dielectric function for metals

[muhammadhasan]

Hi,

I have a question regarding the calculation of the dielectric function for metals.

For metals, the intraband contribution is crucial for describing the dielectric function. However, this contribution is not explicitly included in Yambo at (q = 0), whereas it is included at any finite (q).

I understand that when running IP-RPA calculations in Yambo, we need to provide (omega_p) and (gamma), which are used in the Drude model. The equation has the following form:

Epslion_drude = 1- (w_p)^2/(w^2 + i*w*gamma).

My question is: when presenting the general equation for readers who want to calculate the dielectric function of a metal from first principles, what should be the final form of the dielectric function?

Is it simply the sum of the IP-RPA dielectric function from linear response theory, as shown in the Yambo cheatsheet(https://wiki.yambo-code.eu/wiki/index.p ... 5.0_P5.png), and the Drude contribution? In other words, should the final expression be written as:

Epsilon_metal = Epsilon_IP_RPA + Epslion_drude

Does Yambo treat the problem in this way? At very low energies, drude contribution dominates, while at higher energies, the IP-RPA contribution becomes more important.

Thank you.

Best regards
M J Hasan, PhD Candidate, Mechanical Engineering
University of Maine

[Davide Sangalli]

Dear M J Hasan,

yes, only at q=0, in the code a drude term is added

Epsilon_metal = Epsilon_IP_RPA + Epslion_drude

This is the source file which computes the drude term: https://github.com/yambo-code/yambo/blo ... /X_drude.F

Best,
D.

[muhammadhasan]

Hi Professor,

Thank you so much for your comment.

So, does this mean that at (q = 0), Yambo predicts the dielectric function using the parameters provided to it, omega_p and gamma? Based on my understanding, epsilon should therefore not change with temperature. However, in my simulations, it does change. I plotted the dielectric function for the equilibrium structure, 300 K, and 450 K, and obtained different results for each case. The plot is shown below:

dielectric_function.png

To briefly explain what I did, I ran QE with the atomic positions at their equilibrium values. I then changed the atomic positions to represent 300 K and 450 K, ran the simulations again, and used the resulting outputs as inputs for Yambo. Since the atomic positions were changed, QE produced different wavefunctions for each case.

However, the following equation:

Drude_Eq.png

indicates that at (q = 0), the Drude model is used. I kept the Drude parameters fixed while running the simulations at different temperatures. Therefore, I am confused about why the results change at (q = 0). They should not change if the dielectric function depends only on the Drude contribution at (q = 0).

Thank you.

Best regards
M J Hasan, PhD Candidate, Mechanical Engineering
University of Maine