Tuesday, March 24, 2015

Is liquid 3He close to a Mott-Hubbard insulator transition?

Is it ever a "bad metal"?

Liquid 3He mostly gets attention because at low temperatures it is a Fermi liquid [indeed it was the inspiration for Landau's theory] and because it becomes a superfluid [with all sorts of broken symmetries].

How strong are the interactions? How "renormalised" are the quasi-particles?
The effective mass of the quasi-particles [as deduced from the specific heat] is about 3 times the bare mass at 0 bar pressure and increases to 6 times at 33 bar, when it becomes solid. The compressibility is also renormalised and decreases significantly with increasing pressure, as shown below.

This led Anderson and Brinkman to propose that 3He was an "almost localised" Fermi liquid. Thirty years ago, Dieter Vollhardt worked this idea out in detail, considering how these properties might be described by a lattice gas mode with a Hubbard Hamiltonian. The system is at half filling with U increasing with pressure, and the solidification transition (complete localisation of the fermions) having some connection to the Mott transition. All his calculations were at the level of the Gutzwiller approximation (equivalent to slave bosons). [The figure above is taken from his paper].
A significant result from the theory is it describes the weak pressure dependence and value of the Sommerfeld-Wilson ratio [which is related to the Fermi liquid parameter F_0^a].
At ambient pressure U is about 80 per cent of the critical value for the Mott transition.

Vollhardt, Wolfle, and Anderson also considered a more realistic situation where the system is not at half-filling. Then, the doping is determined by the ratio of the molar volume of the liquid to the molar volume of the solid [which by definition corresponds to half filling].

Later Georges and Laloux argued 3He is a Mott-Stoner liquid, i.e. one also needs to take into account the exchange interaction and proximity to a Stoner ferromagnetic instability.

If this Mott-Hubbard picture is valid then one should also see a crossover from a Fermi liquid to a "bad metal" with increasing temperature. Specifically, above some "coherence" temperature T_coh, the quasi-particle picture breaks down. For example, the specific heat should increase linearly with temperature up to a value of order R (the ideal gas constant) around T_coh, and then decrease with increasing temperature.

Indeed one does see this crossover in the experimental data shown in the figure below, taken from here.

Aside: the crossing point in the family of curves is an example of an isosbestic point.

Extension of the Vollhardt theory to finite temperatures was done by Seiler, Gros, Rice, Ueda, and Vollhardt.

One can also consider 3He in two dimensions. John Saunders and his group have done a beautiful series of experiments on monolayers and bilayers of 3He. The data below is for a monolayer, of different layer densities, taken from here. They suggest that as one tunes the density one moves closer to the Mott transition.

The experiments on bilayers deserve a separate post.

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