• Support PF! Buy your school textbooks, materials and every day products Here!

Condensed matter open orbit

  • Thread starter ehrenfest
  • Start date
1,996
1
1. Homework Statement
An open orbit in a monovalent tetragonal metal connects opposite faces of a Brillioun zone. A magnetic field is normal to the plane of the open orbit. Describe in real space the motion of the electron on this orbit in the presence of the magnetic field.


2. Homework Equations



3. The Attempt at a Solution
I am having loads of difficulty translating what goes on in k-space to what goes on in real space. The picture in k-space is very clear, but I am just really confused about what it means. It is not even clear to me what how the velocity vector is changing!
 

Answers and Replies

979
1
I don't know if the text says so, but all this is predicated on working in a semi-classical regime. So the particles can be localised with small uncertainties in space and momentum. In that case, remember that the group velocity is the gradient of the dispersion relation. So for an open orbit, you would get oscillations about zero in the group velocity in some direction, but in the other direction it would always be +ve or -ve. So you would get a macroscopic current that flows across the entire sample (or you would, if it wasn't for the fact there's an identical current flowing the other way...)
 

Related Threads for: Condensed matter open orbit

  • Last Post
Replies
0
Views
5K
  • Last Post
Replies
1
Views
1K
Replies
3
Views
946
Replies
8
Views
3K
Replies
1
Views
914
Replies
1
Views
3K
Replies
1
Views
753
Replies
2
Views
2K
Top