Signatures of charge fluctuation mediated superconductivity

Superconducting organic charge transfer salts are diverse. One class that has attracted considerable attention are the kappa-ET and dmit families that can be described by a Hubbard model on the anisotropic triangular lattice at half filling. Superconductivity emerges out of the parent Mott insulating state. The half filling arises because the molecules occur in pairs [dimers] within the crystal structure. Each dimer corresponds to a site in the lattice for the Hubbard model.

In a second class of materials the molecules are not dimerised and the resulting electronic bands are one-quarter filled with holes. Each site in the relevant lattice is a single molecule. The superconductivity emerges out of a charge-ordered [Wigner-Mott] insulator. The simplest possible effective Hamiltonian is an extended Hubbard model at one-quarter filling on a square lattice. In a 2001 PRL Jaime Merino and I showed how superconductivity could occur in these materials as a result of charge fluctuations associated with proximity to charge ordering.

Is this really true? How might you see the charge fluctuations and/or charge order? In crystals where each lattice site is a single atom [e.g. a transition metal ion] one might use inelastic x-ray scattering. However, in molecular systems one has more degrees of freedom since each lattice "site" consists of a large organic molecule. The intramolecular vibrations provide a nice knob to see the local charge density and its fluctuations. Specifically, the frequency and infra-red intensity of an antisymmetric C=C stretch on the BEDT-TTF molecule is particularly sensitive to the charge on the molecule, as parameterised here by Alberto Girlando.

The schematic phase diagram below places two different compounds beta''-M and beta''-SC. The former has a metallic ground state and the latter superconducting and is closer to the charge ordered state.

Bandwidth Tuning Triggers Interplay of Charge Order and Superconductivity in Two-Dimensional Organic Materials
S. Kaiser, M. Dressel, Y. Sun, A. Greco, J.A. Schlueter, G.L. Gard, and N. Drichko

One can contrast the infra-red vibrational spectra of these two compounds. In the lower right of the figure below one sees two sharp vibrational features corresponding to two distinct charge states of the molecule in the beta''-SC compound. At higher temperatures there are large charge fluctuations between these two charge states. In the beta''-M compound one does not see the charge order, just charge fluctuations.

The figure is taken from
Spectroscopic characterization of charge order fluctuations in BEDT-TTF metals and superconductors
A. Girlando, M. Masino, S. Kaiser, Y. Sun, N. Drichko, M. Dressel, H. Mori

The authors fit the spectra to a "jumping two-state" model of Kubo [described in a1969 Adv. Chem. Phys. review], which involves a hopping [or exchange] rate, about 10-30 cm-1 between the two charge states.

There are several interesting issues this work raises and some opportunities for future work.

1. What exactly does the hopping rate [exchange frequency] extracted from the experiment represent physically? How is it (not) related to charge mobility or the diffusion constant associated with charge fluctuations with wave vector (pi,pi)?

2. The theory predicts d_xy superconductivity. This means there should be nodes in the energy gap? are they present? There is some evidence from one penetration depth measurement.

3. Both materials should be bad metals at temperatures of the order of tens of Kelvin. The resistivity is certainly large and a Drude peak is only seen at low temperatures. It would be nice to see some thermopower measurements since they are particularly sensitive to a Fermi liquid bad metal crossover.  Theoretical calculations [using the Finite Temperature Lanczos Method] do predict a bad metal close to the charge ordered phase.

4. The title of this post may be an over-simplication. A weak coupling analysis may reveal it is not so easy to separate out spin and charge fluctuations.

I thank Alberto Girlando and Matteo Masino for explaining their work to me.

Computational chemistry versus chemical concepts

Robert Mulliken was one of the founders of quantum chemistry. In 1965 he gave a conference talk
Molecular Scientists and Molecular Science: Some Reminiscences. In it he made a commonly quoted statement highlighted below. I reproduce it in context.

....I would have liked first to say something about Molecular Quantum Mechanics (MQM) problems.  .... The general idea [of Lowdin's conferences] was that with old-fashioned chemical concepts, which at first seemed to have their counterparts in MQM, the more accurate the calculations became the more the concepts tended to vanish into thin air. So we have to ask, should we try to keep these concepts-do they still have a place-or should they be relegated to chemical history. Among such concepts are electronegativity....., hybridization, population analysis, charges on atoms, even the idea of orbitals, ....

Roald Hoffmann has argued these concepts do have a role. I would certainly agree. Computations should support, elucidate, and clarify concepts, not eliminate them. The issues are nicely discussed in 5 papers every computational chemistry student should read.

I thank Anna Painelli for bringing this quote to my attention.

Convoluted sentences and policies

Maybe I am slow, but when I read the introductory sentence below in an ABC [Australian version of NPR in the USA] news article I began to worry about both the convoluted state of  education policy and the quality of journalism in Australia:  

Education Minister Christopher Pyne has denied he is planning to renege on a promise not to restore limits on university places

I think this simply means, "The Education Minister may limit the number of students that can enrol."

Essential state models for complex organic dye molecules

Tomorrow I am giving a seminar, "Essential state models for fluorescent protein chromophores and methine dyes," in the Chemistry department at Parma University, Italy. Here is  the current version of the slides.

My host is Anna Painelli. Over the past few years she and her collaborators have done some very nice work showing that the optical properties of a diverse range of complex chromophores can be described by "essential state models" that are effective Hamiltonians acting on a just a few valence bond states. These models include dominant molecular vibrations and the effect of the solvent.
For example, an earlier post mentioned their work on crystal violet.

This work nicely complements work done by Seth Olsen giving a rigorous quantum chemical justification for such essential state models, as in this J. Chem. Phys. paper.

Three lies that ambitious undergraduates must reject

In some of my interactions with undergraduates who wish to make a career in science I observe unrealistic expectations about what is required to survive, let alone succeed. Here are three lies they have been told and some have believed.

1. You are special.
If you grew up in the Western world you are part of Gen Y and it is likely you have been continually told you are wonderful and you can be anything you want to be.
Furthermore, if you are moderately bright and enthusiastic about science you may have received a lot of affirmation from high school teachers, career counselors, some peers, and/or undergraduate advisors.
This is particularly true if you attend an average or mediocre institution that desperately wants to recruit students to go to graduate school.
The problem is that once you get to a respectable graduate school you will discover that you are just average. Why does this matter?
Don't expect or demand special treatment.
You are going to have to work much harder than you have so far to get anywhere.

Aside: I found it interesting that in the popular book/blog Adulting the twenty-something author considers "accept that you are not special" is one of the key (and most difficult) steps to adulthood.
[I thank my own special adult children for bringing the book and blog to my attention].

2. Society wants you to become a scientist. We need more scientists.
Society does want this in principle, just not in practice.
Society is unwilling to pay for the high financial cost of supporting basic long-term research and the associated career structures. This means your scientific career will probably stall and end at the post-doctoral stage.
Consider the simple statistics. For example, the huge ratio of the number of physics Ph.D graduates each year in the USA to the number of advertised faculty positions at research universities.

3. You can have it all.
High grades, summer research projects, social life, international vacations, romantic relationships, the latest electronic toys, a car, a part-time job, hobbies, ... If you are going to excel/survive in science you are going to have to focus, set priorities, and make sacrifices.
I am not saying you should have no life outside of science. That is both unhealthy and boring.

Hydrogen bonding highlights

I have really enjoyed the Hydrogen Bonding conference this week. There are about 120 people which is a good size.
The diversity of the topics covered is a testimony to just how ubiquitous, important, and challenging hydrogen bonds are. The participants ranged from old timers who have probably been to all twenty conferences to many newcomers like me who tthis was their first time. People were quite friendly and any contested discussion was quite cordial. I also enjoyed the lack of hype or sef-promotion. I got a lot of positive feedback for my simple model, showing that the field is quite open to new people and new approaches, particularly from physicists.

Here is a somewhat random commentary. If you want more details, ask.

Double proton transfer in porphycenes. This proceeds via a concerted mechanism and quantum tunneling is clearly present. Jacek Waluk's group has some beautiful results.

Water. [The basic questions never go away!]
Ali Hassanalli gave a nice talk about Proton transport through the water gossamer. Car-Parrinnello simulations show the preponderence of directed rings of water molecules.
What is the local environment around an hydroxide anion (OH-)?
There was animated discussion about whether it is H-bonded to four or five of the surrounding water molecules.

High resolution infra-red (IR) spectroscopy is a powerful probe that was widely featured. One problem is identifying lines with specific vibrations. This often requires comparison with an electronic structure calculation (usually DFT-based or MP2). I think this usually means all the frequencies have to be scaled by some mysterious factor (0.94-0.99). For strong hydrogen bonds identifying the lines is difficult.

Computational chemistry featured heavily as a tool for understanding specific experiments and to gain insight into the nature of bonding in specific complexes. Perhaps MP2 [Hartree-Fock + second order perturbation theory] featured more than DFT [with some dispersion corrected functionals]. CCSD was mentioned but not higher level methods (e.g. CAS-SCF). They would certainly be possible for some of the small molecules studied. Atoms In Molecules Theory featured significantly. Energy decomposition analysis featured some. As an ignorant outsider I am somewhat skeptical about how robust the decomposition is and so how much reliable insight it can provide.

Halogen bonding. Some of the motivation for resurgence of interest is that 20 per cent of drugs actually involve halogen bonds. The 1969 Nobel Prize in Chemistry, was partly for halogen bonding.
[Aside: they are also present in superconducting organic charge transfer salts, along with practically every other type of bond].
It seems to have some similarities to hydrogen bonding. Theoretically this can be seen within Weinhold's Natural bond orbital donor-acceptor picture.  It was claimed it can be viewed as a 4 electron, 3 orbital bond. However, no real evidence for this was actually presented. I think this could be nicely shown with a CAS-SCF treatment looking at different active spaces.
Interestingly, they have a stronger tendency to symmetric bonds than H-bonds.

New types of bonding: Halogen bonds, Charge Inverted Hydrogen bonds, Carbon bonds, Agostic, .... Various speakers claimed to have discovered new types of bonds. Some people think this is just nomenclature. Some suggested the "new" bonds" were really just "old bonds." Others think that there are fundamental issues here. It is interesting that Charles Coulson [my hero] actually claimed that bonds, like molecular orbitals, are a figment of our imagination and cannot be rigorously defined from a quantum point of view. I think the advent of natural orbitals and Atoms in Molecules Theory show that he was wrong on both counts.

Biomolecules featured some, but not as much as might have been expected, given the crucial role, H-bonds play in biomolecular function. Several participants who work on biomolecules told me they really enjoyed being at a meeting with a more fundamental focus.

Vibrational circular dichroism and Raman optical activity featured significantly. They is sensitive to the chirality of molecules and so can detect alpha-helices and beta-sheets in biomolecules. This is particularly important for studying carbohydrates [sugars and starch] which make up a large fraction of the planet's biomass. Unlike proteins they do not crystallise and so there is very little structural information about them.
Interesting to me, is that there are fundamental questions about the spatial extent of coherence [quantum or classical?] of vibrational excitations along alpha-helices and beta-sheets.

Microsolvation. How many water molecules does it take to make an acid? Four! i.e., if you add four water molecules to HCl the latter will dis-associate.

A political metaphor for the correlated electron community

It is the conservatives vs. the radicals, the right vs. the left.

A colleague recently suggested to me that this is a good metaphor or analogue for describing and understanding the divisions in the physics community working on the theory of correlated electron materials.

In the USA political divisions have led to a "gridlock" that is stopping the country moving forward. Both conservatives and liberals have a rigid ideology that prevents them from seeing the merits
of their opponents concerns and from being willing to compromise. Conservatives believe one should never raise taxes. Liberals believe one should never cut social welfare programs.
Both "cherry pick" economic data to support their point of view.

Historically, political radicals believe that capitalism is a flawed and unstable system that must be replaced by some new, but unknown, system.

The world is more complex than political ideology concedes.
Both radicals and conservatives have extreme beliefs that I sometimes find simplistic.
"The only way to reduce crime is to put more people in prison."
vs.
"Crime is just a result of social injustice."
"Poverty can only be solved by economic growth. That means less taxes on big business and the wealthy."
vs.
"The poor are helpless. Government welfare programs will solve their problems."

I really like the book Poor Economics because the authors [MIT economists Abhijit Banerjee and Esther Duflo] do not see the developing world through the extreme eyes of the left [represented by Jeffrey Sachs] or the right [represented by William Easterly].
Instead, the authors actually do randomised trial experiments to obtain empirical data to see what does and does not work in poverty alleviation. They find that sometimes the right is correct and sometimes the left is correct. Sometimes neither. The world is complex.

So what does this have to do with the theory of correlated electron materials?
On one side we have the conservatives who believe that the key ingredients are atomistic detail, good density functionals, perturbation theory, mean-field theory, and the random-phase approximation.
New concepts and methods are not really needed. They have a good system [just like capitalism].
In particular, we don't need a revolution, just bigger computers!
Perhaps they are represented by Igor Mazin, David Singh, Warren Pickett, Olle Andersen, ... The former three all have a career connection to Naval Research Laboratory.
Unlike the radicals below, it is not clear to me that the conservatives have a clear ideological or inspirational leader.

The radicals believe in universality. Atomistic detail is largely irrelevant. It is all about collective behaviour [not individuality].
Completely new conceptual structures and techniques are needed. We must go beyond Landau's mean-field theory and Fermi liquid theory: topological order, quasi-particles with fractional quantum numbers, AdS-CFT, quantum criticality, ...
To the barricades!
Phil Anderson is an enduring inspiration for the radicals just as Marx still is for political radicals.
Indeed many of the radicals [Wen, Patrick Lee, Viswanath, Haldane, ...] have some historical connection to Princeton or Anderson.
I think Anderson is like Marx in that he defines the problems, and asks the hard questions; but I am not sure the answers are right.
But for some, even Marx is not radical enough.
Perhaps, Subir Sachdev is like Lenin with his AdS/CFT comrades. Anderson accuses them of "quasi-journalism". Perhaps, just like Leninists they consider propaganda is also good for their cause.
Bob Laughlin is an aging dis-illusioned radical who has become dis-engaged from the political process. He was a Berkeley undergrad, after all!
Perhaps, Piers Coleman is like a European Social Democrat.

Each side is largely dis-engaged from the other and appears unwillingly to acknowledge the merits of their opponents point of view. This is bad for the field, just like uncompromising political divisions are bad for countries.

Gabi Kotliar has roots on the left, but is moving more towards the right as he grows older.  He and Andy Millis are probably a disappointment to both the left and the right, just like Obama!
I am also caught in the middle, with slightly more sympathy for the left than the right, just like in politics. As in politics, I am troubled at some of the extreme views I see on both the left and right. Inconvenient data is ignored.

Can the community move beyond ideology, see and respect others point of view, and work together?
It is interesting that topological insulators have actually led to some constructive dialogue and co-operation between left and right.

Aside: What about the theoretical chemistry community?
I feel it is dominated by the conservatives. Do they need some radicals to shake them up?

Note to university administrators: this is a personal blog and has a disclaimer at the bottom of the page.