Monday, October 31, 2011

From quantum chemistry to many-body theory of frustrated antiferromagnets

There are a wide range of organic charge transfer salts that can be described by a Hubbard model at half filling on the anisotropic triangular lattice. [See this review for a full discussion]. This model can also be viewed as a square lattice with hopping t' along one diagonal.
An important parameter is the ratio t'/t. The values t'=0, t'=t, and t=0, correspond to the square lattice, isotropic triangular lattice, and decoupled chains, respectively.

The actual value of t'/t is critical because the ground state of the Heisenberg model for the Mott insulating state [Neel, spiral order, valence bond crystal, spin liquid] is quite sensitive to the value of J'/J=(t'/t)^2. For example, as J'/J increases from 0.6 to 0.9 the order can change from Neel to valence bond crystal or spin liquid to spiral order.

So, what value do specific materials have? Do they vary with the counter anion?

Previously the parameters t and t' have been estimated from Huckel theory. An earlier post discusses recent progress at calculating these parameters for BEDT-TTF materials from computational methods based on Density Functional Theory (DFT).

My UQ colleagues Edan Scriven and Ben Powell recently reported new results for dmit materials in this preprint. J'/J varies from 0.4 to 1.4 with the counterion. Furthermore, if the calculated values are combined with the results of many-body theories of the corresponding Heisenberg model one obtains a consistent picture between theory and experiment.

The results should be compared with the figure below (taken from a recent review article by Kanoda and Kato) attempts to present a unified picture of the relationship between the ground state and the value of t'/t for a range of materials. However, the values used are based on Huckel calculations and the DFT calculations give significantly different values.

Outstanding challenges include
  • finding a simple physical explanation for the origin of the parameter variation with counterion.
  • calculating the pressure dependence of t'/t
  • calculating Hubbard U values consistent with experiment [it seems screening is important]
  • the previous two need to be combined to describe the pressure-temperature phase diagram, including the transition from a Mott insulator to a superconducting state

Thursday, October 27, 2011

Universal magnetic excitations in the cuprates

I heard a nice talk by Bernhard Keimer which included a discussion of recent RIXS [Resonant Inelastic X-ray Scattering] results on the cuprates. The relevant Nature Physics article  states
As a major result, we demonstrate the existence of spin-wave-like dispersive magnetic excitations (paramagnons) deep inside the electron–hole spin-flip continuum (up to ~300meV), for all the investigated doping levels, with spectral weights comparable to those of magnons in the undoped parent compounds.
The work is nicely put in context in a News and Views article by Matthias Vojta.

Tuesday, October 25, 2011

Interlayer charge transport in the pseudogap state

Previously I have posted about the unusual anisotropies present in the temperature dependence of the resistivity in the pseudogap phase of the cuprates. In particular, the intralayer resistivity exhibits a metallic temperature dependence whereas the the interlayer resistivity exhibits a semi-conductor like temperature dependence. Much had been made of this previously with exotic explanations in terms of spin-charge separation. However, I posted about recent work showing how the data has a natural explanation in terms of the presence of a pseudogap with nodes in the same direction as that at which the interlayer hopping vanishes.
[This interlayer hopping anisotropy is quite important in understanding Angle-Dependent-MagnetoResistance (ADMR)].

I recently became aware of earlier phenomenological work by Tao Xiang and collaborators which also gives this explanation. In particular, this PRB gives a nice "universal" phenomenological form for the temperature dependence of the interlayer conductivity. This form is compared to data from a wide range of cuprates.

Seeking a unified theory for unconventional superconductors

I am currently in Sydney at the Gordon Godfrey workshop on Spins and Strong Correlations.
Yesterday Rajiv Singh began his talk on orbital effects in the iron pnictide superconductors with some general remarks about the relationship between magnetism and superconductivity. The two were once considered inimical (one of Bernd Matthias' rules). But we now see classes of superconductors (heavy fermions, organics, cuprates, and pnictides) where they appear to be intimately connected.

Rajiv then took a philosophical position: there should be a common physics for all of these non-electron-phonon superconductors.

This certainly reflects a physicists desire for universality and simplicity. This is in distinct contrast to a chemists focus on particularity.

I am not convinced that it is or should be the case that there is some common underlying physics. Here are a few disordered thoughts.
  • For pnictides it seems that orbital (multiple band) effects matter. In contrast, in cuprates and organic it seems a single band is sufficient.
  • If there is a unified theory I think the strongest candidate is a weak-coupling spin fluctuation RPA picture (with renormalised interactions and Fermi liquid quasi-particles). To hold to this one will have to show that "exotica" (e.g., non-Fermi liquid effects) are just some higher order perturbative effects.
  • Similar sentiments of a unified picture of cuprates and pnictides is presented by Basov and Chubukov.
  • To me the two biggest problems for a "common physics" scenario are the pseudogap state in the cuprates and the spin liquid states in organics. They represent a "discontinuity" from the other materials and from any weak-coupling picture.
I welcome comments. Is there a common physics for non-electron-phonon coupled superconductors?

Saturday, October 22, 2011

Should you use Turnitin?

Turnitin is commercial software that detects student plagiarism by comparing submitted assignments to everything on the web and a vast database of other assignments.

A few years ago I would have thought this was might be relevant to people teaching large courses of undergraduates in the humanities. However, I was wrong. Unfortunately, experience has shown that plagiarism does occur, even in physics courses, and at the graduate level. There are cases of students submitting Ph.D proposals and literature reviews that involve cutting and pasting text from papers and the internet. Although certainly not confined to them this can be more of a problem with students from non-Western countries. There do seem to be some "cultural" differences as to what is acceptable practice and what is not. This does not excuse it, but does mean that sometimes first-time offenders need to be gently cautioned and educated.

A range of offences can occur, ranging from sloppy referencing to blatantly copying large swathes of text and presenting them as ones own.

So if you don't use Turnitin (or something equivalent) try it. You won't know if there really is a problem until you check.

If you do detect plagiarism make sure you report it to the relevant academic authority. Do not just give the student a private warning. It is important that someone is keeping track.  Otherwise repeat offenders may not really understand the severity of their offence and get appropriately disciplined.

Another issue, which is harder to detect, is that of ghost writing.

Friday, October 21, 2011

Superconductivity video goes viral

Today Ben Powell gave a great colloquium at UQ on 100 years of superconductivity. During it he showed this great video. A shorter version went viral on the internet receiving more than 3 million views within less than a week of being posted!
It is great to see superconductivity is so popular.

Thursday, October 20, 2011

An energy gap is not necessary for superconductivity

A common misconception about superconductivity is that the presence of an energy gap at the Fermi energy is fundamental to the phenomenon. This is not correct. The key property is long range phase coherence.
I give several counter-examples to the necessity of an energy gap.

If in BCS theory you take an s-wave superconductor and add magnetic impurities there is a critical range of impurity concentration for which there is no energy gap (i.e. the density of states is non-zero at the Fermi energy) but superconductivity (i.e. a non-zero Cooper pairing amplitude and superfluid stiffness exists).

Superfluid 3He (p-wave triplet pairing) and high-Tc cuprates (d-wave singlet pairing) have nodes in the energy gap on the Fermi surface.

A gap is also not sufficient. A charge density wave state can have a gap at Fermi energy but is not be a superconductor.

Wednesday, October 19, 2011

A victory for curve fitting

I have previously written many posts (rants?) about the dangers of curve fitting. In particular in one of the first posts The naked truth versus self deception I stated
 I believe that any significant physical effect/discovery should be able to be seen by the naked eye in the experimental (or computational) data and should not require curve fitting.
However, the graphs below represent a significant counter example to my view.
The data is considered to be consistent with the upper solid curve.
This is the data which ultimately led to the 2011 Nobel Prize in Physics.
When I see such graphs I am immediately skeptical. But the authors and the broader community were not and subsequent measurements supported the original claims and parameters deduced from this data. In particular the graph below [taken from a Physics Today article Supernovae, Dark Energy, and the Accelarating Universe by Saul Perlmutter]  shows how several independent methods constrain the parameters.
I am curious to hear what others think.

Tuesday, October 18, 2011

Deconstructing Transport properties of strongly correlated electron metals

I have been working through a really nice article Electrothermal transport coefficients at finite frequencies by Sriram Shastry. The key idea is that there are certain transport coefficients [the Hall coefficient (Hall resistivity), Lorenz ratio, and Thermopower] for which have a weak frequency dependence and so one can obtain a reliable estimate of the dc value from the high frequency value. This greatly simplifies the computation because the latter is determined by the expectation value of a specific operator in the ground state (or thermal ensemble). Unlike the dc transport coefficient this expectation value is not particularly sensitive to finite size effects and so can be evaluated from Lanczos (exact diagonalization) on a small lattice. Alternatively it can be evaluated from a high temperature series expansion.

Is this high frequency approximation justified? It can motivated in a heuristic manner from the fact that in the Drude model the relevant transport coefficients [the Hall coefficient, Lorenz ratio, and Thermopower] are all independent of the relaxation time.
For the t-J model on the triangular lattice Shastry also compares explicit evaluations of the Hall coefficient at zero, non-zero, and infinite frequency and finds there is little variation between them.
Here are a few highlights of the paper.

1. Strong correlations cause qualitative differences. Consider the Hubbard model as a function of doping. There are three changes in the sign of the Hall and Seebeck coefficients, in contrast to the one change in sign (at half filling) that occurs for the uncorrelated (U=0) band. In particular one can have a "hole-like" band structure and Fermi surface but an "electron-like" Hall coefficient.
[I think the solid line in the above graph is the Heikes formula which holds in the infinite temperature limit and is related to the entropy of the charge carriers in the Hubbard model in the atomic limit U >> |t|].

2. On the triangular lattice changing the sign of the hopping t can lead to significant changes in the magnitude and temperature dependence of the thermopower. [Although I wonder if some of this difference is related to the relative proximity to van Hove singularities and the associated differences in the non-interacting density of states near the Fermi energy as discussed here].

3. On the triangular lattice at high temperatures there are contributions to the thermopower and Hall resistance which are first order in t/T. In contrast on the square lattice the leading terms are of order (t/T)^2. This arises because on the triangular lattice one can perform closed loop hops involving only 3 lattice sites.

4. A connection is made [with some interesting history] to the expression of Thomson [Lord Kelvin] for the thermopower in terms of entropy. This is relevant to this post.

I thank Subroto Mukerjee for helping me gain a better understanding of Shastry's work.

Monday, October 17, 2011

A "big picture" book worth re-reading

Almost 2 years ago I posted about how much I liked the book Five Minds for the Future by Howard Gardner. That post enunciated how his "5 Minds" relate to development of a research career. I also later mentioned how the book is helpful for thinking through what the goal of a physics undergraduate education might be. I am now reading the book with my son to help him think through how do get the most of his undergraduate education which he starts next year. It is one of those books that I find that each reading is like the first one because each reading produces new insights and understanding.

If when teaching you struggle with filling out a "Course profile" which requests information about "Learning goals" and "Graduate attributes" you may also find the book helpful. These can be an exercise in "mumbo jumbo". I used to think they were a complete  waste of time. But, if done thoughtfully and in a concrete manner I believe that they can be helpful to both students and teacher. The book helped me see the value of these exercises and how to do them in a more effective manner.

Friday, October 14, 2011

Essential ingredients in the high-Tc puzzle

On monday I had a nice meeting in Bangalore with T.V. Ramakrishnan who told me about recent work on a Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates done together with Sumilan Banerjee and Chandan Dasgupta.

They assume that there is singlet pairing along each bond on the square lattice at some temperature which linearly decreases with increasing doping x. A key ingredient is the coupling between neighbouring horizontal and vertical bonds. This coupling C is assumed to have a negative sign to produce d-wave pairing. Furthermore, to produce a superfluid density which for small x scales x it is assumed that C is also proportional to x. [They also give a simple argument suggesting that this C scales with t' the diagonal hopping in an underlying band structure].

From this simple model they can extract some of the key phenomenology of the cuprates, including the doping dependence of the transition temperature. Coupling the order parameter fluctuations to electrons produces a self energy and spectral density consistent with ARPES experiments, including the existence of Fermi arcs.

A few things I found interesting
  • Quantum fluctuations are argued to be important in the underdoped andoverdoped regime. Indeed Tc goes to zero for small non-zero dopings.
  • Past the optimum Tc the superfluid density decreases with decreasing doping.
  • I would be interested to see these relatively simple ideas extended to the half-filled case corresponding to organic charge transfer salts. Then, x will have to replaced with something like U-Uc where Uc is the critical value of the Hubbard U for the Mott transition.

Thursday, October 13, 2011

A concrete test of the Morse potential in a complex molecule

Just how accurate is the Morse potential? A key feature is the equidistance of adjacent energy levels.
This graph below illustrates the high quality of the Morse potential for describing a C=O bond within a protein. The data (taken from this PNAS paper) is via a technique which induces transitions from the v'th vibrational energy level to the (v+1) level.

Thus we see the Morse potential describes the true anharmonic potential at least up to v=7, which corresponds to energies of about 1.5 eV above that of the potential minimum.

This success also underscores the local character of these bond stretching vibrations.

Monday, October 10, 2011

Different routes to the Mott insulator

Today I am giving a seminar Destruction of quasi-particles near the Mott transition (slides) at the Physics Department of the Indian Institute of Science in Bangalore.
The talk is largely based on a PRL which shows how Dynamical Mean-Field Theory (DMFT) can give a quantitative description of the optical conductivity of a family of organic charge transfer salts close to the Mott transition.
For a much broader context see this review. The talk briefly stresses that the nature of the quasi-particles in the metallic phase near the Mott transition for the band-width controlled and the filling-controlled Mott transitions are distinctly different.

Saturday, October 8, 2011

Remembering Coulson

Charles Coulson is definitely one of my heroes and I found this nice memorial talk by Roy McWeeny on a history of quantum chemistry site. It emphasizes how Coulson made the transition from applied mathematics to theoretical chemistry:
The broadening of his philosophy is summed up in a sentence .... in a lecture on mathematical models, .... "It is likely that one cannot be a good applied mathematician unless one has the ability to simplify to the point of absurdity!" — recalling at the same time a remark by Eddington that "If the model is right, the rest is easy".
Two trivia about Coulson I also learned:
He was chairman of Oxfam from 1965-1971.
He was Ph.D supervisor of Peter Higgs (of Higgs boson fame).

Friday, October 7, 2011

Seminar on hydrogen bonding

Today in Bangalore I am giving the theory seminar at the Jawaharlal Nehru Centre for Advanced Scientific Research. I will be talking about my recent preprint on hydrogen bonding. Here are the slides.

Thursday, October 6, 2011

2011 Nobel Prize in Chemistry

I was pleased to see that the Chemistry prize was awarded to Dan Shechtman for the discovery of quasi-periodic materials that led to a new definition of crystal (quasi-crystals). Back in 2003 APS News published a nice discussion of the background to the paper which appeared in PRL in 1984 and is the 8th most cited PRL of all time.

An earlier post discusses why I teach undergraduates about quasi-crystals. It illustrates the fundamental logical principle that A implies B does not mean that B implies A. Specifically, just because a periodic arrangement of atoms is a sufficient condition for a discrete X-ray pattern does not mean that it is a necessary condition. It also shows students that what they read in textbooks may be wrong.

Shechtman is not the first condensed matter physicist to be awarded the Nobel Prize in chemistry. Other recent examples include Walter Kohn and Alan Heeger.

Wednesday, October 5, 2011

Directionality is a key property of hydrogen bonds

Today I re-read a nice paper The hydrogen bond: a molecular beam microwave spectroscopist’s view with a universal appeal, by  Mausumi Goswami and E. Arunan

I found the following sentences very helpful
one aspect about hydrogen bonding that is widely accepted is the directionality, i.e. X–H[cdots, three dots, centered]Y is found to be linear in most cases. Although secondary interactions in a system could force X–H[cdots, three dots, centered]Y away from linearity, it is the directionality in hydrogen bonding resulting in an anisotropic intermolecular potential that separates it from the more general ‘van der Waals forces’, which are expected to be isotropic.
The main point of the paper is
For a ‘hydrogen bonded complex’, the zero point energy along any large amplitude vibrational coordinate that destroys the orientational preference for the hydrogen bond should be significantly below the barrier along that coordinate so that there is at least one bound level. These are vibrational modes that do not lead to the breakdown of the complex as a whole. If the zero point level is higher than the barrier, the ‘hydrogen bond’ would not be able to stabilize the orientation which favors it and it is no longer sensible to characterize a complex as hydrogen bonded.

Next week I will be visiting the Indian Institute for Science in Bangalore and look forward to meeting the authors then.

This directionality of is incorporated in my effective Hamiltonian for hydrogen bonding via the directional dependence of the matrix element which couples the two diabatic states. It is also responsible for the hardening of vibrational modes associated with rotation of the D-H unit relative to the acceptor atom A (discussed in my last H-bond post).

Tuesday, October 4, 2011

2011 Nobel Prize predictions

It is that season again. In 2009 I posted about this but forgot last year. There is an article in Science (which was wrong about the Medicine prize)
Here are a few sites with predictions.

David Pendlebury at Thomson Reuters
Although I disagree with the methodology, based on citations, I think their choice of Aspect-Clauser-Zeilinger for quantum entanglement is an likely and good one.

Paul Braker at Chembark lists odds for different people/topics for the chemistry prize. For physicists this is worth reading because it is a brief education in significant discoveries in chemistry.

Everyday scientist predicts Moerner for single molecule spectroscopy, whose name comes up for chemistry in some other lists.

The curious wave function has predictions for all fields.

Some of these lists suggest a prize for biomolecular dynamics simulations. But, what is the really significant new discovery that goes with this technique?

Aharonov and Berry's name comes up for quantum phase effects. This could be combined naturally with Duncan Haldane or David Thouless for the role of topological phases in many-body systems.

I welcome your suggestions and comments.

Monday, October 3, 2011

More hydrogen bond correlations

Previous posts have considered correlations between different physical properties of hydrogen bonded complexes (D-H...A).  A key correlation is that as the donor-acceptor (D-A) separation R decreases the D-H stretch vibrational frequency (corresponding to varying r in the figure below) decreases.
There is a second vibrational mode associated with angle phi in the figure above. This can also be viewed as a torsional or bending mode. Hydrogen bonding leads to a stiffening of this mode. 
The figure below shows how the frequency of this mode (horizontal axis) is correlated with the D-H stretch frequency (vertical axis). 
The figure is taken from a classic 1974 review by Novak.

Low-tech solutions change the world

The New York Times has an excellent section Small Fixes: Low cost innovations that can save thousands of lives. One example are Liquid Lens, self-adjustable eyeglasses, developed by Joshua Silver, a physicist at Oxford.

Saturday, October 1, 2011

Quantifying breakdown of Born-Oppenheimer

Yesterday I read a nice paper An unusually large nonadiabatic error in the BNB molecule by John Stanton.
Here are a few choice quotes:
A simple analysis shows that significant nonadiabatic corrections to energy levels should occur only when the affected vibrational frequency is large enough to be of comparable magnitude to the energy gap involved in the coupling. 
The results provide evidence that nonadiabatic corrections should be given as much weight as issues such as high-level electron correlation, relativistic corrections, etc., in quantum chemical calculations of energy levels for radicals with close-lying and strongly coupled electronic states even in cases where conical intersections are not obviously involved. 
One would be tempted to prepare a manuscript based on this result, but such an action would be premature.
Well.  [Yes. This is a sentence in the paper!]
One thing of particular interest to me is that the adiabatic potential energy curves of both the ground and lowest excited state can be described very accurately by the eigenvalues of a two-state effective Hamiltonian [ascribed here to Koppel, Domcke, and Cederbaum]. This is identical [modulo a 45 degree rotation] to the Hamiltonian considered in a recent paper by Laura McKemmish, Jeff Reimers, Noel Hush, and myself.

The paper makes no mention of the "twin state" concept or how the vibrational  frequency is exalted in the excited state relative to the ground state.

This article was one of the 20 most downloaded articles from Journal of Chemical Physics this month. I found it encouraging that people aren't just reading papers about the latest DFT functional recipe book!