From b8dc0f6343b474e61ee478708cccd0ac2d3ffc2e Mon Sep 17 00:00:00 2001 From: "T. van der Sar" <t.vandersar@tudelft.nl> Date: Mon, 14 Jan 2019 20:38:17 +0000 Subject: [PATCH] Update lecture_6.md - first formulation of learning goals --- src/lecture_6.md | 26 +++++++++++++++++++------- 1 file changed, 19 insertions(+), 7 deletions(-) diff --git a/src/lecture_6.md b/src/lecture_6.md index fa031cb3..338942d8 100644 --- a/src/lecture_6.md +++ b/src/lecture_6.md @@ -10,20 +10,25 @@ pi = np.pi _(based on chapters 15–16 of the book)_ Exercises 15.1, 15.3, 15.4, 16.1, 16.2 +!!! summary "Learning goals" + + After this lecture you will be able to: + + - 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? -- GitLab