The paper is another victory for

**Dynamical Mean-Field Theory**(DMFT) as it shows how LDA+DMFT calculations can give a quantitative description of a whole range of experiments on this strontium ruthenate.

Aside and context: This material originally attracted a lot of interest because it is a transition metal oxide with the same perovskite crystal structure as the cuprate superconductors. But, it turns out to be very different because it has a Fermi liquid metallic state and the superconductivity is triplet rather than singlet.

But here are some physical insights I found particularly interesting in the paper

a. It explains why the coherence temperature and band renormalisation (effective mass) is different for the different bands, and not just determined by the band width. The key issue is the

**Hund's rule coupling.**

**b. The temperature at which the Fermi liquid properties occur is much lower for two-particle properties than from single-particle properties.**This also occurs in the Kondo problem where the Kondo resonance persists up to temperatures of about 2 times the Kondo temperature, T_K, whereas the magnetic susceptibility only becomes weakly temperature dependent below about 0.2 T_K.

n.b. This is an order of magnitude difference.

c. The Hund's rule coupling tends to suppress the coherence scale because it projects the spin degrees on freedom onto a subspace of low-lying states which have a reduced effective Kondo coupling to their environment. This occurs in several contexts:

- Single impurity models [see this recent PRL by Nevidomskyy and Coleman, which contains the figure below]
- DMFT studies of model Hamiltonians
- transition metal oxides due to screening of U by large spatial extension of correlated orbital
- iron pnictides due to screening of U by large polarizability of screening orbitals

**why is the interlayer resistance a non-monotonic function of temperature**? The authors hint that this is related to the destruction of quasi-particles. But, showing this connection and actually calculating such a temperature dependence with one set of parameters seems to be rather difficult, particularly without a momentum dependent self energy. Urban Lundin and I wrote a paper about the problem several years ago.

Another aspect discussed in the paper is about the influence of the proximity to van-Hove singularities. The higher density-of-states around the Fermi level translates into a narrower effective band-width the quasi-particles experience at low energies. In consequence, the gamma-sheet (that of the widest band but with a van-Hove singularity nearby) electrons are renormalized most. The influence of van-Hove singularities has recently been investigated in several model studies (see e.g. Refs in the paper) and in Sr2RuO4 this influence is realized.

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