Computational electronic structure theory of solids and applications - Winter Term 2021/22

Lecturer: Dr. Jan Wilhelm

Lectures (2 SWS)
Monday, 10:15 – 11:45, PHY 7.1.21 (We offer an additional Zoom live stream of the lecture, link available on Grips. Zoom streams are recorded, link available in Grips.)

Exercises (1 SWS)
Monday, 12:45 - 14:15, PHY 9.2.08A (CIP-Pool PHY2), every 2 weeks

Lecture period: 18.10.2021 - 07.02.2022

Links: Grips, Vorlesungsverzeichnis

Summary

The electronic band structure describes the energy levels that electrons occupy in a solid. Many important properties follow from the electronic band structure, for example whether the material is a conductor or insulator. On the technological side, information on the electronic band structure can be used to decide whether a material is a promising candidate for building photovoltaic cells or for designing a catalyst for artificial photosynthesis, i.e. to split water into hydrogen and oxygen utilizing sunlight.

In the lecture, we will discuss electronic structure theory of solids, i.e. we will address the following questions:

1) How can we accurately calculate the equilibrium crystal structure and lattice parameters of a solid only knowing the chemical composition (e.g. NaCl)?

2) From a theoretical point of view, how can we define the electronic band structure of an interacting many-electron system?

3) How can we accurately calculate the electronic band structure of a material solely with the knowledge of its chemical composition?

4) How can we measure the electronic band structure in an experiment and how does the measurement correspond to the calculation?

In the last decades, density functional theory (DFT) has been widely used for computing the crystal structure and lattice parameters of solids. The GW method has emerged as an accurate method to calculate electronic band structures. This lecture offers a pedagogical presentation of the conceptual ideas underlying DFT and GW. In the exercises, students apply state-of-the-art software packages to scientifically relevant examples.

Exercise sheets
Exercise sheets and solutions are available on Grips.

Examination
Oral exam during the semester break (approx. 20 min, on lecture material and exercises, dates: 18 February 2022 and 08 April 2022). The lecture is a special lecture ("Spezialvorlesung") with 5 ECTS points.

Outline
1. The many-electron problem
2. Computing properties from solutions of the many-electron Schrödinger equation
3. Foundations of density functional theory for the many-electron ground state
4. DFT with accurate kinetic energy: Kohn-Sham DFT
5. Approximations to exchange-correlation functionals
6. Implementation of Kohn-Sham DFT for crystals in software packages
7. Single-electron levels in DFT
8. GW approximation for quasiparticle energies
9. Spin-orbit coupling (as time permits)

Prerequisites
This course presumes good knowledge of quantum mechanics, e.g. from the course Quantum Theory I, and basic knowledge of solid state physics, e.g. from the course Struktur der Materie II (Festkörperphysik). In the exercises, elementary Linux computer skills are required (bash commands), that will be recapitulated in the first exercise sheet. Prior experience in any kind of programming language is not needed. The lecture is open to Master students of Physics, Nanoscience, Computational Science and Chemistry. Interested Bachelor students are welcome as well. The lecture is also a course within the Integrated Research Training Group of CRC 1277.

Literature
• Lecture notes are available as pdf via Grips.
• R. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, International Series of Monographs on Chemistry. Oxford University Press (1994).
• R. M. Martin, Electronic Structure, Cambridge University Press (2004).