Wednesday, October 31, 2012

Scaling plots near the Mott transition

Earlier this year Jure Kokalj brought to my attention an interesting PRL
Quantum Critical Transport near the Mott Transition
by H. Terletska, J. Vučičević, Darko Tanasković, and Vlad Dobrosavljević.

My interest in this paper increased this week when Vlad emailed me to tell me about a recent talk at KITP by Kazushi Kanoda. The right side of the slide below [click on it to see it larger] shows a scaling analysis of the temperature and pressure dependence of the resistivity of the organic charge transfer salt kappa-(ET)2(CN)3 near the pressure driven Mott transition. This scaling analysis is based on the theory in the PRL.

The left side shows the Dynamical Mean-Field Theory (DMFT) results [for a Hubbard model at half filling] in the PRL. The top shows the scaling of the resistivity curves and the bottom the T vs. U phase diagram where the yellow region is the "quantum critical" region above the Mott transition.

It is striking that the experimental curves involve scaling over about 6 orders of magnitude of the resistivity.

There are several things that are rather strange/exotic/interesting about the theory. 
First, there is a "duality" between the resistivity in the metallic and insulating sides of the transition.
Second, the critical resistivity is an order of magnitude larger than the Mott-Ioffe-Regel limit.
Third, connections are suggested with the "holographic duality" picture of in papers such as this one by Subir Sachdev.

Aside: This same organic material is also of considerable interest because the Mott insulating phase seems to exhibit a spin liquid ground state and metallic state becomes superconducting at low temperatures. (See this review).

1 comment:

  1. Thanks for the interesting comment Ross!

    We are very excited by these development, but the big question at this time is how general this phenomenon is. We believe that our definition of the "instability" line around which we perform the scaling analysis, that can also be called the "Quantum Widom Line", should allow proper analyses to be performed in a broader class of quantum critical points separating metals from insulators.

    Other questions are also of much interest: (1) can one find models where the critical end point Tc is much smaller, so the quantum critical region extends to much lower temperatures? (2) can disorder suppress coexistence and stabilize a true quantum critical point at T=0? These questions should be possible to examine both experimentally and theoretically. This line of work seems to open very exciting directions for future work.