Monday, September 30, 2013

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.

Saturday, September 28, 2013

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.

Thursday, September 26, 2013

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."

Tuesday, September 24, 2013

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.

Monday, September 23, 2013

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.

Friday, September 20, 2013

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.

Thursday, September 19, 2013

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."
"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."
"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.

Don't show tables in your talk

Previously I have written about that tables are wonderful in papers.
This is because science is all about comparisons.

However, I think tables should not be shown [banned?] in seminars and conference talks.
Flashing a detailed table of data on the screen for a minute is useless. The audience does not have nearly enough time to absorb and process the table, even when you verbally explain the main points. This will increase the tendency of the audience to tune out.

I suspect computational chemists are particularly bad at this. They like to show all these quantities they have calculated with different levels of theory and different basis sets.

If you want to highlight a trend [or lack of one] you need to graphically represent the data. The audience can then quickly understand and assess the result.

I can think of a couple of exceptions from my own talks. Then I have merely a the table as an "existence proof".
For example,
"The parameters describing the spectral density for a wide range of chromophores in a wide range of solvents and proteins have been determined experimentally. Here is a table from my paper showing that. Nevertheless, some theorists write papers with unrealistic spectral densities."

Tuesday, September 17, 2013

Antwerp talk on quantum hydrogen bonds

Here is the current version of the slides for my talk I am giving tomorrow at the Horizons in Hydrogen Bond Research conference. The first half of the talk is based on this paper.

I worked hard to cut down the number of slides, since the talk is only fifteen minutes, and the last one before morning coffee. I have lots of backup slides. I also included a slide suggesting that the model and approach might be readily extended to apply to topics considered in other talks at the conference. Hopefully this will generate more discussions.

Aside: the lecture room is like nothing I have seen before. It is in an historical building and is long and narrow with low rafters from the roof. On each set of rafters as you go towards the back of the room there is another screen, leading to about 6 different screens. Hence, there is no point in using a laser pointer on the front screen. Only the people in the front 4 rows will be looking at it. You have to use your mouse cursor as a pointer. This means it must be big enough to see. How do you change the cursor size on a Mac? I found the answer here. 

Monday, September 16, 2013

New horizons in hydrogen bonding

If it's tuesday, this must be Belgium. Somehow I can't get that out of my head, partly because I have been travelling a lot. I first saw the movie in 1969, strangely in Princeton, while on an 3 month overseas trip with my parents. My father was visiting Walter Kauzmann, who knew all about hydrogen bonding. I think we thought the movie was pretty funny. I was only 8 years old. But I watched it again a few years ago and did not think it was that funny anymore. But, I digress...

This week I am in Antwerp, Belgium attending the 20th International Conference on Hydrogen Bond Research. Why am I here? It is part of the process of trying to break into a new field.

The program and attendees are diverse ranging from theoretical physicists like me to quantum chemists to experimental physical chemists to biochemists. The challenge for me will be filtering through all the chemical detail to figure out what is really important and what is not. I am looking forward to learning more about halogen bonding, a hot topic lately. How is it similar and different from hydrogen bonding? In the abstract book I also found some interesting talks and posters, including the figure below, that looks pretty exciting to me.
I am giving a talk on tuesday about my simple model for hydrogen bonding and the role of quantum zero point motion.

Saturday, September 14, 2013

Deconstructing iridates and many-body time scales

Iridates such as Sr2IrO4 have attracted considerable attention because they are 5d systems that exhibit a strong interplay between spin-orbit coupling and strong electronic correlations.
[See this earlier post].

Sr2IrO4 is a focus because it has been argued that it is a J=1/2 Mott insulator, just like La2CuO4, the parent compound for cuprate superconductors.
A current holy grail is to dope this material in the hope of producing high-Tc superconductivity. Many are trying. No one is succeeding.

There is actually a whole series of layered compounds, the Ruddlesden-Popper perovskites that differ, not just in their stoichiometry, but also their crystal structure, and consequently how the Iridium ions are coupled together. Sr_n+1Ir_nO_3n+1, where n is the number of SrIrO3 perovskite layers sandwiched between extra SrO layers.

Resonant-Inelastic-X-ray-Scattering (RIXS) experiments show that spin excitations in the Mott insulating phase of Sr2IrO4 appear to be well described by a spin-1/2 Heisenberg model with a small amount of spin anisotropy due to crystal field effects. However, for Sr3Ir2O7, RIXS suggests a large spin gap and spin anisotropy.
However, a different experiment suggests a small anisotropy.
In contrast, SrIO3 is a metal.

A major theoretical challenge is describe this whole family of materials and the disparate results, starting just from the crystal structures.
This has been done in an impressive paper,

Effective J=1/2 insulating state in Ruddlesden-Popper iridates: An LDA+DMFT study
Hongbin Zhang, Kristjan Haule, and David Vanderbilt

The calculations are based on GGA+DMFT, and represent another landmark achievement for the combination of Dynamical Mean-Field Theory with Density Functional Theory methods.

A key ingredient to understanding the apparent inconsistency between the results of different experimental probes is that in the many-body treatment the matrix describing the hybridisation of the three d-orbitals is frequency dependent. This is in contrast to the static matrix associated with crystal field theory.

The X-ray and thermodynamic experiments probe the system on different time scales. Thus they are respectively, more sensitive to the high- and low-frequency part of the hybridisation matrix.

The Figure below shows the calculated optical conductivity for the first three compounds in the RP series.

They also show how 0.2 per cent epitaxial lattice strain can have a big effect. [Aside: These are the kind of calculations I would like to see to address thermal expansion in organic charge transfer salts.]

I thank Kristjan Haule for explaining this work to me.

Friday, September 13, 2013

Inspiration from condensed matter veterans

Annual Reviews in Condensed Matter Physics has two inspirational articles

Why I Haven’t Retired
by Ted Geballe [aged 93!]

Sixty Years of Condensed Matter Physics: An Everlasting Adventure
by Philippe Nozières [aged 81]

Here are a few random Nozieres quotes to motivate you to read his whole article:
equations without a phenomenological background remain a formal game. Only simple qualitative arguments can unveil the underlying physics. 
A dialogue between experiment and theory is a difficult venture, which requires a lot of patience on both sides to find a common language. When it succeeds it is incredibly rewarding. I often made proposals to experimentalists, who always had the same initial reaction: “one more crazy theorist’s idea!” But my experimentalist friends are smart and sometimes they accepted the challenge, with spectacular results. I am very grateful to them. A corollary of that view is that theorists should not live in ghettos, but be immersed in experimentalist communities. 
I dislike extreme specialization, especially when it goes together with fashions. All too often a novelty becomes a must.
the sociology [of condensed matter physics] I find worrisome 
I am convinced that the ... link [with chemistry] should grow stronger: The views of chemists and physicists are complementary and we have a lot to teach each other. 
The bosses who govern us should realize that putting all efforts on a few fashionable topics, strangling more traditional work that provides their technical background, is tantamount to killing the hen that lays golden eggs. 
Live the scientific challenge as an adventure, not as a civil service routine.
He also highlights the significance of Dynamical Mean-Field Theory [DMFT] and rants about citations, metrics, and rankings.

I thank Premi Chandra for bringing the articles to my attention.

Thursday, September 12, 2013

Quantum many-body physics on Mathematica

A common problem in the practical implementation of quantum many-body theory [whether for quantum chemistry, solid state physics, or nuclear physics] goes like this. One starts with a Hamiltonian and observables that are written in terms of second quantised operators. Real calculations of observables requires diagonalising the Hamiltonian matrix. It must then be written as a symmetric real matrix in some basis of many-body states.

To do this means manipulating large numbers of creation and annihilation operators. This  can quickly become cumbersome, particularly for fermions. It is easy to loose track of signs when calculating matrix elements. It would be nice to be able to do this in an automated way, e.g., using Mathematica.

Sriram Shastry and John Wright have developed a Mathematica program DiracQ that will do all this. It can be downloaded for free and is described in detail in a preprint. The latter contains some highly non-trivial examples, e.g., finding the conserved quantities of the one-dimensional Hubbard model.

This should be very useful, both for research and teaching.

Tuesday, September 10, 2013

Seminar on bad metals at Rutgers

On Tuesday I am giving a Condensed Matter Seminar at Rutgers.

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

The main results in the talk are in a recent PRL, written with Jure Kokalj.
The organic charge transfer salts and the relevant Hubbard model are discussed extensively in a review, written with Ben Powell.

Saturday, September 7, 2013

Exotica: a blessing or curse to condensed matter physics?

One of the exciting things about condensed matter physics is that we are continually discovering exotic new phenomena. Many are unanticipated and understanding them presents a rich intellectual challenge. That is the nature of emergence.

Due to chemical complexity and the richness of quantum many-body physics it seems the frontier is endless.

Superfluid 3He, heavy fermions, sliding charge density waves, weak localisation, giant magnetoresistance, organic superconductors, quantum Hall effects, quantum point contacts, cuprate superconductors, non-Fermi liquids, buckyball superconductors, Luttinger liquids, colossal magnetoresistance, spin liquids, pseudogap, composite fermions, strontium ruthenate, topological order, quantum dots, sodium cobaltates, solid state quantum computing, fluctuating gauge fields, spinons, topological insulators, iron pnictide superconductors, ultracold atomic gases, quantum criticality, spin-charge separation, anomalous Hall effect, Majorana fermions, ....

Exotica are a blessing. They keep us excited and busy. The field will never die out or get boring.

However, I believe that exotica can also be a curse to the field.

1. The field can be too driven by fashions.
Every few years a new system is discovered which grabs attention. Lots of people work on it grabbing the "low-lying fruit" before jumping on the next band-wagon. Painstaking long term studies needed for a deep understanding are neglected.
The current fixation with citation metrics accentuates this problem. People want to publish quickly in a field in which lots of other people are working.
Twenty years ago Pantelides made this criticism.

2. Problems that are old, difficult and important get neglected: water, ice, metallic ferromagnetism, glasses, high-Tc superconductors, polarons, correlated two-dimensional electron gases, bad metals, fracture, enhanced thermoelectricity, multi-scale modelling, magnetite, high quality materials synthesis....

3. One can end up focusing on some exotic system or very specific material that is so finely tuned or rare or fragile or difficult to fabricate that it is not representative of any significant class of materials or phenomena.

4. One ends up with exotic theories in desperate search for a experiment, rather than constructing realistic theories that explain the many existing materials or phenomena waiting to be explained.

5. Students can get too narrow a training and perspective on the field.

6. We end up focusing too much on materials and devices that are so exotic and expensive to make that they will never be of any commercial use. This will ultimately diminish funding for the field.

A real challenge and struggle for me is for each new discovery to try and critically assess whether it is going to be important in the long term. I think the community could benefit from more critical reflection and self control.

What do you think?

Friday, September 6, 2013

Weak coupling can give important insights

Until last week I had several misconceptions about unconventional [i.e., non s-wave] superconductivity due to purely electronic interactions.

I thought weak coupling approaches tend to give a clear "pairing mechanism" and the symmetry of the Cooper pairs is related to the type of fluctuations or collective mode responsible for the pairing
For example, d-wave singlet pairing tends to go with antiferromagnetic spin fluctuations and p-wave triplet tends to go with ferromagnetic spin fluctuations.

There is a very nice paper
Band structure effects on the superconductivity in Hubbard models
by Weejee Cho, Ronny Thomale, Srinivas Raghu, and Steve Kivelson

They consider a weak-coupling renormalisation group (RG) treatment of a Hubbard model with specific band structures that are varied by changing tight-binding parameters.
The relevant Feynman diagrams are below

Calling this "spin fluctuation exchange" is not clear as there is no well defined collective mode that can be thought of as the superconducting "glue." The authors state, instead "the pairing is a result of overscreening by the whole band".

The authors show/claim

1. different order parameter symmetries can emerge from the same underlying mechanism, depending on the band structure.

2. in the weak-coupling limit, it is not possible to attribute the pseudogap entirely to a non-superconducting order. [Since the cuprates are in the intermediate coupling regime, this does not preclude the real pseudogap being due to non-superconducting order].

3. "The structure of the favored superconducting gap along the Fermi surface can be inferred in large part from a catalogue of wave vectors, Q, at which the susceptibility is large....
The most important portions of the Fermi surface are either those in which this approximate nesting condition is satisfied over a substantial region of the Fermi surface, or in which the Fermi velocity is small (density of states is large)."

4. For a spatially anisotropic [nematic] band structure there is a large parameter range where is a remarkable near degeneracy of a singlet (d + s)-wave and a triplet p-wave pairing channel.
5. a well ordered orbital current-loop state is incompatible with superconductivity, at least for weak-coupling. [This does not preclude superconductivity due to fluctuating orbital currents, as proposed by Varma].

There are three more situations I would like to see this weak-couping approach and formalism applied to.

a. The Hubbard model on the anisotropic triangular lattice at half filling.
Ben Powell and I showed that within an RVB [strong coupling] theory that as the frustration t'/t changed [and the band structure and Fermi surface changed accordingly] that the superconducting pairing symmetry changed from  A2 [dx^2-y^2] to A2+iA1 [d+id] to A1 [d_xy].
We interpreted this as "Symmetry of the Superconducting Order Parameter in Frustrated Systems Determined by the Spatial Anisotropy of Spin Correlations"

[The isotropic triangular lattice [t'=t] case was considered earlier with perturbative RG by Raghu, Kivelson, and Scalapino, and with functional RG by Honerkamp. Both found d+id superconductivity.]

b. The "purple bronze" Li0.9Mo6O17
Jaime Merino and I recently considered the simplest possible extended Hubbard model that might describe this quasi-one-dimensional material. It consists of ladders that are weakly coupled to one another and at quarter-filling.
An outstanding question concerns whether this model will produce the observed superconductivity, which is probably triplet.

c. The extended Hubbard model on the square lattice at one-quarter filling.
Using a slave boson approach Jaime Merino and I showed that  due to charge fluctuations near the charge-ordering transition there is d_xy superconducting order.

b. and c. require the extension of the weak-coupling approach that including the nearest neighbour repulsion V. This is included in this paper using the same formalism.

I thank Srinivas Raghu for bringing this work to my attention and explaining some key details. He also provided some helpful corrections to the first version of this post.

Thursday, September 5, 2013

Thirty years ago in Princeton

This month many bright and ambitious young people will begin science Ph.D's in the USA.
What might they anticipate?

Exactly thirty years ago I was one of sixteen young men in the incoming Physics class at Princeton. Here is a photo of fourteen of us outside Jadwin Hall. Thanks to Stephen Naculich and Bill Somsky for providing this copy.

Also, here is a picture of me in the front of Jadwin this week.

Here are a few random observations about my class and where we ended up. I am not sure I have all the history correct so others should feel free to correct me.

There were no women in the class. We came from the USA, Canada, Greece, Italy, Australia, China, and India.

Our future appeared to be bright and exciting.
Prospective advisors included two Nobel laureates [Phil Anderson and Val Fitch] and three future Nobel laureates [Joe Taylor, David Gross, and Dan Tsui]. Other faculty included a young Ed Witten, Bob Austin, Ian Affleck, David Wilkinson, James Peebles, Bob Dicke, Elliot Lieb, and Arthur Wightman. [Wigner still shuffled around the department].
At the time, I did not appreciate the stature of some of these people.

Most of the class wanted to be high energy theorists. But the first year we were assigned to work twenty hours a week for a specific experimental research group as "research assistants" [cheap labour] in the hope we might switch to one of these groups.  No one did.

Two big scientific events happened during our time, affecting some of our futures and thesis topics: the first string theory "revolution" [Schwartz-Green, 1984] and high-Tc superconductors and RVB theory, [1986]. Three students did theses on string theory. One did a thesis on RVB [not me]. I still have a preprint copy of Anderson's RVB paper.

The department was dominated by high energy physics, gravitation, and cosmology. There were no tenured faculty doing experimental condensed matter! Ong and Chaikin came at the end of our time. Anderson was the only tenured condensed matter theorist!

Biophysics was a new field. Apparently there were some faculty who did not think it was legitimate. There were two young assistant professors, Sol Gruner and Bob Austin. It was not clear they would both get tenure. [They did].

Generally, most of the assistant professors did not get tenure or left to elsewhere.

When we started there were no laptops, internet or email. The latter only came as we were graduating.
Some faculty had desktop computers. Most of the computing was done on mainframes.
To get journal articles one went to the library and photocopied them.
Reprints of articles written by Princeton faculty from the reprint room in the basement.
As there was no arXiv; preprints were obtained from faculty who were on snail mail lists.

John Nash was stalking Jadwin and Fine Hall, leaving weird encyrptions on the many chalk boards and sitting in the library reading Scientific American.
But, I did not know who this strange man was.

The General exam [taken by most after 2 years] was much harder and more comprehensive than it is today [see this book]. I learnt a lot from studying for the exam. We did not have to take any classes. Just pass the exam. Some of us formed a study group, which we found very helpful.

What happened to people ?
I have written before that I don't think comparisons are healthy and so avoid them here.

Everyone got a Ph.D. Two did transfer to other universities.

Everyone did a postdoc.

Here is the most shocking and discouraging statistic.
I believe that 15 years after commencing the Ph.D only three or four out of sixteen had tenured/permanent positions.
On the other hand I think now only four have left basic science research and teaching. The rest have permanent jobs in science. But, it sure took us a long time to get them.

We entered a very tough faculty job market in the early 90's. It was flooded with prominent scientists from the former Soviet Union and the collapse of industrial labs (Bell, IBM, Kodak, Xerox, ..).

Only one of us failed the General Exam. He passed second time and was the first to get a tenure track job!

One went to Wall street.

Two became assistant professors at Ivy League universities, did not get tenure, and are now doing quite different science.

One published a single author Nature paper that has been cited more than 2,000 times.

Three-quarters have stayed in the US.

What do I think now about the experience?
Would I do it again? Yes.
What do I wish I had known then?

I consider I was very privileged to have had the opportunity. But, I wish I had made more of it.
Particularly, I wish I had taken more initiative at talking to people.
I wish I had known something about mental health issues then.
I wish I had known how hard it would be to make a living in science.
We were naive.

Wednesday, September 4, 2013

Emergence of dynamical particle-hole asymmetry

Largely due to the work of Sriram Shastry I have recently become aware that particle-hole asymmetry in strongly correlated electron systems is an important issue (and challenge).
This was flagged in an earlier post.

There are a number of experimental anomalies that suggest the asymmetry is much larger than that associated with band structure effects. These include:

-highly asymmetric ARPES line shapes in the cuprates
-the slope of the I-V characteristics for some STM spectra
-a thermoelectric power that is large and changes sign with temperature in some cuprates

Theoretically it has been a puzzle that theoretical calculations for doped Mott insulators often give self energies that have a large particle-hole asymmetry. See for example Figure 3 in this PRL, Figure 13 of this PRB, and the figure below. It is very different from the perfect particle-hole symmetry implicit in Fermi liquid theory and marginal Fermi liquid theory. Also the quadratic frequency dependence only appears over a narrow frequency range, leading to kinks in the quasi-particle dispersions.

There is a new preprint
Extremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model
by Sriram Shastry, Edward Perepelitsky, and Alex Hewson

The frequency dependence of the self energy for a range of impurity occupations n is shown below.

The authors show how this asymmetry emerges naturally in terms of Shastry's theory of an Extremely Correlated Fermi liquid that has two Fermi liquid type "self energies", elucidated in this PRB and particularly in this talk. In particular, there is an emergent low-energy scale Delta associated with the asymmetry.

I thank Sriram and Edward for helpful discussions about their work.