Monday, March 2, 2015

Quantum criticality near the Mott transition in organics?

There is an interesting paper
Quantum criticality of Mott transition in organic materials 
Tetsuya Furukawa, Kazuya Miyagawa, Hiromi Taniguchi, Reizo Kato, Kazushi Kanoda

Some of the results were flagged several years ago by Kanoda in a talk at KITP.

Key to the analysis is theoretical concepts developed in three papers based on Dynamical Mean-Field Theory (DMFT) calculations

Quantum Critical Transport near the Mott Transition
by H. Terletska, J. Vučičević, Darko Tanasković, and Vlad Dobrosavljević

Finite-temperature crossover and the quantum Widom line near the Mott transition 
J. Vučičević, H. Terletska, D. Tanasković, and V. Dobrosavljević

Bad-metal behavior reveals Mott quantum criticality in doped Hubbard models
J. Vučičević, D. Tanasković, M. J. Rozenberg, and V. Dobrosavljević

The experimental authors consider three different organic charge transfer salts that undergo a metal-insulator transition as a function of pressure, with a critical point at a finite temperature. One of the phase diagrams is below.
The dots denote the Widom line determined at each temperature by the inflexion point in the resistivity versus pressure curve shown below.

They have different insulating ground states (spin liquid or antiferromagnet) and different shapes for the Widom line associated with the metal-insulator crossover above the critical temperature. Yet, the same universal behaviour is observed for the resistivity.

Aside: there is a subtle issue I raised in an earlier post. For these materials the resistivity versus temperature is non-monotonic, raising questions about what criteria you use to distinguish metals and insulators.

Here one sees that if the resistivity is scaled by the resistivity along the Widom line, then it becomes monotonic and one sees a clear distinction/bifurcation between metal and insulator.

This "collapse" of the data is very impressive.
The above universal curves then determine critical exponents through a relation

+ for insulator, - for metal
z= dynamical exponent
nu = exponent for the correlation length
The metal and insulator have the "same" temperature dependence, modulo a sign!

The data give z nu = 0.68, 0. 62, and 0.49 for the three different compounds.
This compares to the value of z nu = 0.57 obtained in the DMFT calculations, and 0.67 from a field theory from Senthil and collaborators. In contrast, Imada's "marginal theory" gives 2 and Si-MOSFETs give 1.67.

But the devil may be in the details. Some caution is in order because for me the paper raises a number of questions or concerns.

The interlayer resistivity near the critical point is about 0.1-1 Ohm-cm. Note that this about three orders of magnitude larger than the Mott-Ioffe-Regel limit.
[Aside: but caution is in order because it is very hard to accurately measure intralayer resistivity in highly anisotropic layered materials.]

Here, a rather limited temperature range is used to determine magnitude of critical exponents. The plot below shows less than a decade was used (e.g. 75-115 K). Furthermore, the authors focus on temperatures away from the critical temperature, Tc.
Ideally, critical exponents are determined over several decades and as close to the critical point as possible. The gold standard is superfluid helium in the space shuttle!

I thank Vlad for bringing the paper to my attention.

Update (26 March).
Alex Hamilton sent the following helpful comment and picture and asked me to post it.
Not that my experience in the 2D metal-insulator transition community has jaded me, but my experience is that one has to be extremely careful interpreting such 'collapses'.

1. If you have 6 orders of magnitude on the Y axis, there is no way if you can tell if an individual trace misses its neighbours by a significant margin unless there is a huge  overlap between datasets (which there usually is not) - e.g. dataset Y(1) missed Y(2) by 30% for all data points. 
2. Almost anything can be made to scale. For example consider an insulator with hopping. By definition this will show scaling behaviour. Now consider a metal with linear or quadratic in T resistance correction due to phonons. This will also fit on a scaling curve as long as the range of data in each individual dataset does not change too much on the Y-axis for the range of data in the dataset. In other words, if the overlap is not large, then I can often get scaling behaviour just by adjusting T_0 for each dataset to make them fit a common curve, because dataset Y(1) isn't that different from dataset Y(2), and neither covers an order of magnitude on the Y-axis.


  1. Hi Ross, thanks very much for the very nice Blog about Kanoda's exciting results.

    I have just a short comment. In your Blog, you mention several candidate theories for calculating the critical exponent znu, including our DMFT, the gauge theory of Senthil, and also a (phenomenological) theory from Imada.

    While the latter (Imada) predicts an exponent znu=2 quite different than the experiment, it is interesting that both our DMFT and Senthil predict similar values close to 2/3.

    Here I would like to point out that these two theories, however, have very different physical content, and are, most likely applicable in different temperature windows.

    DMFT is a local self-energy approximation, as as such is more appropriate to intermediate and high temperatures, while the gauge theory of Senthil focuses on long wavelength corrections, hence it should apply to the lowest temperatures. Furthermore, a key ingredient in Senthil's picture are the spinon excitations, which indeed are found at T < 10K in one of the compounds studied.

    Remarkably, the seemingly universal high temperature behavior reported in the latest Kanoda paper seems quite insensitive to the nature of the low energy spin excitations and on the presence or absence of magnetic order. This seems to suggest, as the authors point out, that such spatial spin correlations do not play a significant role in the high temperature region studied, while they represent the primary focus of, for example, the gauge theory of Senthil.

    1. Vlad,

      Thanks for the very helpful clarifying comment.