Desperately seeking Weyl semi-metals

In 2011 it was proposed that pyrochlore iridates (such as Y2Ir2O7) could exhibit the properties of a Weyl semi-metal, the three-dimensional analog of the Dirac cone found in graphene.
Since the sociology of condensed matter research is driven by exotica this paper stimulated numerous theoretical and experimental studies.
However, as often is the case, things turn out to be more complicated and it seems unlikely that these materials  exhibit a Weyl semi-metal.

This past week I have read several nice papers that address the issue.

Variation of optical conductivity spectra in the course of bandwidth-controlled metal-insulator transitions in pyrochlore iridates
K. Ueda, J. Fujioka, and Y. Tokura

There is a very nice phase diagram which shows systematic trends as a function of the ionic radius of the rare earth element R=Y, Dy, Gd, ...
Most of the materials are antiferromagnetic insulators.

The colour shading describes the low energy spectral weight in the optical conductivity up to 0.3 eV.
Blue is an insulator and red actually means a very small low energy spectral weight.
N can be thought of as the number of charge carriers per unit cell. Specifically, if this was a simple weakly interacting Fermi liquid N=1. Thus, the value of 0.05 for Pr signifies strong electron correlations. [Unfortunately, the paper talks about this as "weak correlations"].

In fact, as shown below even in the metallic phase at T=50 K one cannot see the Drude peak down to 10 meV.
This presents a theoretical challenge to explain this massive redistribution of spectral weight.

Slater to Mott Crossover in the Metal to Insulator Transition of Nd2Ir2O7
M. Nakayama, Takeshi Kondo, Z. Tian, J. J. Ishikawa, M. Halim, C. Bareille, W. Malaeb, K. Kuroda, T. Tomita, S. Ideta, K. Tanaka, M. Matsunami, S. Kimura, N. Inami, K. Ono, H. Kumigashira, L. Balents, S. Nakatsuji, and S. Shin

This ARPES study does find band touching at the magnetic metal-insulator transition temperature but as the temperature is lowered the spectral weight is suppressed and there is no sign of Weyl points.

Phase Diagram of Pyrochlore Iridates: All-in–All-out Magnetic Ordering and Non-Fermi-Liquid Properties 
H Shinaoka, S Hoshino, M Troyer, P Werner

This LDA+DMFT study shows that a three-band description is important for the R=Y compound.
This sets the stage for describing the phase diagram above.

I thank Prachi Telang for discussions at IISER Pune about these materials and bad semi-metals that stimulated this post.