Solid State in tight binding approximation, Brillouin zone, Fermi

In summary, for the upcoming examination, the person is seeking advice and resources to help clarify their understanding of determining energy levels and wavefunction of localized electronic states on a defect in a periodic lattice. They also have questions about electrons on a two-dimensional square lattice and determining if it is a metal or insulator. The best resources to consult for these topics are textbooks on solid state physics and online resources.
  • #1
Plasmon1212
1
0
Hello,

In few days, I have an examination, and I still have some dark zone in my head! If somebody could help me by giving me some advices/answers/way of reflexion/books to consult, it could be very great!

Here is my questions:
How to determine energy levels and wavefunction of the localized electronic states on
the defect for a periodic lattice?

Electrons on a two dimensional square lattice in tight-binding approximation
-how to obtain band structure?
-how to obtain E(kx; ky) in the first Brillouin zone?
-how to draw the Fermi surface with one and two electrons per site?
-how to determine if it is a metal or insulator?

Thank's a lot

(I'm sorry, but I'm not English speaker, so mistakes are possible;))
 
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  • #2
The best way to answer these questions is to consult a textbook on solid state physics. Some key topics to look for are: tight-binding approximation, band structure, Brillouin zone, Fermi surface, metal vs insulator. Many of these topics will also have associated solved problems that can help you better understand the concepts. Additionally, there are many online resources available that may be able to answer any specific questions you may have. Good luck with your examination!
 
  • #3


Hello,

I am happy to provide some guidance and resources to help you with your examination on the topic of solid state in tight binding approximation, Brillouin zone, and Fermi. The following is a brief explanation of these concepts and some suggestions for further reading.

In solid state physics, the tight binding approximation is a method used to describe the electronic structure of a solid material. It assumes that the electrons in a crystal are localized around individual atoms and interact with each other through their overlapping wavefunctions. This allows us to simplify the problem of calculating the electronic properties of a solid to one of solving for the energy levels and wavefunctions of these localized electronic states.

The Brillouin zone is a concept used to describe the periodicity of a crystal lattice in reciprocal space. It is the first Brillouin zone that is of particular interest, as it contains all the information about the electronic properties of the material. The boundaries of the first Brillouin zone are determined by the reciprocal lattice vectors of the crystal.

To determine the energy levels and wavefunctions of localized electronic states on defects in a periodic lattice, you can use the tight binding approximation. This involves solving the Schrödinger equation for the localized states at the defect, taking into account the interactions with the surrounding lattice. Some recommended resources for further reading on this topic are "Introduction to Solid State Physics" by Charles Kittel and "Solid State Physics" by Neil W. Ashcroft and N. David Mermin.

To obtain the band structure of electrons on a two-dimensional square lattice in tight binding approximation, you can use the Bloch theorem, which states that the wavefunction of an electron in a periodic potential can be written as a product of a plane wave and a periodic function. This allows us to express the energy levels as a function of the wavevector k in reciprocal space.

To draw the Fermi surface, which represents the boundary between occupied and unoccupied energy levels at absolute zero temperature, you can plot the energy levels as a function of the wavevector k. The Fermi surface will be a closed curve in the first Brillouin zone. If there is one electron per site, the Fermi surface will be a single point, whereas if there are two electrons per site, the Fermi surface will be a closed curve.

To determine whether a material is a metal or insulator, you can use the concept of the band gap. If there is a gap between the
 

1. What is the solid state in tight binding approximation?

The solid state in tight binding approximation is a theoretical model used to describe the behavior of electrons in a solid material. It assumes that the electrons are tightly bound to the atoms in the material and only interact with their neighboring atoms. This approximation is often used to study the electronic properties of materials such as metals, semiconductors, and insulators.

2. What is the Brillouin zone?

The Brillouin zone is a concept in solid state physics that represents the periodicity of a crystal. It is a mathematical construct that helps to simplify the complex interactions between electrons and atoms in a crystal. The Brillouin zone is the unit cell of a reciprocal lattice and contains all the information about the electronic band structure of a material.

3. How is the Brillouin zone related to the reciprocal lattice?

The Brillouin zone is the unit cell of the reciprocal lattice. It is defined as the set of all points in reciprocal space that can be reached by adding any integer multiple of the reciprocal lattice vectors. The Brillouin zone is a reflection of the underlying symmetry of the material's crystal structure and provides a convenient way to visualize and analyze the electronic band structure of a material.

4. What is the Fermi level in solid state physics?

The Fermi level is the highest occupied energy level in a material at absolute zero temperature. It is a measure of the energy required to add an electron to the material and is often used to determine the electrical conductivity and other properties of a material. In solid state physics, the Fermi level is a crucial concept in understanding the behavior of electrons in a material.

5. How does the Fermi level relate to the electronic band structure of a material?

The Fermi level lies within the band gap of an insulator, at the bottom of the conduction band in a metal, and at the top of the valence band in a semiconductor. It determines the highest energy level that electrons can occupy at absolute zero temperature and is a key factor in determining the electrical and thermal properties of a material. The position of the Fermi level in the electronic band structure can also provide information about the material's electronic and magnetic properties.

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