Saturday, February 27, 2010

Getting to the heart of quantum chemistry

For physicists like me struggling to understand quantum chemistry it often seems a plethora of acronyms, software, and approximations that appear to be detached from my knowledge of quantum many-body theory and chemical intuition. However, Seth Olsen recently recommended a review article by Michael Schmidt and Mark Gordon to me. I have started reading it and am fin
ding it understandable and helpful. I loved the introductory paragraph:

The essence of chemistry involves processes such as the formation and dissociation of chemical bonds, the excitation of an atom or molecule into a higher electronic state, and atomic or molecular ionization, in which electron pairs are separated. Although the end points of such processes (that is, the reactants and products) may frequently be reasonably well described using a simple wavefunction that corresponds to a single Lewis structure, this often cannot be said for the key species in between, such as transition structures, reactive intermediates, and excited electronic states. Such species often must be described with more complex wavefunctions in which several different arrangements of the electrons (electronic configurations) are taken into account.
[Aside: practically all chemical research concerning new materials for energy and information technologies is concerned with "key species in between". Density functional theory based methods work for the starting and ending species but generally fail miserably for the in between species.]
The key problem the article addresses is
The general form of a MCSCF [Multi-Configuration Self-Consistent Field] wavefunction is

which is a linear combination of several configurations [referred to as configuration state functions (CSFs), ΦK] [i.e. Slater determinants]. Each CSF differs in how the electrons are placed in the MOs [Molecular Orbitals], i. The MOs are usually expanded in a basis of AOs [Atomic Orbitals], χμ. A MCSCF wavefunction is one in which both the configuration mixing coefficients AK and the MO expansion coefficients Cμiare variationally optimized. Such a wavefunction is therefore distinct from a configuration interaction (CI) wavefunction, in which only the configuration mixing coefficients are variationally optimized.

Friday, February 26, 2010

When interactions do not seem to matter

At wednesday's meeting of the Quantum many-body theory reading group, we discussed the following points about the chapter, "Non-interacting electron gas".

To get more context on this chapter read, Chapter 2 of Ashcroft and Mermin, Solid State Physics. In particular, they show how the non-interacting fermion model of Sommerfeld can give a good semi-quantitative description of a wide range of properties of elemental metals such as heat capacity, magnetic susceptibility, and bulk compressibility.

Why is this success surprising? A simple estimate suggests that average potential energy due to the interactions of the electrons between each other is 1-10 times larger than the kinetic energy. Yet, the non-interacting fermion model ignores these electron-electron interactions.
So why does the theory work so well? For profound reasons embodied in Landau's Fermi liquid theory, the elementary excitations (quasi-particles) in a three-dimensional electron liquid (chapter 5) have a one-to-one correspondence to those of the non-interacting fermion model.
A key aspect to this is that the electron liquid has sufficiently high density that the Fermi energy is of the order of several eV (1 eV= 11,000 K)...
Consequently, most properties of elemental metals are determined by properties of the Fermi surface, i.e. only states near the Fermi energy.

All of this breaks down in one dimension (chapter 9) .
In two dimensions the existence of non-Fermi liquids is still controversial.

Next week we discuss chapter 2, "The Born-Oppenheimer Approximation."

Thursday, February 25, 2010

An excellent (and depressing?) question

My colleague, Ben Powell, recently sent me the thought provoking email below. I think it raises an excellent question. I want to think about my answer more, before I post something. Although, it is a little depressing that I cannot immediately rattle off several things....
Others should feel free to post their thoughts, provided it does not involve self-promotion.
When I was walking home last night I started wondering about the following question (brought on by the fact I realised that it is now more than 10 years since I started my PhD).

What do we KNOW now about CMT [Condensed Matter Theory] that we didn't know 10 years ago?

I stress the T in CMT as I specifically want to rule things like "that the pnictides superconduct" as the seem like chance discoveries - however interesting they are, but really I want understanding about real materials, which is clearly rapped up in the border between theory & expt. I'd like things to be on a firm footing and generally agreed upon, but really I'm happy to be a little fast and lose with

Advice for undergraduates

Next week classes for the year begin at Australian Universities. On sunday night I was at a dinner for new undergraduate students at Emmanuel College at UQ. The Principal, Stewart Gill, urged the students to look at a book What's wrong with University and how to make it work for you anyway, by a Canadian student Jeff Rybak.
I read some of the extracts on his website and found them quite helpful, partly because my daughter is starting university this year! She read some of it and we discussed it this morning.
Also, I think for faculty it is also important to look at such material to see things more from the students point of view, what they are struggling with, and how we can serve them better.

Wednesday, February 24, 2010

Reading group on quantum many-body theory

Today I am starting a weekly reading group on the basics of quantum many-body theory, mostly for postgraduate students. This is to partly fill the gap from the fact that we do not have graduate courses in Australia. We are going to read a chapter each week from the book, Advanced Solid State Physics, by Philip Phillips. I chose this for its clarity, brevity, and treatment of modern topics.

This initiative was inspired by a highly successful group that a colleague, Andrew Doherty, ran on quantum field theory last.
Previously, I was involved in groups that looked at Fulde's book, Electronic correlations in molecules and solids, and a review by Shaik and Hiberty on valence bond theory (now superseeded by their excellent book). I found both immensely valuable.

What is the value of such ventures?
I find understanding increases greatly when I read something and then talk about it. Furthermore, rather than getting stuck at points of derivations talking to someone else can remove the logjam.
The weekly meeting also provides accountability and discipline to keep reading.

Tuesday, February 23, 2010

Are you local or non-local?

I wrote in a previous post about the importance of listening to referees. I recently got back a referee report for this review on oxygen vacancies in cerium oxides (written with Elvis Shoko and Michael Smith). The report ended:

Finally, I cannot avoid suggesting the authors to have a look at: “A Conversation on VB vs MO Theory: A Never-Ending Rivalry? Roald Hoffmann, Sason Shaik, Philippe C. Hiberty. Accounts of Chemical Research 2003 36 (10), 750-756”. Perhaps, they will hear some familiar tones.

I read and enjoyed the paper [inspiring the post Marriage Counseling for Chemists] and am now trying to make concrete the connection with our work.

By a bond valence sum analysis of the structure around oxygen vacancies we consider the charge distribution arising from the two electrons left behind by removing an oxygen atom. We find rather subtle charge distributions; the two electrons do not simply localise on the two Ce ions next to the vacancy [the standard picture which is either assumed or claimed ot be supported by density functional theory based calculations]. Instead the two electrons can delocalise over the next nearest neighbours, but do not delocalise into the whole crystal.

At first the connection with the VB vs. MO debate was not clear but on reflection there may be some profound ones such as:

  • Valence Bond (VB) theory tends to localise electrons too much. Molecular Orbital (MO) theory tends delocalise electrons too much.
  • Our empirical valence bond sum approach is a very local picture and somehow capturing the same physics/chemistry as VB theory.
  • LDA is close to MO theory (it is a band theory, i.e., a non-local picture) and tends to delocalise electrons too much. Many of the LDA, and LDA+U calculations on cerium oxides artificially force electrons to localise on cerium ions.

Can we make any more connection than the above?

Monday, February 22, 2010

Polite physicists do not discuss this at dinner parties

I had some interesting but brief discussions today with Andrew Briggs about Tony Leggett's perspective on the quantum measurement problem. (see his Viewpoint in Science in 2005). Personally, I find Leggett's perspective a little extreme. I just think we need to have a more nuanced view of what "reality" is.
He considers three different views on the interpretation of Quantum Mechanics (QM):

(a) QM is the complete truth about the physical world, at all levels, and describes an external reality.

(b) QM is the complete truth (in the sense that it will always give reliable predictions concerning the nature of experiments) but describes no external reality.

(c) QM is not the complete truth about the world; at some level between that of the atom and that of human consciousness, other non–quantum mechanical principles intervene.

...... Personally, if I could be sure that we will forever regard QM as the whole truth about the physical world, I think I should grit my teeth and plump for option (b).

Surviving a Ph.D with humour

For those of us who completed our Ph.D a long time ago and now advise/supervise students it is good (and scary?) to go to to see things from the opposite side of the office door.

Saturday, February 20, 2010

Proton conduction in organic FETs?

This title is deliberately provocative. It is keeping with the notion of multiple alternative hypotheses. I note the following concerning organic Field Effect Transistors
  • The mobility of protons in water is 3 x 10-3 cm^2/Vs.
  • This is larger than the hole mobility in many OFETs.
  • Fabrication of many OFETs involves treatment with acids at some stage.
  • Gate dielectric surface treatments significantly affect device performance, as described in this review.
So can someone rule out the following hypothesis?
In some organic FETs there is actually a contribution to the current from protons (rather than holes) moving in the interface between the organic "semiconductor" and the gate dielectric.

Perhaps a systematic study of OFET performance as a function of humidity?

Friday, February 19, 2010

Is "organic semiconductors" a misnomer?

A wide range of organic molecular materials such as pentacene and polythiophene are attracting considerable interest because of the prospect of "plastic electronics". They can be used to fabricate devices such as light emitting diodes, photovoltaic cells, and field effect transistors, which are traditionally made with inorganic semiconductor materials such as silicon and gallium arsenide. Consequently, these organic materials are often referred to as organic semiconductors. This may seem reasonable because:
  • they have a conductivity that is activated in temperature
  • there is an energy gap of several eV to the lowest optically excited state
  • they can be used to make "semi-conductor type" devices
On the other hand, they have properties that are significantly different from inorganic semiconductor materials. These all relate to the fact that electronic states tend to be localised on single molecules whereas in inorganic semiconductors one can have states which are delocalised over many atoms.
  • they do not have well-defined conduction and valence bands (e.g., their mobility is almost always much less than that required for band transport) [just because you can calculate something does not mean it exists!]
  • they have a mobility that is thermally activated
  • energy gaps associated with optical absorption and conduction are significantly different
  • electronic correlations significantly modify the ordering of electronic states (e.g. there is a large gap between singlet and triplet excited states)
Because there is no band transport one cannot define a scattering time and one should not talk about "band bending" near an interface.

I think that referring to these materials as organic semiconductors has led a lot of confusion and debatable reasoning in the literature. I think "organic electronic materials" or "organic photonic materials" is much more appropriate.

Desperately seeking a smaller Hilbert space

Following up on an earlier post (with a great cartoon!) How big a Hilbert space do you need?, I have been trying to teach myself some of the basics of Schmidt decompositions of bipartite quantum states (before moving onto multi-particle states). A few things I learnt:

Schmidt decomposition is a restatement of Singular Value Decomposition in a different context.

The number of Schmidt coefficients in the Schmidt decomposition is the Schmidt rank.

The eigenstates of the reduced density matrix on one subsystem are the states in the Schmidt decomposition.

I have a basic question that hopefully some of my quantum information readers can answer.

For pure bipartite states can the minimal value of the Schmidt rank be related to the entanglement of formation (von Neumann entropy of the reduced density matrix)?

The Schmidt decomposition is unique if all of the expansion coefficients are non-zero and non-degenerate. But if some are zero the expansion is not unique. Is there a way to find the shortest possible expansion?

If so, this seems it could be useful when dealing with specific quantum states for which one is trying to find the shortest possible Schmidt decomposition which is "close" to the true state. This is what a lot of quantum chemistry is about: finding the best orbitals and the shortest expansion of Slater determinants.

Thursday, February 18, 2010

Exploiting entanglement for sensitive measurements

On Monday, Andrew Briggs from Oxford will be visiting UQ for the day. He will give a seminar about a recent Science paper from his group, Magnetic Field Sensing Beyond the Standard Quantum Limit Using 10-Spin NOON States.
Andrew was one of my hosts of a very nice sabbatical I had in Oxford back in 2004-2005, and I am looking forward to catching up with him. Four years ago our two families had a wonderful week sailing in the Whitsunday Islands...

Tuesday, February 16, 2010

Postdoc available

The official advertisement for a two year postdoctoral position to work with me is here. If you want to apply reading the "career advice" and "magnetoresistance" entries on this blog may be helpful.

Monday, February 15, 2010

Two-site Hubbard model for ethylene

Seth Olsen brought to my attention a nice paper from 1985 from the Journal of Chemical Education by M.A. Fox and F.A. Matsen which gives a detailed description of the electronic structure of the pi states in ethylene in terms of a two site Hubbard model.

Amongst other things it contains a discussion of singlet and triplet states in terms of Young tableau, something I have never understood....

Aside: In the Appendix a value for U/t is estimated by comparison of the energy levels with experiment. But, this looks a little inconsistent because the expressions used look like they are only valid for small U/t....
This was a paper that I was thinking of writing in terms of second quantised notation. Maybe that would still be helpful....

A more detailed quantitative description of the potential energy surfaces for the valence states of ethylene based on high level quantum chemistry (but does not explicitly mention a Hubbard model but can be mapped onto one) is by Krawczyk et al.

Sunday, February 14, 2010

When faculty politics becomes deadly

The Christian Science Monitor reports

A neuroscience professor at the University of Alabama-Huntsville has been charged with capital murder for killing three people after opening fire at a faculty hearing. Dr. Amy Bishop reportedly had learned that her request for tenure had been denied for a second time.

Saturday, February 13, 2010

A Ph.D without knowledge?

Sometimes I struggle with defining the minimum that someone should be able to do and know before they are allowed to graduate. Here is a story (possibly an urban legend) which might put things in perspective.
At Princeton after a student submits their Physics Ph.D thesis they are given an oral exam by a faculty sub-committee. After a short presentation on the thesis by the student they are asked questions about it for half an hour or so. Then the faculty can ask the student ANY question about ANY area of physics (e.g., why is the sky blue? why is diamond called "ice" by criminals? explain the twin paradox in special relativity.) I believe the purpose of this is to show students how much they do NOT know, particularly about basic physics.
Many years ago there was a very bright young student who completed a thesis on general relativity and was about to go and do a postdoc with Stephen Hawking. He was asked, "How big is an atom?" He did not know!
But, he got his Ph.D.
So, who was the student? Someone once told me it was Nathan Myhrvold, who for many years was Chief Technology Officer at Microsoft.

Friday, February 12, 2010

Breakdown of the Born-Oppenheimer approximation

The Born-Oppenheimer approximation is the starting point for all quantum chemistry and crystal band structure calculations. It allows one to factorise the electron-nuclear quantum state. It can be justified because nuclei are much heavy than electrons. However, it breaks down near electronic degeneracies. A case that has attracted a lot of attention are conical intersections between two potential energy surfaces for different electronic states of molecules. Such intersections provide a rapid means for non-radiative decay of excited states.

Going beyond Born-Oppenheimer represents a major challenge. A nice recent review for molecules is by Worth and Cederbaum.
A few years ago in a Phys. Rev. A paper, Andrew Hines, Chris Dawson, Gerard Milburn and I considered two different Jahn-Teller model Hamiltonians and quantified the entanglement of the electronic and nuclear degrees of freedom. One of these models has a conical intersection.

Thursday, February 11, 2010

A metal and an insulator at the same time?

Michael Smith brought to my attention a really nice preprint, Interplay charge dynamics in a valence-bond dynamical mean-field theory of cuprate superconductors, by Michel Ferrero, Olivier Parcollet, Gabriel Kotliar, and Antoine Georges.

This helps resolve the following major puzzle about the metallic state of the cuprate superconductors. In conventional metals (insulators) one observes that the resistivity monotonically increases (decreases) with increasing temperature. Indeed for currents parallel to layers the cuprates show the temperature dependence characteristic of a metal. But, for currents perpendicular to the layers underdoped systems show a temperature dependence characteristic of an insulator.
How can it be a metal in one direction and an insulator in another?

It turns out that the key physics involved is:
  • the interlayer tunneling matrix element is momentum dependent (as required by the symmetry of the crystal) and vanishes in the parts of the Brillouin zone in which the nodes of the pseudogap occur in the underdoped system.
  • this means that the interlayer charge dynamics is dominated by the antinodal region and so particularly sensitive to the pseudogap
  • the temperature dependence of the scattering rate in the nodal region is sensitive to doping and at low temperatures the nodal quasi-particles become more coherent
Some of this physics was anticipated in a phenomenological "cold spots" model by Ioffe and Millis in 1998. What is new and important about Ferrero et al.'s work is that they start with a Hubbard model and calculate the temperature, frequency, and doping dependence that are consistent with experiment.

It is also interesting to me that rho* in the figure above has the value characteristic of a bad metal.

Tuesday, February 9, 2010

Marriage counseling for chemists

Roald Hoffmann, Philippe Hiberty, and Sason Shaik are probably my three favourite theoretical chemists. They write beautiful papers which focus on the quantum mechanical basis for chemical concepts and understanding rather than computation. Being a fly on the wall when they are all in one room for a scientific discussion would be fascinating. Well I don't have to dream. There is a really nice paper in Accounts of Chemical Research, A Conversation on VB vs. MO theory: a never ending rivalry. The three discuss and argue the relative merits and relationship between valence bond theory and molecular orbital theory. Here are a few choice quotes:

RH: A standard technique in marriage counseling (and I do think that MO and VB are a partnership) is to have the two parties stop and repeat, with an effort at understanding, what was said by the other partner. Can we try that? ......

PH: .......Pauling was smart enough to disguise all these “physical” elements of VB and packaged it as simple resonance theory. This was good for the 1930s, but now chemists have more theoretical savvy, and can digest these bits of physics, couldn’t they?

RH: Maybe. Some of them think theory is computation, and dignify that with the name of physical insight. The best physicists I’ve known - people like Ed Purcell - were after a quality of understanding that is ... almost chemical.

SS: ........ what tipped the balance in favor of MO may have been simply the computer implementation of MO-based theories. Chemists are a practical lot; they simply went where they could calculate.

RH: As they are doing now with the software available - it’s amazing what gains prominence just because there is a button in Gaussian to do it!

Monday, February 8, 2010

Monitoring blog traffic

Google Analytics provides any easy way to track traffic on your web page or blog. This blog normally gets about 40-80 page views per day. Certainly, enough to encourage me that there is enough interest that it is worth my effort. But, I got a bit of a shock when I last checked. Here are the number of page views for the past week:

Monday 70
Tuesday 91
Wednesday 159
Thursday 369
Friday 1877
Saturday 326
Sunday 117

Why the spike centered on Friday? It seems the post on the Nature paper using 17 parameter fits was featured by Hacker News, producing 1300 hits. I was impressed that they went back and read my earlier posts about curve fitting, particularly the Nature article by Freeman Dyson about getting the elephant's trunk to wiggle.

The cartoon is from a Physics Today article, Encouraging good science on the web, by Alexander Antunes.

Quantum dynamics of nuclei

John Negele wrote a really nice Physics Today article in 1985 on the role of mean-field theory in nuclear physics.
Ideas discussed include:
-nuclei are small drops of a dense, strongly interacting quantum liquid
-why the success of mean-field theory is astonishing
-but it works because of Landau's Fermi liquid theory
-in nuclei the density varies smoothly (they are not billiard balls)
-instantons (imaginary time trajectories) provide a natural way to describe tunneling effects such as fission and fusion
-the effective nucleon-nucleon interaction is density dependent
-as the density of nuclear matter increases the effective interaction increases and neutrons can escape the nucleus and form a "gas". this is what happens in neutron stars

I have been reading this in preparing for the visit of Cedric Simenel to UQ this week. I am looking forward to hearing his seminar which will feature the picture above and discuss significant advances in dynamical simulations since Negele's article.

Saturday, February 6, 2010

What resources make a great teacher?

Believe it or not, this post was inspired by a stirring (and amusing) piece, Beware the ego trip, by columnist Kathleen Noonan in Brisbane's tabloid newspaper. The relevant bit for readers of this blog is the reference to an article in the Atlantic Monthly, What makes a great teacher? Noonan summarises:

More than any other variable in education - more than schools or curriculum - teachers matter.

First, great teachers tended to set big goals for their students. They always were looking for ways to improve their effectiveness. Great teachers constantly re-evaluate what they are doing.

Great teachers had four other tendencies in common: they avidly recruited students and their families into the process; they maintained focus; they planned exhaustively and purposefully - for the next day or the year ahead - by working backwards from the desired outcome; and they worked relentlessly, refusing to surrender to poverty, bureaucracy and budgetary shortfalls.

The other thing that predicted success in the classroom was . . . wait for it . . . happy teachers. Teachers who scored high in "life satisfaction" were 43 per cent more likely to perform well in the classroom than their less satisfied colleagues. Their zest and enthusiasm spreads.

University middle managers should take note.

Friday, February 5, 2010

Desperately seeking spin liquids III

It was wonderful having Bruce Normand visit UQ this week. It is great having a visitor come who meets individually with students, postdocs, and faculty and discusses their work at length. I think we all learnt a lot and appreciated the constructive feedback.

Bruce made me aware of a nice accessible review Frontiers in frustrated magnetism that he just published in Contemporary Physics.
The focus is on spin liquids: whether they exist in real materials and/or Heisenberg lattice models. This gives more background relevant to a conjecture I discussed in two previous posts. From Bruce's seminar and discussions I now realise there is a strong candidate counter-example to the conjecture. That is the Heisenberg model on the isotropic triangular lattice with multiple spin exchange. The best numerical evidence of a spin liquid (unbroken lattice symmetry, spin gap) is in this paper. It would be great if more numerical work was done on this model using new methods such as those based on tensor-network states.

The challenge of science journalism

Thursday, February 4, 2010

Nature publishes 17 parameter fits to 20 plus data points

Today's issue of Nature has a paper which features the Figure above. According to the Supplementary Material the curves shown involve 17 free parameters. The authors showed me a draft of the paper and I pointed this out to them. It was this experience which inspired the "curve fitting" posts on this blog.

Wednesday, February 3, 2010

Alternative quasi-particles in nuclei

Describing a nucleus with quantum many-body theory is a fascinating and challenging problem with a long history. Previously I wrote about the highly successful shell model which treats the nucleons as weakly interacting with one another.

A complementary approach for nuclei with an equal even number of protons and of neutrons is to view the basic "quasi-particle" as an alpha particle (a bound set of 2 neutrons and 2 protons). This takes into account some aspect of the strong short-range interactin between nucleons. A really nice accessible review by Martin Freer is worth looking at (especially figures 1, 4, and 5). This gives a natural description of the Hoyle state, "The importance of this state is arguably unparalleled in nuclear science." [In order to explain stellar nucleosynthesis of carbon, Sir Fred Hoyle successfully predicted the existence, energy, and quantum numbers of this state in carbon.]

There is a nice Physics article by Michael Carpenter which considers Do alpha particles cluster inside heavy nuclei? and gives a viewpoint on a recent PRL showing evidence for a alpha + 208Pb state in 212Po.

A Ph.D without scholarship?

An interesting and controversial question for Ph.D's in science and engineering is too what extent students should be expected to have become "scholars." This issue also came in an earlier post about whether being able to write should be a necessary requirement for getting a Ph.D.

To me, some key characteristics of scholarship are the ability to frame and answer questions, ability to put a problem in the context of a discipline, a knowledge of and critical appreciation for earlier work in the field, and the ability to communicate about the topic.
On the other hand, a really important Ph.D will probably involve some highly technical (and specialised) achievement whether it is making a new molecule, developing a new computer algorithm, deriving or solving an equation, fabricating a new electronic device, or developing a new experimental technique, ....
Scholarship and technical achievement may be almost orthogonal to each other.

At UQ after one year of enrollment in the Ph.D program students must write a ten page report which defines their project, gives a literature survey, and sets goals and a timeline for finishing their Ph.D. I am on the committee which reviews each student. I increasingly struggle with the lack of scholarship and the highly technical focus of the student reports. I have tried to come up with a list of what I would like a student to be able to do at this stage. Here is a rough attempt which will hopefully generate some discussion. (The numbers are extremely rough).

State three big scientific questions in this field.

State a specific scientific question that your project will answer.

What are five key concepts in this field?

What are five landmark papers in the field from the last century? For each paper write several sentences saying why it is so important.

Which three papers from the last 5 years are most relevant to your project?

Monday, February 1, 2010

Evolution does not optimise everything

When discussing biological molecules performing some function I often read statements by physicists and chemists along the lines, "evolution over billions of years has optimised this physical property so the molecule can perform its function."

My understanding of evolutionary biology is limited. However, I think these statements present a mis-understanding.
Evolutionary pressures lead to changes that will increase the chances of survival, or perhaps more correctly over time the biomolecular systems which can survive best in their environment survive....
But the crucial point is that the "fitness function" of a biomolecule depends on many variables. The optimum fitness function will not optimise all variables.

Consider the specific example of light-harvesting complexes for photosynthesis. The fittest will not necessarily be those which transport energy the fastest. There are many other variables such as robustness to UV light, sensitivity to changes in pH, matching the solar spectrum, .....

A similar issue arises with photovoltaic cells. Everyone is trying to achieve a greater efficiency and there are often statements such as "if we can make organic cells operating at 12 per cent (or some other number) we will save the planet". But there are many other key variables: cost, durability, stability, scarcity of materials, .....
If someone found a way to make 2 per cent solar cells that were made of naturally occuring materials, cost 1 cent/square metre to manufacture, and were completely reliable for 30 years, ..... well I think we would be done....

Please correct my mis-understandings....

Postdoc available

Subject to final administrative approval, I am about to advertise a two year postdoc to work on the theory of interlayer magnetoresistance in strongly correlated electron materials. Previous posts on magnetoresistance give the flavour of the relevant science.
I will post a link to the official advert when it is approved.