Fermi Surface squashed by potentials

In summary, the conversation discusses the behavior of fermi surfaces in relation to zone boundaries and potential symmetry. It is noted that states near the zone boundaries get pushed down in energy, causing the fermi surface to be shifted to higher k values. The potential is also shown to affect the shape and position of the fermi surface.
  • #1
unscientific
1,734
13
Taken from my textbook:

fermisea1.png


My understanding is that:

  • One valence electron, 2 spin states -> Half-filled Brillouin zone
  • Seeking inspiration from "Nearly Free Electron Model": gaps open up at zone boundaries
  • States nearer to zone boundaries get pushed down in energy further

Since a fermi surface is a surface of constant energy in k-space, shouldn't the surfaces nearer to the zone boundaries that get pushed down in energies get repelled even more? It seems that surfaces nearer to the boundaries get closer even! Why are the fermi seas like these below?

fermisea2.png
 
Physics news on Phys.org
  • #2
Take a simple potential with this symmetry as an example: ##V(x,y)=A \cos(x)\cos(y)##. Can you find a direction along which the potential is constant? To which lines do these directions in reciprocal space? What happens at the cell boundary?
 
  • #3
DrDu said:
Take a simple potential with this symmetry as an example: ##V(x,y)=A \cos(x)\cos(y)##. Can you find a direction along which the potential is constant? To which lines do these directions in reciprocal space? What happens at the cell boundary?
cosxcosy.png


The surfaces of constant potential are the circles* about (0,0). Given this is the fermi surface, these surfaces are the reciprocal space. Still doesn't answer my question about "pushed down in energy -> decrease in radius, squashed inwards"?
 
  • #4
bumpp
 
  • #5
Sorry, I was on the wrong track and had no time to think about your problem recently. Now I think I understand the behaviour. Near the BZ boundary, the lower energy band will be lowered as compared to the free electron case, so the Fermi surface will be shifted to higher k values. At stronger potentials, it will even protrude into the second BZ or even farther.
 
  • #6
DrDu said:
Sorry, I was on the wrong track and had no time to think about your problem recently. Now I think I understand the behaviour. Near the BZ boundary, the lower energy band will be lowered as compared to the free electron case, so the Fermi surface will be shifted to higher k values. At stronger potentials, it will even protrude into the second BZ or even farther.

I get the downward shift in energy due to a perturbation. Why will the fermi surface be shifted to higher k values?
 
  • #7
The fermi surface is a surface of constant energy. If the levels split, this constant energy value will be reached at higher values of k. Think of an irregularly shaped plate: where the rim is lower, soup will ooze out more.
 

1. What is a Fermi Surface and how is it affected by potentials?

A Fermi Surface is the boundary between occupied and unoccupied energy levels in a solid material. It represents the set of all allowed electron energy states at zero temperature. When potentials, such as external electric or magnetic fields, are applied to a material, they can modify the shape and size of the Fermi Surface.

2. How do potentials affect the shape and size of the Fermi Surface?

Potentials can alter the Fermi Surface in several ways. They can shift the position of the Fermi level, change the curvature of the energy bands, and introduce additional energy gaps. These modifications can lead to changes in the shape and size of the Fermi Surface.

3. What is the significance of studying a squashed Fermi Surface?

Studying a Fermi Surface that has been distorted or "squashed" by potentials can provide valuable information about the electronic properties of a material. It can reveal details about the energy bands, band gaps, and the behavior of electrons in response to external fields.

4. How can the squashing of a Fermi Surface be experimentally observed?

The squashing of a Fermi Surface can be observed through various experimental techniques, such as angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. These methods allow for the direct visualization and measurement of the Fermi Surface and its modifications under the influence of potentials.

5. Can the squashing of a Fermi Surface be controlled or manipulated?

Yes, the squashing of a Fermi Surface can be controlled and manipulated by varying the strengths and directions of the applied potentials. This can lead to the creation of new electronic states and can be utilized in the design and development of novel materials for various applications in electronics and technology.

Similar threads

  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
4
Views
2K
  • Atomic and Condensed Matter
Replies
2
Views
4K
  • Atomic and Condensed Matter
Replies
2
Views
3K
  • Atomic and Condensed Matter
Replies
12
Views
5K
  • Atomic and Condensed Matter
Replies
2
Views
988
  • Atomic and Condensed Matter
Replies
4
Views
3K
  • Atomic and Condensed Matter
Replies
3
Views
2K
Back
Top