# Square lattice electron gas

1. Sep 25, 2007

### noospace

Hi all,

I'm struggling to understand the relationship between electrical conductivity and Bragg reflection in a 2D square lattice free electron gas with lattice spacing $a$.

Is it the case that Bragg reflection in the electron gas results in electrical resistivity?

My understanding of Bragg reflection is that it will occur when the change in wave-vector is equal to some reciprocal lattice vector.

But what happens if the radius of the Fermi circle is less than half the spacing of the reciprocal lattice points $2\pi/a$? In this case it should be impossible for any wavevector in the electron gas to undergo Bragg reflection. Does that mean that the electron gas has zero resistance in any direction?

If we compress the lattice into a rectangular shape, then it may be the case that Bragg reflection can occur in a specific direction. Would this then increase the resistance in the same direction?

If anyone would be able to comment on this logic it would be much appreciated.