Tight binding fermi surface

In summary, the attached file describes the tight binding dispersion for a 2d square lattice and assumes that the fermi surface is a square. It is possible for 2 electrons to occupy each lattice site, but the "half filled" case corresponds to only 1 electron per lattice site. The chemical potential μ=0 is also a characteristic of the half filled case. The calculation of the fermi level for actual computation is a significant issue in this context.
  • #1
aaaa202
1,169
2
On the attached file the tight binding dispersion for a 2d square lattice is described. It is then assumed that the fermi surface is a square. My question is: How can it ever be a perfect square when the dispersion looks as it does.
Also can someone explain:
Why does the half filled case correspond to:
-1 electron per lattice site (why will 2 electrons not occupy the ground state etc.)
- chemical potential μ=0
 

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  • #2
aaaa202 said:
On the attached file the tight binding dispersion for a 2d square lattice is described. It is then assumed that the fermi surface is a square. My question is: How can it ever be a perfect square when the dispersion looks as it does.
Also can someone explain:
Why does the half filled case correspond to:
-1 electron per lattice site (why will 2 electrons not occupy the ground state etc.)
- chemical potential μ=0

I suppose that the formula (1) on the attachment file supplied by you has already answered your question,i.e., "How can it ever be a perfect square when the dispersion looks as it does."

Not noly tight binding can describe it,but also perturbation theory can support it.
 
  • #3
You are exactly right that in principle 2 electrons could occupy each lattice site; this would be the "completely filled" case. If there is only 1 electron per lattice site, we call that "half filled."
 
  • #4
t!m said:
You are exactly right that in principle 2 electrons could occupy each lattice site; this would be the "completely filled" case. If there is only 1 electron per lattice site, we call that "half filled."

Actually,I think the more important problem here is "how to caltulate the fermi level for actual computation",for example,how to make it come true in some DFT softwares ,and how about its effictiveness,and so on.
 

1. What is a tight binding fermi surface?

A tight binding fermi surface refers to the shape and arrangement of the electron energy bands in a solid material. It is a representation of the allowed energy states of the electrons in a material, which determines its electronic and magnetic properties.

2. How is a tight binding fermi surface calculated?

A tight binding fermi surface is calculated using a mathematical model that takes into account the crystal structure of the material, the energy levels of the atoms, and the interactions between the electrons. This model is then solved to determine the allowed energy states and their corresponding momentum values.

3. What is the significance of the fermi surface in materials?

The fermi surface is a crucial concept in understanding the electronic and magnetic properties of materials. It provides information about the electrical conductivity, thermal conductivity, and other important properties of a material. It also helps in predicting the behavior of materials under different conditions, such as temperature or applied magnetic fields.

4. How does the shape of the fermi surface affect the properties of a material?

The shape of the fermi surface is closely related to the electronic and magnetic properties of a material. For example, a perfectly spherical fermi surface is associated with good electrical conductivity, while a complex and distorted fermi surface can lead to interesting magnetic properties, such as superconductivity or magnetism.

5. Can the fermi surface of a material be experimentally observed?

Yes, the fermi surface can be indirectly observed through various experimental techniques, such as angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. These techniques provide information about the allowed energy states and their corresponding momentum values, which can be used to construct the fermi surface of a material.

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