Hydrogen bonds fluctuate like crazy

When I was in Slovenia a few weeks ago I spent a nice afternoon at the National Institute of Chemistry discussing hydrogen bond dynamics and spectroscopy with Jernez Stare and Joze Grdadolnik.

Janez Mavri was busy fielding phone calls from the press about his collaborator Ariel Warshel who had been awarded the Nobel Prize in Chemistry the previous day. I also met Dusan Hadzi, who was a real pioneer in hydrogen bond studies. He is now 92 years old but still comes into the lab each day, and is working on a several papers with younger collaborators!

Of particular interest are the Car-Parrinello simulations of sodium hydrogen bissulfate performed by Gordana Pirc, Stare, and Mavri.
This crystal has an O...O distance of R=2.432 Angstroms with slightly asymmetric O-H distances of r=1.156 and 1.276 A.
The Car-Parrinello runs show R fluctuating between 2.24 and 2.69 A!
Snapshots of the associated one-dimensional potentials for the OH stretch are shown below.

For each potential they solve the vibrational Schrodinger equation and calculate the associated OH stretching transition frequency. This then leads to frequency distribution and the infrared absorption line shape shown below.

Similar fluctuations [both thermal and quantum] occur in water but that is another story.

Getting an elephants trunk to wiggle II

Enrico Fermi told Freeman Dyson "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk".

Phil Nelson kindly brought to my attention a nice paper
Drawing an elephant with four complex parameters
by Jürgen Mayer, Khaled Khairy, and Jonathon Howard

There is also an interactive Mathematica Demonstration that allows you to see how the quality of the fit increases with the number of parameters [but does not have a wiggling trunk!].

Quantum emergence is not strong emergence

Is there any difference in the nature of emergence in quantum and classical systems?
What is the difference between strong and weak emergence?

An emergent property of a system is one that is:
a. not present in the individual components of the system
b. difficult to predict a priori from a knowledge of the components and their interactions
c. independent of the finer details of the components

Equivalently emergent properties are
a. qualitatively different
b. usually discovered empirically and sometimes are given a reductionist explanation a posteriori
c. universal and stable to perturbations

This can be illustrated with the rigidity of a solid
a. the individual atoms that make up a solid are not rigid.
b. elasticity theory preceded crystallography
c. all solids are rigid, regardless of their chemical composition.

Emergence occurs in both quantum and classical systems.  The properties that emerge can be distinctly different.  Superconductivity  and superfluidity are intrinsically quantum.
However, the associated issues and challenges: scientific, methodological, and philosophical are essentially the same. Emergence in classical systems is just as fascinating and challenging as for quantum systems.

Hence, last year I was surprised and disappointed to read the details of The Physics of Emergence program at the Templeton Foundation.
It appears to be based on two significant misunderstandings:
Emergence in quantum and classical systems is profoundly different.
In particular, quantum and classical emergence should be identified with strong and weak emergence, respectively.
I disagree with both the preceding two statements.

What is the difference between strong and weak emergence?
Some philosophers equate these with ontological and epistemological emergence.
For practical scientists the issue boils down to the following possible
answers to the question, "Is it possible to predict emergent properties?":
i. No. It is impossible.
ii. No. But, one can make postdictions, i.e., once the phenomena has been observed very smart people can construct reductionist models that explain the phenomena.  [BCS theory is an example].
iii. Yes. But, it is difficult. BECs and topological insulators give us hope.
iv. Yes. We just need a little more computer power and creativity.

The believer in strong emergence says i. All the other answers amount to weak emergence.
Different scientists will answer ii, iii, or iv.
I would probably go with ii.
The only scientist who I think might answer i. is Bob Laughlin on his more cantankerous days.
Yet i. appears to be serious option for many philosophers. This seems to be largely because of the thorny issue of consciousness.

Science is broken

Science is all about creating reliable and reproducible knowledge.
The Economist has a cover story How science goes wrong.
It is worth reading, pondering, and discussing.

I agree with the general observations of the article. Unfortunately, some of my worst fears are confirmed. Some of the problematic issues that are highlighted have been discussed on this blog before. Problems discussed include:

• the career pressure to publish leading to a lot of low quality work
• the pre-occupation with "sexy"new results that can be published in high profile journals
• poor quality of refereeing, meaning many erroneous papers get published
• there are few papers about negative results because they are hard to get published
• there are few papers testing/confirming the results in other papers because they attract little attention

I like the article because it is constructive in proposing reform, particularly from within science, and does discuss various initiatives, including some funded by private foundations to address the problems. The article is not "anti-science", does not lead to postmodern conclusions, or suggesting cutting science funding.

I welcome discussion about the scope of these problems and ways we can address them.

Universal? properties of thermoelectric power in bad metals

There is a nice preprint Universal thermopower of bad metals
Veljko Zlatic, G.R. Boyd, Jim Freericks

It contains calculations of the temperature and doping dependence of the thermoelectric power for the Falicov-Kimball model within the approximation of Dynamical-Mean Theory [DMFT].

This spinless fermion model is even "simpler" than the Hubbard model. Yet it captures some of the same physics, particularly the Mott metal-insulator transition. It also has the advantage that DMFT has an exact analytical solution. One does not need an "impurity solver", such as for the Hubbard model. There is an extensive Rev. Mod. Phys. on this, by Freericks and Zlatic.

Below I discuss one significant disadvantage of the model.

The figure below shows the calculated temperature dependence of the thermopower for several different dopings. The solid lines are the result from the Kubo formula [essentially exact] and the dashed line is the approximate Kelvin formula [the derivative of the chemical potential with respect to temperature].

Note that both the magnitude [of order k_B/e=80 microVolt/K] and non-monotonic temperature dependence are similar to what one sees in many strongly correlated electron materials. [Compare for example this post about heavy fermion compounds.]

Furthermore, it is striking that the Kelvin formula gives semi-quantitative results that are reliable.

However, when it comes to detailed comparison with experiment on actual materials, it is important to keep in mind a significant shortcoming of the Falicov-Kimball model. It does not seem to have a low-energy coherence scale associated with the formation of Fermi liquid quasi-particles. In many strongly correlated electron materials this energy scale is much less than the bare energy scale t, of the intersite hopping. In the Figure above one can see that the temperature dependence of the thermopower occurs on a scale of order some significant fraction of the hopping t. For example, in organic charge transfer salts this is of order 400 K, and in the cuprates t is of order 4000 K. In these materials the thermopower varies on a scale that is one order of magnitude smaller.

I thank Nandan Pakhira for bringing the preprint to my attention.

90th Birthday conference for Phil Anderson

If there is any one individual who has influenced both the scientific content and philosophy of this blog it is Phil Anderson. There are 45 posts with "P.W. Anderson" as a label, more than any other individual. However, his influence goes far beyond that.

In December Princeton will host a 90th birthday celebration conference in his honour.

Belgrade bad metal talk

On thursday I am giving a seminar at the Institute of Physics in Belgrade, Serbia.
My host is Darko Tanasković. He recently did some nice work with Jaksa Vučičević, Hanna Terletska, and Vlad Dobrosavljević showing quantum critical scaling of the resistivity near the critical point of the Mott transition in Dynamical Mean-Field Theory [DMFT] of the half-filled Hubbard model. A recent PRB describes this in terms of a quantum Widom line.

Here is the current version of the slides for my talk.

In preparing the talk I realised that in some recent versions of this talk I did not includes a slide, "Open questions and future work." That is bad. Perhaps every talk should have such a slide. I want other people to work on problems I am working on and certainly don't want to create the impression that my recent work [on any topic] has "solved" the problem and there is not much left to do.

Serendipity remains the best quantum materials discovery method

Materials by design has long been a holy grail of computational materials design. The idea is that one could predict both the chemical composition, structure, and desired functional physical properties of materials based on "ab initio" electronic structure calculations.

There is a nice Physics Viewpoint, "Materials prediction scores a hit", by Filip Ronning and John Sarrao. The two pages are worth reading and digesting. The authors puts in context the recent successful prediction of superconductivity in a high pressure phase of iron tetraboride.

Why is predicting superconductors so hard? Particularly, in strongly correlated electron materials? It is a problem with multiple energy scales. Basically, superconductivity is an emergent low-energy phenomena that is an instability in a metallic state, that itself involves emergent low-energy scales.

Given the above one can debate the merits of the White House Materials Genome Initiative, but be excited about the recently announced $90 million dollar initiative "Emergent Phenomena in Quantum Systems" of the Gordon and Betty Moore foundation. The focus is on Quantum materials with a significant emphasis on solid state synthesis.

What does my supervisor expect of me?

Different Ph.D and postdoctoral advisors/supervisors/mentors can have very different expectations of students/postdocs who work for/with them. Furthermore, these expectations can be significantly different from what students/postdocs expect. I have written before that it is important at the beginning [or better still, before] starting to work together that these expectations are clarified and discussed. At one Australian university it is part of the formal Ph.D induction process. Unfortunately, this is often not done.

Vitaly Podzorov is a physics faculty member at Rutgers University. On his website, he has a very clear and detailed description of what he expects from group members. It is worth reading carefully. Some of it is specific to his field, experimental organic electronics. Some of it may appear a little harsh. I don't necessarily agree with some of it [e.g. TeX is outdated software!]. I worry that the tone may lead students being scared to make mistakes, to take risks and fail. But, it clearly shows things from his perspective. Potential and new group members are not left guessing. Doing good science is hard and competitive.

Are there other examples where faculty web pages spell out expectations?
I welcome comments.

2013 Nobel Prize in Chemistry: Where is the quantum-classical boundary?

This is relevant to the 2013 Nobel Prize in Chemistry, awarded to Martin Karplus, Michael Levitt, and Arieh Warshel, for "Development of multiscale models for complex chemical systems."

This question means somewhat different things to physicists and chemists. To physicists it means "how big does a system have to get for it start behaving in a classical manner?"
To chemists it means "where can I draw a spatial boundary between the part of the system of interest that I want to treat quantum mechanical and the part I will treat classically.
This is illustrated in the Figure below, taken from the official "Scientific background for the prize."
It is worth reading.

This partition of the system is central to the tutorial, "Effective Hamiltonians for quantum dynamics in functional molecular materials," I gave on monday.

To be honest I have some mixed feelings about this prize. First, I wonder if the citation should read, "Development of multiscale computational modelling techniques for complex chemical systems." To me "a model" and "computational modelling" are quite different things. Although, perhaps the point is that "a model Hamiltonian" is at the heart of the simulations.

On the one hand, the recipients have all made monumental contributions to an incredibly difficult and important problem. They have stimulated a whole new research field, for better or for worse. But, to some the nagging question remains as to how robust and useful these simulations are. What new chemical insights do they give? In some cases, they have been successfully used to elucidate reaction mechanisms and rule out alternatives. I fear the answer is that the simulations are very useful in the hands of Karplus, Levitt, Warshel, and a few others. In the hands of the masses they may be just misleading and dangerous.

In particular, are the simulations falsifiable? A good outcome for science will be if the Prize stimulates renewed efforts to attack the fundamental scientific problems that these simulations aim to address. A bad outcome would be if more money is just spent hiring people to run existing codes to "simulate" more complex systems.

What do you think?

ARPES reveals non-Fermi liquid nature of overdoped cuprates

There is a nice paper that just appeared in Nature Communications
Anisotropic breakdown of Fermi liquid quasiparticle excitations in overdoped La2−xSrxCuO4
Johan Chang,  M. Månsson,  S. Pailhès,  T. Claesson,  O. J. Lipscombe,  S. M. Hayden,  L. Patthey,   O. Tjernberg, and J. Mesot

A fundamental question concerning the cuprates is how and why the metallic state changes with increasing doping from a pseudogap state to a non-Fermi liquid to a Fermi liquid. The authors report Angle Resolved PhotoEmission Spectroscopy [ARPES] measurements on the cuprate LSCO at a doping x=0.23(bulk Tc=25 K) corresponding to overdoping. From the ARPES data they extract the quasi-particle dispersion and damping rate at different points on the Fermi surface.

Significantly, they find significant variation of the damping rate and its frequency dependence over the Fermi surface. Specifically, a Fermi liquid picture breaks down as one moves away from the zone diagonals, the same region in where the nodes in the superconducting energy gap and the pseudogap appear. The figure below shows the spectral intensity as one crosses the Fermi surface at different points. The far left is in nodal direction and as one goes to the right one is moving towards the anti-nodal direction. Clearly as one moves from the left to right the quasi-particles are less well defined.

The results are significant for several reasons:

1. they connect the anisotropies of the pseudogap state with the overdoped state. 

2. the observed anisotropy goes against theories that assume or claim that the overdoped state is a simple isotropic Fermi liquid.

3. they confirm the anisotropic breakdown of a Fermi liquid proposed previously based on angle-dependent magnetoresistance measurements on overdoped thallium based materials.
These ideas were developed more theoretically in this PRL and PRB.

4. ARPES provides explicit angular resolution whereas the magnetoresistance measurements require a more significant input from theory to extract the angular dependence.

Tutorial on effective Hamiltonians for quantum dynamics in functional molecular materials

Today I am giving a seminar in the Theoretical Physics Department of the Stefan Institute. The abstract is below. The slides are here. The most important equation [the general form of the Hamiltonian] is missing (!) because I will write it on the white board and discuss at length. It is included below.

This informal tutorial will introduce some of the key concepts and approaches associated with modelling and understanding quantum dynamical processes in complex molecular materials.
This will provide background and motivation for understanding some of my work [1-4].

1. Examples of functional materials: optically active biomolecules, organic light emitting diodes and solar cells, enzymes, …
2. Examples of dynamical processes: charge separation, proton transfer, exciton transport, …
3. Partition: discrete quantum system + environment (solvent or protein)
4. Form of Model Hamiltonians
5. Diabatic states and potential energy surfaces
6. Example: spin boson model
7. Outstanding questions: quantum coherence, sequential vs. concerted, breakdown of Born-Oppenheimer, ...

[1] J. Gilmore and R.H. McKenzie, J. Phys. Chem. A 112, 2162 (2008).
[2] J. Bothma, J. Gilmore, and R.H. McKenzie, New. J. Phys. 12, 055002 (2010).
[3] S.C. Olsen and R.H. McKenzie, J. Chem. Phys. 130, 184302 (2009).
[4] R.H. McKenzie, Chem. Phys. Lett. 535, 196 (2012).

Condensed matter experiment faculty position in Melbourne

I am always keen to encourage people to move down under and promote the development of condensed matter physics in Australia.
Given all the current problems in the USA and Europe, Australia provides an increasingly attractive environment for science.

Monash University have a junior faculty position available for a Condensed Matter experimentalist. The advertisement is here.

The successful applicant will have Michael Fuhrer as a senior colleague. He recently moved to Monash from University of Maryland.

This is a great opportunity for someone.

4 keys concepts: Colloquium in Ljubjlana

For the next two weeks I am visiting the Stefan Institute in Ljubjlana, Slovenia. My hosts are Peter Prelovsek and Jure Kokalj.

On thursday I am giving a Physics Colloquium in the Faculty of the University, "Bad metals, good superconductors, and quantum spin liquids."

Here is the current version of my slides. I am concerned the talk is not at a basic enough level for the general audience. I highlight four key concepts stimulated by the discovery of cuprate superconductivity:

1. Mott insulator
2. Superconductivity resulting from purely repulsive electronic interactions
3. Quantum spin liquids
4. Bad metals 

These all find a nice realisation in organic charge transfer salts.

Picture is of Lake Bled, near Ljubljana, which we visited last saturday.

Are bad metals non-Fermi liquids?

One of the scientific agendas of this blog is the promotion of the concept of "bad metals" as an organising principle for understanding the properties of strongly correlated electron materials.

What is the relationship between bad metals, non-Fermi liquids and the strange metal phase of the cuprate superconductors?

They are not the same thing, although some people interchange the terms. Here are my definitions and clarifications, with particular emphasis on temperature regimes.

A Fermi liquid is a low temperature state of a metal characterised by well-defined quasi-particles, a Drude peak in the frequency-dependent conductivity, a thermopower much less than k_B/e, and a resistivity much less than the Mott-Ioffe-Regel limit h a/e^2, and certain characteristic temperature dependences (e.g. specific heat is linear in T, resistivity ~T^2. The Fermi liquid only occurs below some coherence temperature T_coh. In some formal theoretical sense (a la the renormalisation group) it is a statement about a zero-temperature fixed point (all the interactions become irrelevant).

A non-Fermi liquid does not have have well-defined quasi-particles or has quasi-particles with different quantum numbers to a Fermi liquid (spin-1/2 and charge -e).  It is also a statement about a zero-temperature fixed point.

The strange metal of the cuprates is the part of the phase diagram at optimal doping. One characteristic of it is a resistivity that is linear in temperature, and of order the Mott-Ioffe-Regel limit. Since, the low temperature properties are hidden by the superconducting dome, we can't say definitely whether or not it is a non-Fermi liquid.

A bad metal is an intermediate temperature state of a metal. It is characterised by ill-defined quasi-particles, no Drude peak in the frequency-dependent conductivity, a thermopower of order k_B/e, and a resistivity of order the Mott-Ioffe-Regel limit. This definition makes no commitment about what happens at low temperatures. A bad metal can evolve into a Fermi liquid or a non-Fermi liquid. A key issue is how low in temperature does one have to go to be in the "scaling" region of the zero-temperature fixed point.

The above view of a bad metal is distinctly different from that originally proposed by Emery and Kivelson. In their 1995 PRL, "Superconductivity in bad metals," they stated that

The failure of bad metals to exhibit resistivity saturation [at the Mott-Ioffe-Regel limit] strongly suggests that any theory based on conventional quasiparticles with more or less well-defined crystal momenta suffering occasional scattering events does not apply. Since there is no crossover in the temperature dependence of the resistivity as the temperature is lowered, this conclusion applies by continuity even at lower temperatures where the putative mean free path deduced from the measured values of the resistivity would not, of itself, rule out the possibility of quasiparticle transport. In other words, a bad metal behaves as if it is a quasiparticle insulator which is rendered metallic by collective excitations.

[Italics is theirs].
i.e. They claimed that a bad metal must be a non-Fermi liquid at low temperatures.

However, Dynamical Mean-Field Theory provides a counter example to this argument. As the temperature increases one smoothly evolves from a Fermi liquid to a bad metal. This was pointed out by Jaime Merino and I in 2000. Organic charge transfer salts also provide a counter example. At low temperatures one observes beautiful Shubnikov de Haas oscillations [described by a Fermi surface and Lifshitz-Kosevich theory] and a bad metal about 50 Kelvin.

Aside: I don't think that a resistivity that is linear in T over some limited temperature range is really much of a signature of anything.

I welcome discussion of these issues.