Periodic electron motion in a perfect conductor using a semiclassical model

[dRic2]

TL;DR

Imagine to have a perfect conductor, i.e. no impurities and no thermal motion (0K)

According to the semiclassical approximation, in response to a constant electric field I would get a periodic motion of the electron, like this:

The sinusoidal type function is the velocity, while the function that goes to infinity is the effective mass. Thus I was wondering, since $v$ also gets negative values, does it means that an electron oscillates back and forth ?

Thanks,
Ric

 

[fluidistic]

Yes, this is called Bloch oscillations.

 

[dRic2]

Yes, this is called Bloch oscillations.

Thanks! Does the electron lose energy due to radiation emission ?

 

[fluidistic]

Thanks! Does the electron lose energy due to radiation emission ?

Good question. I think not, because radiation is a surface phenomenon while we are considering a perfect crystal (and at 0 K), i.e. a bulk. But then it's very strange, because we have a time varying current (AC), but no radiation. I'm not sure what's going on.

 

[dRic2]

Good question. I think not, because radiation is a surface phenomenon while we are considering a perfect crystal (and at 0 K), i.e. a bulk. But then it's very strange, because we have a time varying current (AC), but no radiation. I'm not sure what's going on.

That's reasonable. At least it is the only think I can think of... I am dumber than usual when it comes to radiation, but assuming that there is a continuous exchange of radiation between electrons in the bulk, wouldn't you expect a more complicated motion instead of simple oscillations ?

 

[fluidistic]

That's reasonable. At least it is the only think I can think of... I am dumber than usual when it comes to radiation, but assuming that there is a continuous exchange of radiation between electrons in the bulk, wouldn't you expect a more complicated motion instead of simple oscillations ?

Yeah for sure. For one, Bloch oscillations are derived from the idependant electrons assumption.

 

[dRic2]

Yeah for sure. For one, Bloch oscillations are derived from the idependant electrons assumption.

Then I find very surprising that they have been detected experimentally