and Casey) is inconsistent with the observed temperature and doping dependence of the scattering rate and with the magnitude of the specific heat.

The figure below shows the doping dependence of the density of states at the Fermi energy (which is a measure of the quasi-particle renormalisation) that is implied by the form of the imaginary part of the self energy required by the results of ADMR experiments.

We welcome feedback and comments.

The Horrible truth about thermodynamics

When my kids were younger and we were on sabbatical in the UK we came across the wonderful series of kids books, Horrible History and Horrible Science. 

Below is a scan of the pages on the laws of thermodynamics. Note the stereo-typically British view of Australians (bunch of lazy boozers)!

If you click on the images you can see a larger view.

A string of anecdotes does not make an argument

Previously I have posted that one key to giving a good talk is to never offer undefendable ground. i.e., don't make dubious claims that will distract your audience from your main point and undermine your credibility.

On Friday at UQ, David Jamieson, Head of the School of Physics at the University of Melbourne gave a colloquium Physics, Power, and Climate change.

I found the colloquium rather disappointing and frustrating because he made a number of debatable claims. But, perhaps I mis-heard or mis-understood him. I welcome others to clarify or correct me.

1. He began by briefly promoting his own research saying "it is difficult to imagine future technologies if you are not working in our centre", referring to the ARC Centre for Quantum Computing and Communication Technologies, which works on the Quantum Internet.

2. Chemists may find  strange the claim that quantum computing was essential to understanding how caffeine works.

3. People in the majority world need access to electricity so they can get on Facebook!
Actually, I thought more people in India have access to mobile phones than to clean water!

4. It was claimed that arguments for the widescale adoption of solar power were flawed "because they ignored the second law of  thermodynamics", i.e. the problem of the low efficiency of solar cells. I felt this was a cheap shot since I have never heard anyone who advocates photovoltaic cells claim they were anything more than 10-20% efficient. The internal combustion energy and coal-powered stations also suffer from the second law. I believe a Carnot efficiency of the latter is about 20-40%, but we are quite comfortable with that.

The climax of the talk was the idea that power from nuclear fission is the only viable option for responding to climate change.

5. He stressed how dangerous hydroelectric power, citing an accident in Russia which killed 75 people.This was compared to the Three Mile Island nuclear accident which killed no-one. Furthermore, it was claimed that since then there are been no major nuclear accidents since then.

The colloquium normally ends by 5pm but Jamieson was still speaking at 5:20pm and so I left. [Never go overtime. To me it just communicates either arrogance, rudeness, or dis-organisation]. But, perhaps I missed some important qualifiers in the conclusions and question time.

He began to discuss pathologies of argument concerning climate change and
alternative energy. It seemed to me Jamieson himself adopted some of these same pathologies himself. e.g., arguing by anecdote, by analogy, gaining emotional sympathy by tapping into peoples frustration about biased and unbalanced media coverage,...

The colloquium was entertaining and thought provoking. I learnt a few things I did not know. But, to me the debatable claims above created too many credibility problems for me to be convinced of the conclusions.

Some might claim that I did not like the colloquium because I did not like its conclusions. However, I am actually quite open to the possibly painful conclusion that the future energy mix must include a nuclear fission component.

Much better talks on this subject are those given by David MacKay (Cambridge) and by Nate Lewis (Caltech) which you can watch online. To me they are thorough, balanced, and scholarly.

This friday Paul Meredith from UQ will present a colloquium Sun, Power, and Energy: Opportunities and Perspectives for a Solar Powered Australia. Unfortunately, I will miss it as I will be in Sydney.

Coherent insights into destruction of a Fermi liquid

Today I read a beautiful paper, Coherence-Incoherence and Crossover and the Mass-Renormalization Puzzles in Sr2RuO4 by Jernej Mravlje, Markus Aichhorn, Takashi Miyake, Kristjan Haule, Gabriel Kotliar, and Antoine Georges

The paper is another victory for Dynamical Mean-Field Theory (DMFT) as it shows how LDA+DMFT calculations can give a quantitative description of a whole range of experiments on this strontium ruthenate.

Aside and context: This material originally attracted a lot of interest because it is a transition metal oxide with the same perovskite crystal structure as the cuprate superconductors. But, it turns out to be very different because it has a Fermi liquid metallic state and the superconductivity is triplet rather than singlet.

But here are some physical insights I found particularly interesting in the paper

a. It explains why the coherence temperature and band renormalisation (effective mass) is different for the different bands, and not just determined by the band width. The key issue is the Hund's rule coupling.

b. The temperature at which the Fermi liquid properties occur is much lower for two-particle properties than from single-particle properties. This also occurs in the Kondo problem where the Kondo resonance persists up to temperatures of about 2 times the Kondo temperature, T_K, whereas the magnetic susceptibility only becomes weakly temperature dependent below about 0.2 T_K.
n.b. This is an order of magnitude difference. 

c. The Hund's rule coupling tends to suppress the coherence scale because it projects the spin degrees on freedom onto a subspace of low-lying states which have a reduced effective Kondo coupling to their environment. This occurs in several contexts:

• Single impurity models [see this recent PRL by Nevidomskyy and Coleman, which contains the figure below]
• DMFT studies of model Hamiltonians
• transition metal oxides due to screening of U by large spatial extension of correlated orbital
• iron pnictides due to screening of U by large polarizability of screening orbitals

 One puzzling experimental result [mentioned in the third paragraph] which the authors do not attempt to explain is why the interlayer resistance has a significantly different temperature dependence to the intralayer resistance. In particular, why is the interlayer resistance a non-monotonic function of temperature? The authors hint that this is related to the destruction of quasi-particles. But, showing this connection and actually calculating such a temperature dependence with one set of parameters seems to be rather difficult, particularly without a momentum dependent self energy. Urban Lundin and I wrote a paper about the problem several years ago.

Learning my academic lineage

I must be getting old. Often as people get older they start to trace their family genealogy to learn "where they came from". I had been told since I was a child that my paternal great-great-grandfather was  Samuel Shannon, one of the first Jewish settlers in Australia.

But, I had heard that scientists sometimes like to trace their academic lineage, where their Ph.D advisor is their parent, and the advisor of their advisor is their grandparent, and so on. Indeed there is a Mathematics Genealogy project which traces everyone back to Euler and Gauss...

So I got intrigued and checked out my own lineage. I was oblivious to this, beyond who my "great-grandfather" was. But, I did not know he had such a distinguished lineage. Finding the rest of my lineage was quite easy using Wikipedia because it listed the advisors of most of my "forebears". Here is the line:

Helmholtz
Arthur Webster (Founder of the American Physical Society)
Albert Wills
Isidor Rabi
Julian Schwinger
Walter Kohn
Vinay Ambegaokar
Joe Serene
Jim Sauls
Ross McKenzie

Exam questions for condensed matter

I find coming up with new tutorial, assignment, and exam questions.  Choosing which questions to use is a challenge. Here are some questions I have used over the years in a fourth year undergraduate Condensed Matter Physics course based on Ashcroft and Mermin. I welcome comments on these questions and links to resources for other questions.

One useful resource [which I should look at more often] is Solid State Physics: Problems and Solutions by Mihaly and Martin.

Was Arrhenius a physicist or chemist?

I was surprised when the speaker at todays Physics colloquium [which was on climate change] David Jamieson kept referring to Svante Arrhenius as a physicist. I always thought he was chemist! This claiming of Arrhenius as "one of our own" probably irritated me a little because the speaker made some other claims which I felt were rather debatable [perhaps more on that in another post...]. So I went and read the Wikipedia page on Arrhenius which turns out to be pretty fascinating reading [e.g. the almost failed thesis which got him the Nobel Prize! and the commitment to eugenics...].

I now concede you could argue that he was a physicist, because he seems to have done a degree in physics and mostly worked in physics institutes. However, he basically worked on and helped found what today is called physical chemistry (electrolytes and reaction kinetics). His contribution to understanding the greenhouse effect was certainly from the perspective of a physical chemist. He was awarded the Nobel Prize in Chemistry, but was a longtime member of the awards committee for physics.
Today I think Arrhenius would be classified as a physical chemist and would be in a Chemistry department.

What about other "physicists" who have received the Nobel Prize in Chemistry?
I would perhaps classify Lars Onsager as 30% per cent physicist, Alan Heeger as 60% physicist, and Walter Kohn as 99% physicist.

But, do such details really matter? Perhaps only to chemists! After all, physicists don't care about the details. Cows are spherical...

First-order phase transitions lecture

Today I gave a lecture on First-order phase transitions including a derivation of the Clausius-Clapeyron relation.
Students particularly like watching the video of the barrel crush. I also use the video as the basis for a tutorial and sometimes exam questions. It is a nice way to illustrate how big the slope of the liquid-vapour phase boundary is.
They also enjoy the ice bomb video.

Mapping out the Fermi surface of KFe2As2

Angle-Dependent Magneto-Resistance (ADMR) is a powerful technique to map out the Fermi surface properties of a quasi-two-dimensional metal [see this earlier post]. I have worked on the theory of ADMR for more than a decade now and it continues to provide new challenges and applications to new classes of materials [see for example this talk].

I was delighted to see recently a PRL by an Aussie Rules football team [18 co-authors!] from Japan which has used ADMR to map out some of the Fermi surfaces for one of the new Iron Pnictide superconductors, KFe2As2 [these are in the Class II which exhibit some evidence for superconducting gap nodes].

The figure below shows the angular dependence of the interlayer magnetoresistance at different magnetic field strengths.

This is the resulting two Fermi surfaces within the most conducting layers.

The authors note that the cross-sectional areas of the Fermi surfaces found by a range of techniques:
ADMR (12 and 17% of the FBZ),
one ARPES study (7 and 22%),
another ARPES (10, 12, and 29%),
dHvA (8 and 13%)
are all inconsistent with one another! 

The authors also state "no band structure calculation can reasonably reproduce the precise topology of the Fermi Surfaces of KFe2As2".

The authors assign the broad peak at theta = 90 degrees in the interlayer resistance as being evidence for coherent interlayer transport. I am not completely convinced of this. The strong angular dependence between 60 and 90 degrees is quite different from the weak angular dependence seen in traditional ADMR. For example, compare the figure above to the calculated ADMR shown below, taken from this PRB.

Physics and chemistry start dating with DMFT

I believe physicists and chemists can learn a lot from each other, particularly when it comes to strong electron correlations. However, getting them to spend time together requires a powerful match-maker, particularly given all the communication problems...
I have earlier written many separate posts about quantum chemistry and about dynamical mean-field theory (DMFT). The latter has led to significant progress in our understanding of strongly correlated electron materials including the Mott transition in the Hubbard model, and bad metals.
Two papers have just appeared which look at possible marriages between DMFT and quantum chemistry, a PRL from Columbia and a J. Chem. Phys. from Cornell.
I am reading them but look forward to comments from others.