2D Electrons in Out-of-Plane Magnetic Field: DOS & Collision Broadening

[jpr0]

Does anyone have a link for the derivation of the density of states for 2D electrons in an out of plane magnetic field, which also details collision broadening leading to the oscillatory density of states?

 

[Gokul43201]

Does anyone have a link for the derivation of the density of states for 2D electrons in an out of plane magnetic field, which also details collision broadening leading to the oscillatory density of states?

I don't have a link, but I can suggest how to do it.

If you've seen the derivation for the DOS of a 2D electrons in a perpendicular field ^*(say, in the Landau gauge), all you need to do is add a component to the vector potential (giving rise to an in-plane component for the field) and solve the SE again with the two extra terms that emerge. Also, you will want to make sure you include the Zeeman energy term.

In the limit where the width of the confining potential, V(z), is small compared to the classical cyclotron radius (i.e, an ideal 2D electron gas), the parallel field will only noticeably affect the spin split nature of the DOS.

^*EDIT : Oops! I thought you were asking about an in-plane (parallel) field. I just realized you were asking about the DOS from an out-of-plane (perpendcular) field. I don't have a link for that either, but you will find this in any book that deals with the Quantum Hall effect.

PS: You will find a partial discussion here: https://www.physicsforums.com/showthread.php?t=133409