# Help request with complex conductivity

1. Jun 10, 2013

### swooshfactory

Hi,

I'm hoping to acheive some intuition regarding the real and imaginary parts of the complex conductivity. The rule of thumb seems to be that the real part is due to the absorptive/dissipative processes and the imaginary part absorbs no work (over a time average).

However, I feel like this doesn't quite explain everything. QUESTION 1. For instance, what exactly is absorption? At low frequencies (compared with the scattering rate) the real part of the conductivity dominates in the Drude model. In this case the light is mostly reflected (this is why metals are shiny). However, in a superconductor or perfect conductor, the light is completely reflected. I've seen a proportionality of the absorption coefficient to the real part of the conductivity. QUESTION 2: Is this proportionality always true (σ1 ~ alpha), and if so how can one interpret it? There is also the conservation of energy equation R + T + A = 1. This is why I'm having trouble with the distinction between absorption and reflection. It seems that in the metal, the light is absorbed (just as it would be for an interband transition), the electron is promoted to a higher energy state i.e. it is oscillated, and then the oscillating electron produces radiation. QUESTION 3: But if this (reflection from a metal) is a real part of the conductivity process, then how can I understand a superconductor, which is a perfect reflector but has essentially entirely an imaginary part of the conductivity? It also temporarily "absorbs" light (via charge carrier oscillation) before emitting it back towards the source. QUESTION 4: Is absorption mainly due to Joule heating and interband transitions, which by integrating F dx over a current oscillation can be shown to be due to σ1?

If anyone can address these conceptual issues I have and/or could provide intuitive ways to think about the complex conductivity (especially in terms of solid state physics) I would be REALLY grateful!

2. Jun 10, 2013

### DrDu

Yes, reflectivity may seem confusing. Reflectivity can be related to conductivity via the Fresnel equations:
http://en.wikipedia.org/wiki/Fresnel_equations as the index of refraction can be related to conductivity via $n^2=i\sigma/\omega$. Inside a metal, due to reflection, the electric field is very small whence there is little energy dispersion as Ohmian currents are also small despite the conductivity not being small.

3. Jun 12, 2013

### swooshfactory

Qualitatively, when is a reflectivity process called absorption? Is there a straight-forward answer?

4. Jun 12, 2013

### DrDu

Err, never. You correctly observed that R+T+A=1.
To obtain the amount of radiation absorbed it is not enought to know some material parameter but you have to solve the electrodynamic problem.

5. Jun 18, 2013

### swooshfactory

Is absorption of a photon by an atom that promotes an electron to an excited state a sigma1 process? If so, why is it classified as dissipation? Is it that the atom reradiates the photon and it's eventually turned into heat?