P-like states in semiconductors

[Amentia]

Hello,

I have read in several textbooks and articles of semiconductor physics that the valence bands are p-like state. So, even in the mathematical calculation in k.p theory, it is widely used, especially to define heavy holes and light holes states.

My question is: How acurate is this? Why do they say p-like and not p if this is exact? If I want to rotate such a state, can I simply use the rotation matrix for the l=1 angular momentum?

I am not very familiar with group theory unfortunately, but is there a way to answer this question by using the symmetry of the crystal? Let's say the zinc blende structure...

Thank you in advance for any help.

 

[eljose79]

Hello,

Thank you for your question. As a scientist in the field of semiconductor physics, I can provide some insight into the accuracy of using p-like states in the valence bands and why they are referred to as such.

Firstly, it is important to understand that the valence bands in semiconductors are a result of the overlapping of atomic orbitals in a crystal lattice. These atomic orbitals have specific symmetries, which can be described by the quantum numbers l, m, and s. The l quantum number represents the orbital angular momentum, and for p orbitals, it has a value of 1.

In the k.p theory, which is commonly used to describe the electronic band structure of semiconductors, the valence band states are approximated as a linear combination of Bloch functions, which are solutions to the Schrodinger equation in a periodic potential. These Bloch functions are characterized by their symmetry under the crystal symmetry operations, and they can be labeled by the irreducible representations (irreps) of the crystal group.

In zinc blende structures, which have a face-centered cubic lattice, the valence band states are described by the irreps A1 and T2. The T2 irrep corresponds to a p-like state, which means that the Bloch function has the same symmetry as a p orbital. However, due to the crystal symmetry, the Bloch function is not an exact p orbital, hence the term p-like is used to indicate this approximation.

To answer your question about rotating a p-like state, you can indeed use the rotation matrix for l=1 angular momentum. This is because the p-like state still retains the same symmetry as a p orbital, and therefore, the rotation matrix for the p orbital can be used.

In summary, the use of p-like states in the valence bands of semiconductors is accurate in the sense that they have the same symmetry as a p orbital. However, they are not exact p orbitals due to the influence of the crystal lattice, and hence the term p-like is used. The symmetry of the crystal can be used to understand the properties of these states, and group theory can be used to analyze their behavior.

I hope this helps to answer your question. If you have any further inquiries, please let me know.