# Kubo formula of conductivity

1. Sep 21, 2015

### Albe5588

Hello everybody,
I'm new. It's a long time a have a big (probably stupid) doubt about the interaction between light and media, and now it's time to solve it. The doubt its essentially concerning the difference between an antenna and a photodetector: the first one is able to detect the amplitude and the phase of an electromagnetic wave, the second one detects the power.

To what I know, the principle of functioning of an antenna is completely different from a detector, because its based on the generation of "surface" alternate current by the electric field impinging a metal, while a detector is based on the photoelectric effect.

An optical wavelength cannot be detected in its amplitude and phase like a GHz one, because electrons in media are too slow to follow the electric field variation at hundread of THz.

Now, we can calculate the conductivity as a function of the frequency of an external electromagnetic excitation, starting from the Kubo formula.

The question is: is the Kubo formula an equation to calculate the conductivity in the sense of an antenna or in the sens of a photodetector? what I mean is: if I calculate the conductivity at a certain frequency, is this conductivity linked with a varying current at the same frequency of the field, or it is linked to a dc current generated by the photoelectric effect?

2. Sep 21, 2015

### PietKuip

The Kubo-Greenwood formula for the optical conductivity is for calculating sigma as a function of frequency; sigma is the ratio of the ac current to the electric field at that frequency.

3. Sep 22, 2015

### Albe5588

Ok , thak you!

I pose this question because I'm working on graphene photodetectors. Graphene exhibits a flat absorbance over a wide range of optical frequencies. There are some experiments that show this, for example http://arxiv.org/ftp/arxiv/papers/0810/0810.1269.pdf. In this work they calculate the conductivity with the Kubo formula and exprimentally verify it.

So, does it means that graphene can detect the phase and amplitude of an hundread of therahertz (optical) electromagnetic field as an antenna does for a GHz signals ?

Moreover, if I send light on graphene at optical wavelengths, I can measure a dc current generated by light; so, I can see this current generation process (photodetection) as a change in conductivity induced by the creation of electron-hole couples. for what you said, this change in conductivity has nothing to do with the kubo formula. Do I am right?