The frequency dependence of the real part of the conductivity of a metal gives a lot of information, both qualitative and quantitatively. For example, one can extract a scattering rate and see if a Drude model is relevant. Hence, it is natural that experimentalists present “measurements” of this quantity.
However, it is important to acknowledge that the conductivity is not directly measured; rather, the reflectivity or absorption of a thin film or single crystal.
The real and imaginary parts of the conductivity are then extracted from a Kramers-Kronig analysis. This procedure is only stable and reliable if there is experimental data out to sufficiently high frequencies.
Several experimentalists have privately told me this can be a can of worms. It is not clear how high a frequency cutoff you need and interband transitions can complicate things…
Hence, one should be particularly nervous about people claiming exotica such as quantum criticality and non-Fermi liquid behaviour such as anomalous power laws.
There is a simple way to avoid these complications and ambiguities when comparing theory and experiment. The reflectivity can be written in terms of the conductivity as follows
From theory one can calculate the full complex conductivity and thus the reflectivity and
compare this to experiment.
This is the procedure followed by Jure Kokalj, Nigel Hussey, and I in this paper about overdoped cuprates.
I thank Swagata Acharya for motivating this post.