- formulate a general way of computing the electron band structure - the **Bloch theorem**.
- discuss that in a periodic potential all electron states are Bloch waves.
- derive the electron band structure when the interaction with the lattice is weak using the **Nearly free electron model**.
Let's summarize what we learned about electrons so far:
* Free electrons form a Fermi sea ([lecture 2](lecture_1.md))
* Isolated atoms have discrete orbitals ([lecture 3](lecture_3.md))
* When orbitals hybridize we get *LCAO* or *tight-binding* band structures ([lecture 4](lecture_4.md))
In this lecture we:
The nearly free electron model (the topic of this lecture) helps to understand the relation between tight-binding and free electron models. It describes the properties of metals.
* Formulate a general way of computing the electron band structure, the **Bloch theorem**.
* Derive the electron band structure when the interaction with the lattice is weak using the **Nearly free electron model**. This model:
- Helps to understand the relation between tight-binding and free electron models
- Describes the properties of metals.
All the different limits can be put onto a single scale as a function of the strength of the lattice potential $V(x)$:
These different models can be organized as a function of the strength of the lattice potential $V(x)$:
@@ -142,6 +147,13 @@ Extended BZ (n-th band within n-th BZ):
* Easy to relate to free electron model
* Contains discontinuities
!!! summary "Learning goals"
After this lecture you will be able to:
- describe how an insulating or conducting nature of a material is related to the material's band structure.
- examine 1D and 2D band structures and argue if you expect the corresponding material to be an insulator/semiconductor or a conductor.
## Band structure
How are material properties related to the band structure?