4.4 Real Bandstructures Flashcards
Describe how charged particles move in a magnetic field
In circular orbits and it can absorb energy from the EM field while doing this
Describe the shapes of the curves on the Energy-k graph for silicon
The conduction band is anisotropic (skewed to RHS +ve)
The valence band is degenerate at k = 0 leading to holes of different masses
What direction is the Lorentz force and does it effect the energy in a B field?
Perpendicular to the velocity and force, doesn’t affect the energy
Define the Fermi surface
A contour of constant energy in k space
Describe the motion of an electron in a k state when a B field is applied
It stays at the same energy but moves through other k states with the same energy.
An electron on the fermi surface will move about on the fermi surface in a direction perpendicular to B
Describe the process to measure the cyclotron resonance for a metal in a B field
Shine an EM wave onto the surface (microwave freq) and either:
- Change the frequency at a fixed B field or
- Changing the field at a fixed frequency
What is the necessary condition for a good resonance?
When the mean free path is much longer than the real space orbit
What is meant by electrons behaving quasiclassically?
Behave as wavepackets forming particles
When do electrons no longer behave as quasiclassical particles?
When the magnetic field is large enough such that the real space radius of the electron orbit is less than the wavepacket size
Why do we expect some sort of quantisation of energy of the electrons in orbit?
They are orbiting so exist in energy shells
Describe where the electrons will orbit if a magnetic field is applied along the z axis
Perpendicular to z, so they will have quantised orbits in the x-y plane
What are Landau levels?
Energies of the free electron motion in a plane perpendicular to the magnetic field are quantised into Landau levels
What are Landau tubes?
The quantisation of the k space areas of orbits
How do the properties of the Landau tubes change in relation to the Fermi surface as the magnetic field increases?
They grow and start to pop out
Where do filled states lie on the Landau levels?
On tubes inside the FS
