How Does Screening Work in a Metal with a Background Charge Density?

[tjny699]

Hello,

Chemistry grad student here about to start a physics-y project...so trying to learn about condensed matter physics.

I get how screening works when you add a single charge to a gas of electrons, but what happens in a metal when you have a whole lattice, ie, a background charge density? Specifically, say the background charge density is

$$n(x)=n_0+\delta n e^{-A*|x|}$$

where $$\delta n$$ is small.

I've tried applying the Thomas-Fermi screening function (dielectric) and using a linear response approximation but can't get a sensible result when I try to calculate the self-consistent potential, distribution of electron charge, and electric field for x>>1/A

Does anyone know any references that contain a discussion of screening for background distributions that aren't just point particles?

Any help or suggestions would be great!

 

[weejee]

I think we should know how the positive background move when a force is applied to it, to answer your question.

However, it seems that only the electron motion is important since electrons move a lot faster than positve ions. The lattice structure still plays an important role in screening, since it determines the band structure and thereby properties of the Fermi surface.

 

[tjny699]

Hi weejee,

thanks a lot for your reply. i think you are correct: i assumed that the motion of the positive background can be neglected.

I think I've figured out how to get the potential and electron charge distribution using one of the Maxwell Equations, something called the "Thomas-Fermi screening dielectric" and by Fourier transforming the potential and charge density.

However, I am a bit stuck on how to determine the electric field for x>>1/A. Perhaps it is easier to find the electric field assuming that there is no screening first? I have a biochemistry background so I'm not quite sure how to go about calculating the E-field.

Thanks again and, as always, any help would be very appreciated.