Title: Summary Breakdown of Band Theory

Choose the correct statement.

- Simple band theory fails to explain the insulating behaviour of some materials, and so additional physics needs to be taken into account to correctly reproduce the observed insulating behaviour. (correct)
- Simple band theory fails to explain the metallic behaviour of some materials, and so additional physics needs to be taken into account to correctly reproduce the observed metallic behaviour.

- Some examples of these metal-to-insulator transitions are Peierls distortion, crystal-field splitting, magnetic exchange, Jahn-Teller distortion and charge ordering. (correct)
- Some examples of these metal-to-insulator transitions are Peierls distortion, the RKKY interaction, Jahn-Teller distortion, Dzyaloshinskii-Moriya interaction and crystal-field splitting.

- The Mott transition is a metal-insulator transition in which the gap is caused by the Coulomb interaction between the electrons. (correct)
- The Mott transition is a metal-insulator transition in which the gap is caused by the Second-Order Jahn-Teller distortion.

- The Hubbard model is the simplest possible extension of band theory to include explicit electron-electron correlations, by adding to the Linear Combination of Atomic Orbitals (LCAO) Hamiltonian a Coulomb repulsion between electrons in the same orbital. (correct)
- The Hubbard model is the simplest possible extension of band theory to include explicit electron-electron correlations, by adding to the Linear Combination of Atomic Orbitals (LCAO) Hamiltonian an anisotropic exchange due to spin-orbit coupling.

- The Coulomb repulsion U corresponds to the ionization energy I minus the electronic affinity A. (correct)
- The Coulomb repulsion U corresponds to the electronic affinity A minus the ionization energy I.

- The bandwidth W is proportional to the interaction energy ß and inversely proportional to the spacing between the atoms. (correct)
- The bandwidth W is inversely proportional to the interaction energy ß and proportional to the spacing between the atoms.

- Metallicity occurs when the bandwidth W overcomes the Coulomb repulsion (W>U), and for W<U the material behaves as an insulator. (correct)
- Insulating behaviour occurs when the bandwidth W overcomes the Coulomb repulsion (W>U), and for W<U the material behaves as a metal.

- Two examples of Mott transitions are found in degenerately doped semiconductors and rare earth nickelates. (correct)
- Two examples of Mott transitions are found in rare earth aluminates and in thin film semiconductors.

- In degenerately doped semiconductors, the insulator to metal Mott transition is due to the change of the spacing between dopant atoms by changing the dopant concentration. (correct)
- In degenerately doped semiconductors, the insulator to metal Mott transition is due to the charge ordering above a certain critical concentration.

- In cuprate high-temperature superconductors, it is believed that the insulating behaviour is due to the superexchange interaction, but it also has some Mott-like contribution. (correct)
- In cuprate high-temperature superconductors, it is believed that the insulating behaviour is due to the superexchange interaction, but it also has some charge disproportionation contribution.