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.