"Seeing" quasi-particles go over the waterfall

Check out this experimental data!
I am very impressed with how over the past two decades the quality and resolution of Angle Resolved PhotoEmission Spectroscopy (ARPES) data has improved so significantly.

Nigel Hussey brought to my attention a beautiful paper  Anisotropic quasiparticle scattering rates in slightly underdoped to optimally doped high-temperature La2−xSrxCuO4 superconductors

This allows one to clearly see real quantum many-body effects with the "naked eye".

The Figure below shows an intensity plot as a function of energy and momentum from
an cuprate superconductor with approximately optimum doping. The intensity is proportional to the one electron spectral function (imaginary part of the Greens function).

If there are well defined quasi-particles this should have a clear maximum which disperses (i.e. defines an energy vs. momentum curve). The blue dashed line is the bare dispersion one estimates from band structure calculations. One can see that near the Fermi energy the actual dispersion curve has a much smaller slope indicative of signficant renormalisation due to many-body effects. The almost vertical slope between EI and EII is known as the "waterfall" (WF).

Notice that the quasi-particle peak gets broader as one moves away from the Fermi energy as one would expect for a "Fermi liquid" (or something similar).

Using a model bare dispersion one can extract both the energy and momentum dependence of the self energy. It turns out that the imaginary part has the form

where phi is the angle around the Fermi surface.

The first term is associated with disorder and the second with inelastic scattering in a marginal Fermi liquid (which scales linearly with frequency).

[In a Fermi liquid the scattering scales quadratically with frequency.].

The momentum (phi) dependence has a "d-wave" form will cold spots near the nodes.

I also found this particularly interesting because angle-dependent magnetoresistance measurements from Nigel Hussey's group on an overdoped cuprate found a similar angular dependence for the inelastic scattering rate and an approximately linear temperature dependence. (A Nature Physics paper describes this result and a PRL shows how the strength of the anisotropic scattering increases as the doping is reduced.)

If two different groups using different techniques on different materials observe the same physics it suggests that there is a significant effect here.

100 most influential living British scientists

Last week The Times (London) newspaper published in their Eureka magazine an ordered list of the 100 most important people in British science and engineering. Dame Athene Donald  (Soft condensed matter, Cambridge) was one of four panelists who made the selection. Condensed matter physicists who I could see on the list included Andre Geim, John Pendry (meta materials), Richard Friend (OLEDs and plastic electronics), and Steve Bramwell (spin ice).
[I have to confess I bought the newspaper for other reasons... to get the latest news for my son about the Liverpool FC sale...]


Perhaps people who could be argued might be on the list include Peter Littlewood (Head of the Cavendish lab, Cambridge), Andrew Taylor (Director of ISIS),  and Gabe Aeppli (Director, London Centre for Nanotechnology).

Bardeen International Airport?

I was intrigued and impressed that the Belgrade airport is called Belgrade Nikola Tesla Airport. This the only case I have encountered of an airport named after a scientist. They mostly seem to be named after politicians (e.g. JFK and Ronald Reagan) and rock stars (John Lennon in Liverpool). Here are a few proposals:

LAX - Linus Pauling
Urbana - John Bardeen
Newark - Phil Anderson
Adelaide - William Bragg

Any other ideas?

It is interesting reading the wikipedia page about Tesla, particularly the observation that he probably suffered from obessive-compulsive disorder. He is another example of where the dividing line between genius and mental illness is a fine one.

An iconic disaster

While in Belgrade, my gracious host Darko Tanaskovic took me to afternoon tea at a really nice restaurant, The Balkan Express, which had spectacular views of the Danube. The restaurant uses the iconic picture below on many of its publicity material. 

I was curious if the train wreck actually was the Balkan Express. It turns to actually have been a French domestic train at Montparnasse station in Paris in 1895.

Correlations clean up crystals

Yesterday I had some nice discussions at the Institute of Physics (Belgrade) with Darko Tanaskovic. One thing fascinating thing I learnt was about how near the Mott transition strong correlations can screen the effect of site disorder in the metallic phase. This is described in a PRL which contains the Figure below.

It shows the scattering rate at zero temperature [normalised to the non-interacting value] as a function of U/Uc where Uc is the value of U at which the Mott transition occurs. The different curves corresponding to increasing disorder strength [bottom to top]. Note that even a long way from the Mott transition [e.g. when U/Uc = 0.5 and so the effective mass may only be enhanced by a factor of 2] the scattering rate can be reduced an order of magnitude by the correlations.

Some of this can be capture semi-quantitatively for weak disorder by a slave boson treatment which gives the following analytical expression for the scattering rate

When I first started working on organic charge transfer salts about 15 years ago I remember people asking Jim Brooks why the crystals were so pure that one could observe beautiful quantum oscillations? After all they are just grown using $100s worth of electrochemistry equipment as opposed to the $M molecular beam epitaxy (MBE) machines used to make semiconductor heterostructures. Jim said that somehow "self assembly" and "self purification" occurs in the crystal growth.

The scattering rate in the actual materials can be less than 0.1 meV, which seems small given that it is easy to imagine variations in the site potential of the order of 10-100's meV [see e.g, the discussion here].

However, Darko's work may give another explanation for the apparent purity of these materials. Most of these organic metals are quite close to a Mott insulating phase and so the correlations actually screen the disorder that is present.

Talk in Belgrade

Tomorrow I am giving a colloquium, "Destruction of quasi-particles near the Mott transition," at the Institute of Physics Belgrade. Here is the current version of the slides for the talk. The key reference is this PRL.

A key property of the cuprate superconductors

First, some trivia. Neville Mott wrote his seminal paper on the metal-insulator transition while at Bristol University. I am writing this in the H.H. Wills building where he worked and down the corridor from the Mott lecture theatre!

This week Nigel Hussey taught me something important about the cuprate superconductors: the electronic density of states (or effective mass) does not vary significantly with doping. This is inconsistent with the Brinkmann-Rice picture which predicts that the effective mass is inversely proportional to the doping.

This figure is taken from a paper by Wade et al.
The effective mass that one deduces from the optical conductivity also shows a weak doping dependence as summarised in the figure below, taken from this  PRB paper.