What is the dynamic conductivity? How it differs from the conductivity we know? What are the types of conductivity?

Question

In the paper I am reading, it was written that "The dynamic conductivity of graphene could elucidate features that would demonstrate unique properties of this system and allow for the identification of characteristic energy scales associated with the band structure." I couldn't really get what is meant by "THE DYNAMIC CONDUCTIVITY" and how it differs from the conductivity we usually use? what types of conductivity are there?

paper: Electronic properties of graphene-based bilayer systems https://arxiv.org/abs/1511.06706

Answer 1

You should be able to find several papers talking about dynamic conductivity in graphene for a more complete answer.

I believe they mean the AC conductivity, where an ac field or optical signal is applied and especially in the case high field and when a resonance is obtained between interband transitions.

In general, ac conductivity might be considered a form of impedance spectroscopy. But in your case, I think the interest is better understanding the band structure, considering that the electron mobility depends on the band structure.

Answer 2

What is "the conductivity we usually use”?

You apply an electric field $E$ to a solid and get a current $j = \sigma E$. The proportionality coefficient $\sigma$ is the conductivity.

If you apply a time-independent electric field, the conductivity $\sigma$ is just a number and is the static conductivity of the medium. If you apply a time-dependent electric field, e.g. $E \left( t \right) = E_{0} \cos \left( \omega t \right)$, the conductivity $\sigma \left( \omega \right)$ becomes a function of the frequency $\omega$ and is the dynamic conductivity of the medium.

The static conductivity $\sigma \left( \omega = 0 \right)$ is a special case of the dynamic conductivity. The static conductivity of a dielectric is zero. The dynamic conductivity of any medium, including dielectrics, is always finite.

The sentence "ac conductivity might be considered a form of impedance spectroscopy" in the previous answer is meaningless, since conductivity is a physical quantity which characterizes a medium, while any spectroscopy is an experimental method to measure some physical properties of a medium, e.g. the dynamic conductivity.