Materials simulations: Introduction to Density Functional Theory

ECTS credits:
5 ECTS

Course parameters:
Language: English
Level of course: PhD course
Time of year: February 2019 – May 2019
No. hours of work: 150
Capacity limits: 20 participants

Objectives of the course:
This course is an introduction to Quantum Simulation of real materials, with particular emphasis on Density Functional Theory (DFT) and its applications. Besides technical hands-on training, the course provides an in-depth introduction to the theoretical foundations of DFT, its standard approximations as well as some of its state-of-the-art generalizations designed for simulating strongly-correlated materials.

Learning outcomes and competences:
At the end of the course, the student should be able to:

  • Account for the formulation of the many-electron problem in second quantization.
  • Construct tight-binding models of solids and molecules.
  • Solve and analyze Free-Fermion models (band theory).
  • Account for the theoretical foundations of DFT and the physical ideas and hypothesis underlying some of its standard approximations such as the Local Density Approximation (LDA).
  • Apply DFT codes to simple solids to compute key quantities such as the total energy and analyze band structures.
  • Critically assess of capabilities and limitations of standard approximations to DFT in relation to Mott physics and account for state-of-the-art generalization to DFT designed for this purpose.

Compulsory programme:
The first 2 modules focus on the theoretical background in many-body theory and DFT. Teaching is structured in weekly cycles consisting of 1 face-to-face class alternated with out-of-class, see Fig. 1. Active participation in out-of-class activities and weekly face-to-face classes is mandatory.

 Fig. 1: Schematic representation of teaching format of modules 1,2.

Module 3 consists in a few hands-on DFT sessions and a small research project (either in group or individually upon request), which will be designed in agreement with the participants (e.g., based on a specific research project of interested to them) or directly assigned by the teacher.

Course contents:

  • Second Quantization, Field Operators and Fermionic Models of solids and molecules.
  • Free-fermion models in second quantization, canonical transformations, Slater determinants.
  • Free Electron Gas and Thomas Fermi Theory.
  • Periodic systems and Bloch Theorem.
  • Green’s functions, ARPES spectra and bands.
  • Bloch Theorem and Electrons in periodic potentials (Band Theory).
  • Hohenberg-Kohn Theorem and Levy-Lieb formulation of DFT.
  • Kohn-Sham construction.
  • Application of DFT codes to simple solids.
  • Strong Electron Correlations and physics beyond band-theory paradigm.
  • Overview of generalizations to standard approximations to DFT for simulating Strongly Correlated Materials.

Prerequisites:
The course is open to PhD students in physics, chemistry and engineering with the following prerequisites:

  • Taken an introductory course in Quantum Mechanics.
  • Some familiarity with many-body electron theory.

Name of lecturer:
Nicola Lanata

Type of course/teaching methods:

  • STREAM-model teaching in modules 1,2 [Godsk, M. (2013). STREAM: a Flexible Model for Transforming Higher Science Education into Blended and Online Learning. In T. Bastiaens & G. Marks (eds.), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2013, (pp. 722-728). Chesapeake, VA: AACE], see Fig. 1.
  • Hands-on tutorial and supervised group project in module 3.

Literature:

  1. Lecture notes on many-body theory, Michele Fabrizio.
  2. Many-body quantum theory in condensed matter physics, Henrik Bruus, and Karsten Flensburg.
  3. Electronic Structure: Basic Theory and Practical Methods, Richard M. Martin.
  4. Electronic Structure Calculations for Solids and Molecules: Theory and Computational Methods, Jorge Kohanoff.

Course homepage:
None

Course assessment:
The out-of-class activities of modules 1,2 include mandatory assignments (evaluated through criteria established by rubrics from 1 to 10). In order to pass the first 2 modules of the course it is necessary (and sufficient) to obtain a grade > 6/10 for all assignments.

Assessment in module 3 is based on the evaluation of the final report inherent in the small research project, (evaluated through criteria established in a rubric).

Provider:
Department of Physics and Astronomy, Aarhus University

Time:
February 2019 – May 2019

Place:
Campus, 8000 Aarhus C

Registration:
Deadline for registration is February 1 2019. Information regarding admission will be sent out no later than February 3 2019.

For registration and questions contact to Nicola Lanata by email at: lanata@phys.au.dk.

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