An ode to superconducting organic charge transfer salts

Organic charge transfer salts such as (BEDT-TTF)2X have a number of unique features that make them a playground for quantum many-body physics. They have several properties, distinctly different, from transition metal oxides, that mean that one can observe rich physics in experimentally accessible magnetic fields and pressure ranges. These properties include:

• they are available in ultra-pure single crystals which allow observation of quantum magnetic oscillations such as the deHaas van Alphen effect.
• the superconducting transition temperature Tc and upper critical field Hc2 are low enough that one can destroy the superconductivity and probe the metallic state in steady magnetic fields less than 20 tesla.
• chemical subsititution provides a means to tune the ground state
• they are compressible enough that in pressures of the order of 10's kbar one can tune between different ground states

Consequently, over the past decade it has been possible to observe several unique properties of strongly correlated electron materials, sometimes ones that have not been seen in inorganic materials. These include

• magnetic field induced superconductivity
• a first-order transition between a Mott insulator and superconductor induced with deuterium substitution, anion substitution, pressure, or magnetic field
  
• valence bond crystal in a frustrated antiferromagnet
• a spin liquid in a frustrated antiferromagnet
  
• a new universality class near the Mott transition
• collapse of the Drude peak (and thus quasi-particles) above temperatures of order 10's K
  
• bulk measurement of the Fermi surface using angle-dependent magnetoresistance
  
• low superfluid density in a weak correlated metal
• multiferroic states
  
• superconductivity near a charge ordering transition

I will try and write some specific details before the Gordon Conference.

Chemistry comes alive!

In Monday's lecture (draft here) I want the students to understand the following key points about applying thermodynamics to chemistry:

• Its all about entropy of mixing. Consequently, chemical reactions never go to completion.
• The equilibrium constant K quantifies the extent to which a reaction has gone to completion.
• K and its temperature dependence allow one to determine the change in Gibbs free energy, enthalpy, and entropy, associated with the reaction.
• All thermodynamic functions are defined relative to a standard state (temperature, pressure, and concentration).

I like to show a few cool video demonstrations from the Chemistry Comes Alive series from the Journal of Chemical Education. I have CD's volumes 2 and 3, which have lots of material relevant to physics too (magnetism, superconductivity, phase transitions, critical points, ...).

When nitrogen triiodide, the dark colored solid, is dry, it is very sensitive to touch or any vibration. Simply touching it with a feather causes it to explode or detonate. One detonation causes another to occur. One product of the reaction is violet iodine vapor.

A mere touch of a feather ... .. causes dry nitrogen triiodide to explode.

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Why blog?

One of the reasons I started this blog was in the hope it would benefit other members of the UQ condensed matter theory group, particularly students and postdocs.
Hence, I am keen they read it and provide feedback.

I want it to be an efficient way of:

• enhancing the mentoring process, learning how I think about science and starting a career in science.
• extending our other meetings
• giving my perspective on some of the seminars we all go to
• communicating some of my excitement about science
• teaching (and re-learning) key concepts
• keeping up with me when I am travelling; where am I? what am I doing? what am I learning?
• providing easy access to information, such as talks I have given, and often-given advice,...

I look forward to having a discussion this week about

1. to what extent are some of the above goals being met?
2. how could the blog be made more useful?

A simple transport criterion for the absence of energy bands

A lot of papers on materials for organic electronics and photonics will discuss transport and optical properties in terms of conduction and valence bands, concepts that are valid and useful for inorganic crystalline semiconductors.

But, I do not think such bands exist for most of these materials. This can be seen from the magnitude of the transport mobility. These notes show a simple self-consistency argument which shows that if band transport is meaningful (i.e., one can talk about electrons with a definite wavevector and which are occasionally scattered) then the mobility must be much larger than about
e a^2/hbar ~1 cm^2/Vsec.

I derived this result over a year ago but then discovered this appears to have been well known back in the 70's, and seems to have been forgotten.

For example, the result is clearly stated:

in equation (24) of a 1963 paper by Glarum.

in equation (224) on page 24, of a classic 1971 review of Metallic Oxides by John Goodenough

page 346, of the second edition of Pope and Svenberg's Electronic processes in organic crystals and polymers.

Against reductionism in chemistry: Hoffmann

Roald Hoffmann shared the Nobel Prize in Chemistry in 1981 and has spent his career using quantum theory to gain insight into molecular structures and reactivity. Yet, in his beautiful book The Same and Not the Same (Columbia, 1995, pp. 19-20) he argues against reductionism:

“Scientists have bought the reductionist mode of thinking as their guiding ideology. Yet this philosophy bears so little relationship to the reality within which scientists themselves operate. And it carries potential danger to the discourse of scientists with the rest of society….

There are vertical and horizontal ways of understanding. The vertical way is by reducing a phenomenon to something deeper –classical reductionism. The horizontal way is by analysing the phenomenon within its own discipline and seeing its relationships to other concepts of equal complexity.

…..there are concepts in chemistry which are not reducible to physics. Or if they are so reduced, they lose much that is interesting about them. I would ask the reader who is a chemist to think of ideas such as aromaticity, acidity and basicity, the concept of a functional group, or a substituent effect. Those constructs have a tendency to wilt at the edges as one tries to define them too closely. They cannot be mathematicisized, they cannot be defined unambigously. But they are of fantastic utility to our science.”

Alternatives to struggling to do significant research

In a previous post The importance of being stupid! I highlighted the point that doing significant research is really hard.

Doing significant research should not be confused with publishing papers, getting grants, setting up a lab, getting tenure, getting cited, getting promoted, getting invited to speak at conferences.... All these activities are actually a lot easier. Because making real contributions over an extended period is so hard it is easier to get distracted or consumed with the "busy" activities listed above. There are also even worse options...

I was reminded of this recently when I read the novel The Masters, by C.P. Snow.
I was stimulated to read it by a lecture on C.S. Lewis and scientism, by Fritz Schaefer who recommends the novel for insights into the internal politics of Oxbridge colleges. The novel is part of a series, Strangers and Brothers, chronicling the life experience of Lewis Eliot as over course of several decades he moves from law office to university to industry to government. Some of the series parallels Snow’s own diverse life experience: he began his professional life as a molecular physicist, turned to writing novels, and eventually became a Baron and held high positions in the U.K. government. He is best known for his Rede lectures: The Two Cultures and the Scientific Revolution, which were delivered exactly 50 years ago this month.


The novel, the Masters, describes the political struggle amongst Fellows in a Cambridge College as they position, posture, and politic in anticipation of the election of the next Master of the college, while they wait for the current Master to die, after being diagnosed with a terminal illness. Snow is perceptive about human nature and paints an intimate portrait of his characters. Here is a random selection (page numbers are from the Penguin 1983 edition):

“I had known for minutes past, that this was coming: I had not wanted to talk of it that night. Jago was longing for me to say that he ought to be the next Master, that my own mind was made up, that I should vote from him. He had longed for me to say it without prompting. It was anguish to him to make the faintest hint without repsonse. Yet he was impelled to go on, he could not stop. It harassed me to see this proud man humiliating himself.” (p. 15)

The Master says, “Do you remember the trouble we had getting him [Calvert] elected [as a Fellow of the College], Eliot? Some of our friends show a singular instinct for preferring mediocrity. Like elects like of course. Or between me and you,” he whispered, “dull men elect dull men.” (p. 20)

Nightingale “was intensely suspicious, certain that there was a web of plans from which he would lose and others gain….. He had once possessed great promise. That was his bitterness. … By twenty-three he had written two good papers on molecular structure… but the spark burnt out… Often he had new conceptions: but the power to execute them had escaped from him. ……It would have been bitter to the most generous heart. In Nightingale’s it made him fester with envy…. Each job in the college for which he was passed over, he saw with intense suspiscion as a sign of the conspiracy directed against him…… as March came round each year, he waited for the announcement of the Royal Society elections in expectation, in anguish, in bitter suspicousness…” (p.46,47)

“Chrystal wanted to be no more than Dean, but he wanted the Dean, in this little empire of the college, to be known as a man of power. Less subltle, less reflective, more immediate than his friend [Brown], he needed the moment-by-moment sensation of power. He needed to feel that he was listened to, ……, that his word was obeyed.” (p.61)

Quantifying antiferromagnetic spin fluctuations

At the Gordon Research Conference on superconductivity, Nicolas Dorion-Leyraud is going to talk about his work described in the very nice preprint, Correlation between linear resistivity and Tc in organic and pnictide superconductors. It contains very detailed measurements of the temperature and pressure dependence of the resistivity of two Bechgaard salts, (TMTSF)2X where X=PF6,ClO4. These materials have a quasi-one-dimensional electronic structure. The resistivity is fit to a quadratic temperature dependence with A the co-efficient of the linear term [not to be confused with the quadratic coefficient associated with the Kadowaki-Woods ratio, and usually also denoted A!]. The Figure below shows how both A and the superconducting transition temperature Tc decrease with increasing pressure, as one moves away from the spin-density-wave phase which occurs below about 5 kbar.



The next Figure below shows how one also observes a similar correlation between A and Tc, for the X=ClO4 material, new pnictide superconductors, and overdoped cuprates. The paper discusses these results in the theoretical framework of recent calculations from two of the authors, Bourbonnais and Sedeki, who have a preprint, Link between antiferromagnetism and superconductivity probed by nuclear spin relaxation in organic conductors. The corresponding theory emphasizes the importance of the interference between superconducting and spin-density-wave fluctuations.

One of my first thoughts is:
how does this compare to what the antiferromagnetic spin fluctuation theory of Moriya and Ueda would predict?
Near an antiferromagnetic quantum critical point in two-dimensions they also predict the temperature dependence of the resistivity will be linear and the nmr T1 relaxation rate will be Curie-Weiss like. They also find that Tc is correlated with the energy scale T0, of the spin fluctuations. It is not clear to me what this theory predicts for the coefficient A as one moves away from the quantum critical point. It looks like at the QCP the resistivity slope A, scales with 1/T0.

It would be really nice to see an analysis that compares the two theories to both nmr, resistivity, and Tc data with a single set of parameters for each pressure.