Hund's rule coupling in multi-band metals

There is a really nice preprint, Janus-faced influence of the Hund’s rule coupling in strongly correlated materials, by Luca de’ Medici, Jernej Mravlje, and Antoine Georges.

The figure below is a helpful summary of the main results. The colour shading shows the quasi-particle weight Z in the metallic phase as a function of U/D and band filling for a system with 3 degenerate bands for a fixed value of J=0.15U. [The relevant multi-band Hubbard model is solved at the level of Dynamical Mean-Field Theory (DMFT)]. The cases n=2 and 4 are particularly interesting because there is a large range of U/D for which one has a metallic phase with small Z. The authors characterise this as a bad metal (i.e. which occurs above some relatively low coherence temperature T*).
One minor comment. The authors mention just a few signatures of bad metals [large resistivity above the Mott-Ioffe-Regel limit and large poorly screened local moment]. Others include no Drude peak in the optical conductivity, and a large thermopower ~k_B/e [see this earlier post].

So what is this about Janus faced? I had no idea. But I found out that Janus was a Roman God of transitions. He looked to the past and future and was often depicted in statues as "two-faced". The point here is that Hund's rule can either enhance or reduce the correlations, depending on the filling.

I thank Jaime Merino for bringing the paper to my attention and for some helpful discussions about it.

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