Monday, June 4, 2012

Effect of disorder on the Mott-Hubbard transition

I have been reading through a very interesting review paper
Mott-Anderson Transition in Molecular Conductors: Influence of Randomness on Strongly Correlated Electrons in the κ-(BEDT-TTF)2X System
by Takahiko Sasaki

It reviews some very nice experiments done by Sasaki and collaborators where they used X-ray irradiation to systematically vary the amount of disorder.

There are several things I find puzzling about the experimental results for X=Cu[N(CN)2]Br. I also think they are inconsistent with the offered interpretation in terms of Anderson localisation.
It is observed that irradiation does longer than 200 hours drive the material from a metallic phase to a Mott insulating phase.

First, I don't think invoking Anderson localization is relevant because the amount of disorder is relatively small, compared to the electronic bandwidth. Specifically, even for doses of 200 hours the sample is still a superconductor [probably d-wave] with a Tc of about 6 K, reduced from about 12 K in non-irradiated samples. This means [cf. Figure 9 in the paper] that the scattering rate due to impurities is about 6 K ~ 0.5 meV which is two orders of magnitude less than the hopping integral t.

Second, theory [at least at the level of DMFT] predicts that disorder [much less than the band width] stabilises the metallic phase not the Mott insulating phase. This can be seen in the phase diagram below taken from this PRL by Krzysztof Byczuk, Walter Hofstetter, and Dieter Vollhardt.
In the experiment Delta would be much less than 1 and U slightly less than 1.

I also note that the experiments found that the for X=Cu[N(CN)2]Cl and X=Cu2(CN)3 irradiation (disorder) drove the Mott insulating phase towards the metallic phase, consistent with the above phase diagram.

So I think the paper shows how a metallic system very close to the Mott transition can be driven into the insulating phase by a relatively small amount of disorder. Current theory seems unable to explain this.

[I thank Andrew Bardin for bringing the paper to my attention at a cake meeting.]


  1. You compare the disorder to the bandwidth. What are the units of disorder for this problem?

  2. The strength of the disorder can be parameterised by the root-mean-squared fluctuation in the potential on every site.
    Hence, it has units of energy.

  3. The idea that small amounts of disorder can drive a correlated metal/superconductor insulating also gains experimental support from Taniguchi et al PRB 67, 014510 (2003). Where they varied cooling rate to control the disorder in the terminal ethylene groups in k-(BEDT-TTF)2[N(CN)2]Br.