- #1

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This model is used to find band structure of metals and semiconductors. I'm interested

in a book which states all needed assumptions and gives logically consistent mathematical

reasoning explaing why energy bands exist.

Thanks.

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- Thread starter paweld
- Start date

- #1

- 255

- 0

This model is used to find band structure of metals and semiconductors. I'm interested

in a book which states all needed assumptions and gives logically consistent mathematical

reasoning explaing why energy bands exist.

Thanks.

- #2

- 25

- 0

Quantum theory of solids, Kittel

Solid state physics, Ashcroft and Mermin

Mavi

Solid state physics, Ashcroft and Mermin

Mavi

- #3

cgk

Science Advisor

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The bands originate from a unitary transformation from the local orbital basis (Wannier basis) to the crystal orbital basis (Bloch orbital basis). In the Wannier basis, there is one set of more-or-less atomic orbitals for each atom in the lattice, and these are orthonormal and degenerate (i.e., equal at each site, apart from position and phase of course). However, they do not diagonalize any kind of Fock matrix. After the CO transformation you don't have atomic sites anymore, but inverse lattice sites; and the matrix element computation is simplified because different k vectors belong to different irreducible representations of the spatial symmetry group, and for most matrix elements there is a theorem that the product representation of all its indices must contain the totally symmetric irrep in order to not vanish.

- #4

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Mavi

- #5

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Thanks for all answers.

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