Hiding the truth

In their wonderful (and provocative) PNAS article, The Theory of Everything, Laughlin and Pines introduced the term protectorate to describe the insensitivity of higher level laws (organising principles) to the details of lower level laws. For example, the laws of thermodynamics are the same regardless of whether the microscopic dynamics of the constituent particles is quantum or classical. Universality in the theory of continuous phase transitions is another important example. Near the liquid-vapour critical point the critical exponents are independent of the chemical composition of the system or of the interatomic forces involved.

Conference highlights

Here are a few things I learnt this week:

Dirk Manske showed that it is very difficult to use electron-phonon coupling to simultaneously explain more than one set of experimental results in the cuprates. Those, such as Devereux and Shen (Stanford) who claim they can must use values for the coupling constants which are as much as an order of magnitude different from what electronic structure calculations give (a case of where the details matter). A nice (but perhaps understated) summary of the results is here.

Jurgen Haase showed how NMR experiments on the cuprates exhibit very large line widths which can be explained in terms of a large spatially inhomogeneous distribution of dopings. Here is one reference, but I would like to find others.
He did not discuss it but he is also a proponent (with Slichter and Williams) of the two-component model for the cuprates, supporting Baryzkin and Pines.

more to follow...

Correlated talks

Yesterday, my colleague Ben Powell gave a talk in the same session as me at the conference. Ben talked about the really nice work he did with Anthony Jacko and John Fjaerestad on the Kadowaki-Woods ratio for strongly correlated electron metals (see here).

A quantity of relevance to their work is the frequency dependence of the self energy, and how it decreases with increasing frequency. It was only listening to Ben's talk, that I realised I showed this quantity in my talk!


For a momentum independent self energy one can calculate the frequency-dependent conductivity, neglecting vertex corrections. Then the left (right) panel gives the frequency dependent scattering rate (effective mass), which is the imaginary (real) part of the self energy.
The top panels are a theoretical calculation and the bottom panels experimental results.

Ubiquitious spin and correlation physics

Today I am giving a talk at the conference. Here is the latest version of the talk. Although it is mostly based on this PRL, I hope I can bring out some of the common physics and issues with a much broader range of systems. A few take home points

• universality (details such as crystal and chemical structures often don't matter)
• some similar physics in organic charge transfer salts and transition metal oxides and heavy fermion compounds
• Kondo physics is even relevant in systems without magnetic impurities!
• Dynamical mean-field captures the crossover from a Fermi liquid (and existence of quasi-particles) to a bad metal at high temperatures.
• But, "low" and "high" are relative (high temperature could be above 20 K!)
• Optical conductivity is a powerful probe to see the destruction of quasi-particles and effects of strong correlations
  

A new iron age (of superconductivity)

Yesterday, Ilya Eremin (MPI, Dresden) gave a really nice talk on the new Ferropnictide superconductors. It was a model of clarity. Here are a few brief notes with a few comments of mine interspersed in parentheses.

Bednorz and Muller changed the landscape of condensed matter physics!
[RHM: Strongly correlated electron materials moved from the peripheral to the centre of the field. ]

Current highest Tc=55 K SmFeAsO1-xFx

Surprising this is a superconductor since it contains iron has a large Hund's rule coupling

Pnictides vs. cuprates: similarities and differences

Similarities
Both are layered (CuO2 vs. FeAs), have d-electrons in a key role, and have AF and SC in close proximity in phase diagram

Differences
FeAs is always metallic, i.e., no Mott insulator in phase diagram
In pnictides d-bands are far from half filling, i.e., almost full (fermi surface close to gamma point) or empty (compensated metal)
EVEN number of electrons (close to 3d6) per iron atom in parent material vs.
one electron per copper atom in cuprate parent

(J. Zhao et al., Nature Materials 2008)

Claims
interactions are smaller than the bandwidth
interesting physis is due to proximity to perfect nesting
whole band is nested, not just the Fermi surface

[RHM: is a key signature of cuprate vs. pnictide difference the size of the magnetic moment in the SDW phase? it turns out to me more subtle than this see below]

For perfect nesting SDW instability occurs for small U

Nesting leads to two competing logarithmic diverges: both in SDW and SC channel
(T.M. Rice for Cr, ) so they must be considered on equal footing and worry about interference effects [this is quite different to the cuprates, where one tends to think in terms of a doped Mott insulator]

[RHM: Similar issues concerning the interference between the particle-hole and particle-particle channels occur in one dimension: cf., Solyom, 1980]

"Toy model":
[I prefer the term "minimal model", perhaps for marketing reasons?]

This has two parabolic bands (alpha and beta band) with identical dispersion and circular Fermi surfaces. One is centred at Gamma point and the other at the corner of the Brillouin zone.
4 types of interactions: both intra-band and inter-band.
There are then 4 possible instabilities:
SDW,
CDW,
s-wave superconductivity
s-wave superconductivity (pi phase shift between bands)

Derives RG equations for the four interactions u1, u2, u3, and u4
[PRB, 2008, Chubukov, Efremov, Eremin]

Strongest instability is SDW then CDW, then extended s-wave. The growth rate of the latter coupling constant changes sign with increasing rescaling (i.e., RG flow) resulting from the interfering logarithms.

Similar results are obtained from functional RG [Visawanath et al, PRL 09]

Can we understand real space magnetism in terms of an itinerant SDW picture?
Two inequivalent As positions leads to ambiguity in Fe sublattice order
Experiment shows (0,pi) order with respect to Fe lattice (stripe like AFM structure)

An alternative picture is that of localised spins in frustrated J1-J2 model. [Uhrig, Holt, Hamer, Oitmaa, and Singh, PRB 2009]. Then the reduced magnetic moment comes from proximity to a quantum phase transition rather than itinerancy.

Look at Fermi surface in unfolded Brillouin zone
Now four pockets alone BZ boundary (i.e., one hole and two electron pockets)
mean-field equations do not specify relative size and magnitude of two
pocket order parameter amplitudes
ground state degeneracy is larger than in J1-J2 model
O(6) degeneracy = 5 goldstone modes

But electron pockets are elliptic, no need for quantum fluctuations in itinerant picture
charge fluctuations are crucial,

Questions:
seems cant get the SDW to SC transition with doping, i.e., moving away from perfect nesting does dominant interaction changes

not clear answer, seems may end up with nodes on fermi surface.

Experimental investigations of Quantum dynamics of excited states of biomolecular chromophores

Last week in Germany I was pleased to meet Roland Wester who does beautiful experiments using crossed molecular beams to image complex chemical reaction dynamics. An example, is a recent Science paper where Roland's group studied a classic S2N subsitution reaction:
Cl^– + CH₃I -> I^– + CH₃Cl

Such experiments can provide significant tests on our basic understanding of reaction mechanisms, quantum dynamics and ab-initio electronic structure calculations.

I was delighted Roland told me he is planning to do some experiments on biological chromophore molecues including the Green Flourescent Protein chromophore. I am interested to learn more about this, particularly how it could provide a test of theoretical work of Seth Olsen and I, such as our recent paper in J. Chem. Phys., concerning photo-isomerisation of the GFP chromophore.

The cast of characters

Hermann Grabert kindly sent the photo of the participants at the 2nd Black Forest Focus on Soft Matter: Quantum efficiency from Biology to Materials Science.

There seems to be uncertainty about anyones position but I guess the camera made a projective measurement of everyones position onto a position eigenstate...