A question about band structure silicene

In summary, silicene is a two-dimensional material with a honeycomb lattice structure made up of silicon atoms. Its band structure is unique due to its buckled structure, resulting in Dirac cones and a linear dispersion relationship for electrons. This has potential applications in electronics and photonics and offers a platform for studying spin-orbit coupling. The band structure can be measured using techniques such as ARPES, STM, and Raman spectroscopy, but there are challenges in synthesizing and understanding the effects of substrate interactions and defects.
  • #1
anahita
39
0
Dear forum people
I consider four atomic orbitals of the silicon atom: s, px , py and pz , thus Hi,j is a 4*4 matrix.
Hi,i is the expression of the diagonal matrix and Hi,j is the expression off-diagonal matrix where the expression for Hi,i and Hi,j is attached.
But I can not calculate the cosine of direction.
Who can help me find the cosine of direction?
 

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  • #2
Thank you very much.The expression for Hi,i and Hi,j are given by: Hi,i= (Z/r) * [1 - (α * Z)/(2 * r)]Hi,j =-(Z/r^2) * (α/4) * [ 3 - (α * Z)/(2 * r)]
 

Related to A question about band structure silicene

1. What is silicene?

Silicene is a two-dimensional material made up of a single layer of silicon atoms arranged in a honeycomb lattice structure, similar to graphene.

2. How is the band structure of silicene different from other materials?

The band structure of silicene is unique because of its buckled structure, which leads to the formation of Dirac cones at certain points in the Brillouin zone. This results in a linear dispersion relationship for electrons, similar to graphene, but with a larger band gap.

3. What is the significance of the band structure of silicene?

The band structure of silicene has potential applications in electronics and photonics due to its unique properties, such as high carrier mobility and tunable band gap. It also offers a new platform for studying the effects of spin-orbit coupling in two-dimensional materials.

4. How is the band structure of silicene experimentally measured?

The band structure of silicene can be measured using various techniques such as angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and Raman spectroscopy. These techniques provide information about the energy and momentum of electrons in the material.

5. What are the current challenges in understanding the band structure of silicene?

One of the main challenges in studying the band structure of silicene is the difficulty in synthesizing and handling the material in a stable form. Additionally, the effects of substrate interactions and defects on the band structure are still not fully understood and require further research.

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