# A Plea for More Plots of the Energy Loss Function

In the modern landscape of condensed matter physics, it seems like while it is important to get a well-rounded and comprehensive view of the experimental status within each topic, that most physicists are biased towards their favorite standard experimental probes. For me, I have to admit that when getting acquainted with a certain topic, that I tend to lean towards reading papers that use ARPES, inelastic neutron scattering and optical spectroscopy.

I especially like the latter two because of the very close relationship to the spin-spin correlation function and the current-current correlation function respectively. This means that these probes are constrained to satisfy certain sum-rules, which provide strong constraints on response functions regardless of the state of matter probed.

With regard to optical spectroscopy, I do have one complaint — it would be great if authors would plot the energy loss function, $-\textrm{Im}(1/\epsilon)$, more often. Recently, when trying to get an overview of the iron-arsenide superconductors, I found that I couldn’t find a paper that plotted the energy loss function for these compounds. Most papers plotted only the reflectivity and optical conductivity. A few plotted the deduced scattering rates, but none seemed to plot the energy loss function.

Below are a list of a few papers (some have paywalls) that I went through, many of which are great. However, I would love it if authors would plot the energy loss function in the future.

Why is the energy loss function important? Well, it gives one an idea of the effective Coulomb interaction in a solid. This is important considering that how the Coulomb interaction is modified by the lattice vibrations and electrons is often critical in the formation of a material’s ground state. Also, interesting collective modes that form in a ground state (usually because of these interactions) will exhibit peaks in the energy loss function.

For instance, this classic paper by Uchida et al. shows the energy loss function in LSCO as a  function of doping in Fig. 9(a), which one could view (perhaps!) as the development of a free carrier plasmon with increased doping. This information is not easily discernible from the other optical constants (except maybe the reflectivity, but even then the development of the plasmon is not clear).

The reflectivity and optical conductivity are extremely useful, but often the energy loss function has information buried that isn’t easily visualized in the other optical constants. So a plea to optical spectroscopists: please plot the energy loss function in the future when it is relevant.

### 2 responses to “A Plea for More Plots of the Energy Loss Function”

1. Nate

Do you have other reasons for wanting the loss function? You can see the free carrier response in the optical conductivity as a Drude peak, a Lorentzian centred at zero-frequency. Mind you renormalization will distort it from the perfect Lorentzian.

Like

• Anshul Kogar

Hi Nate, thanks for your comment.

To me, I’d rather see the energy loss function (ELF) because this is the “most natural” function to plot when looking at collective modes, i.e. it shows the collective modes as peaks. These are the collective modes that are most significant in renormalizing the Coulomb interaction.

The optical conductivity is great for looking at gaps in the charge spectrum, but the relationship between the optical conductivity and the loss function cannot be easily determined in my head. I would love to see plots of this more often, without me having to do a Kramers-Kronig analysis myself. Take a look at this paper for instance:

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.027404

It would be difficult for me to deduce one from the other from just looking at the plot of the optical conductivity.

Like