Universities are failing B+ students

There is an Opinion piece by Bob Herbert in the New York Times, College: The Easy Way that is worth reading. He discusses a systematic study which found a large fraction of American college graduates did not seem any better educated than when they started college. The study is published in a book, Academically Adrift by Richard Arum and Josipa Roska, which raises important and fundamental questions about the responsibilities of both students, faculty, and administrators.

New superconducting state in organics

I found this recent PRB,  Temperature-pressure phase diagram and electronic properties of the organic metal κ-(BETS)₂Mn[N(CN)₂]₃

particularly interesting. This material has a qualitatively different band structure from many of the kappa-(BEDT-TTF)2X family of organic charge transfer salts. In terms of the relevant tight-binding model t' > t so that it is closer to the limit of weakly coupled chains rather than to the square lattice [for background see the PRL referenced below and/or this recent review, which will appear in Reports of Progress in Physics]. The figure below shows the band structure and the Fermi surface for the new kappa-BETS material.

The observed pressure-temperature phase diagram is below. The system is always at half-filling and so the insulating state is a Mott-Hubbard insulator.

What is the symmetry of the pairing in the superconducting state.

Based on calculations reported in a PRL by Ben Powell and I, the superconductivity will have A_1 symmetry with "accidental" nodes in the energy gap. In contrast, in other kappa organics (which have t' < 0.8t or so) we predict A_2 symmetry with nodes required by symmetry.

The picture below shows the phase of the superconducting order parameter over the Brillouin zone for parameter values in a comparable regime to the new kappa-BETS material. The solid line is the Fermi surface (and the diagonals correspond to the Y and Z axes shown above.

The funny state of chemistry

Eric Bittner, who has been a good source of humour for this blog, sent me an abstract for a chemistry paper. Do you think it is funny?
I actually did not laugh but groaned because it is a bit too close to the truth...
Actually, the chemistry abstract which made me laugh was this one, which was completely serious.

Experimental signatures of Berry's phase in solids

Today I was puzzling over quantisation conditions for electrons in magnetic fields and learnt a lot from a paper, Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
 A few things I learnt:

The phase mismatch gamma which occurs in the semi-classical quantisation condition (for the wavefunction) is related to the Maslov index (number of caustics) in the classical periodic orbit.
Aside: I am still confused as to exactly what a caustic is and how to visualise it.

This phase can be observed in the quantum Hall effect and deHaas van Alphen effect. In graphene it is found to have a different value (gamma=0) from conventional metals (gamma=1/2). This is usually stated as being due to Berry phase effects. But there is more to the story...

The phase parameter gamma_L which occurs in the energy quantisation condition is NOT necessarily the same as gamma. This is only the topological part of the Berry phase.
For a system with a gap the total Berry phase depends on the magnitude of the gap, whereas gamma_L does not. 

Chemical reactivity is more than transition states

The concept of a transition state is one of the key concepts in understanding chemical reactivity. It is the maximum on a potential energy surface (PES), for which the reactants and products are local minima. But there is more to the story...

This is nice paper Reaction Force and Its Link to Diabatic Analysis: A Unifying Approach to Analyzing Chemical Reactions, by Peter Politzer, Jeff Reimers, Jane Murray, and Alejandro Toro-Labb in JPC Letters.

It discusses the notion of the reaction force, the derivative of the potential energy, and how its sign and magnitude can be used to classify different parts of a chemical reaction. The blue dashed lines below define different regions: activation -> transition -> relaxation. 

It turns out that some reactions are dominated by activation (the weakening of bonds) rather than transition (the breaking of bonds). Hence, in seeking to speed up a specific reaction with a catalyst one should target that part of the reaction.

This leads to a variation of the Hammond-Leffler postulate that correlates activation energies with heats of reactions.

What is new in this paper? They connect the reaction force and this division of the reaction path with a diabatic state analysis: which divides a reaction into electronic factors (which dominate the transition state) and nuclear reorganisation.

How good is the Drude model?

We teach it to undergraduates [as I am doing today!] and claim that it captures many properties of elemental metals? Then we say it works badly for cuprates and other strongly correlated electron metals. But, just how good is it? Surely, this should be in textbooks. But, it actually took me a long time to find the graph below. It shows the frequency dependence of the real and imaginary part of the dielectric constant for gold. The solid lines are the Drude predictions with two free parameters, the dc conductivity and the quasi-particle scattering time. The experimental data covers the range 50 to 20,000 cm-1.

The figure is from an Applied Optics paper by Ordal et al.

What is a topological insulator?

Today Tony Wright is giving the weekly Quantum Science Seminar on Topological Insulators. Some people consider this new state of matter one of the most important discoveries and achievements of condensed matter theory in the past decade [see this Nature News feature]. Basically they are metallic states which occur on the surfaces of insulators as a result of topological effects associated with the band structure of the solid.
A really helpful introduction, The birth of topological insulators, by Joel Moore appeared in Nature last year.
I think a more accurate and helpful name for this class of materials might be something like "topological surface metals" or "topological metals". What do others think?