Modern electronic structure methods - Département de Physique de l'Ecole Normale supérieure

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Modern electronic structure methods

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Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
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Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
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Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Faculty : Marco Saitta (UPMC), Silke Biermann (Ecole Polytechnique)

Tutor : Michele Lazzeri (UPMC)

ECTS credits : 6

Language of instruction : English

Description :

The main goal of this course is to cover the modern methods of “ab initio” electronic structure theory, to investigate the ground-state, perturbative, and excited-state properties of condensed matter. This will be achieved by lectures and exercises (TD), including numerical ones. We will start with from the Fermi theory of the electron gas, to develop the fundamentals of Density-Functional Theory (DFT), the main framework and starting point of modern electronic structure methods. We will assess its extent, its main approximations, its operative development, and its main applications in determining the ground-state structural, electronic, and magnetic properties of matter.

We will then focus on the perturbative approach to DFT, which allows to describe, with remarkable accuracy, important properties of materials, such as phonons, effective charges, dielectric constants, electron-phonon coupling, BCS superconductivity.

Finally, we will progress further from the single-particle picture towards the excited-state and correlation electronic properties, by introducing the theory beyond the band picture, and the many-body perturbation theory, up to Mott insulators, correlated metals, and the modeling of full many-body behavior.

The second part of the semester will be devoted to “ab initio” projects, where each 2-student team will choose a specific topic, and develop it, under the guidance of the teachers, over 4 computer lab sessions. They will provide an “article-like” report of their study, and present it in a “conference-like” format for the final course evaluation.

Plan of the course
1) Density functional theory (DFT) (3 weeks, course+TD)
Electronic states in molecules and solids, Born-Oppenheimer approximation, Hartree-Fock approximation. Electron gas, Slater approximation for the exchange potential. Introduction to DFT, Hohenberg-Kohn theorem, Kohn-Sham equations, exchange and correlation functional. Practical approximations, local density approximation, generalized gradient approximation. Solved and unsolved problems in DFT : self-interaction, weakly interacting systems, strongly correlated systems, the electronic band gap problem. Realistic/accurate calculations with DFT in atoms. Realistic/accurate calculations with DFT in solids : localized bases/plane waves, finite and infinite systems, pseudopotentials. Examples : structural properties, phase transitions, electronic band structure and electronic charge density plots in real systems, comparison to experiments.

2) Density functional perturbation theory (2 weeks, course+TD)
Hellmann-Feynman theorem, calculation of derivatives (forces). Introduction to screening. Density functional perturbation theory. Calculation of phonons and dielectric properties. Metals and magnetic systems. Third-order perturbation : ab initio calculation of vibrational (Raman, Infrared) spectra. Electron-phonon coupling, superconductivity.

3) Advanced electronic structure : many-body effects, excited-state properties (4 weeks, course+TD)
Spectral properties beyond the band picture. Many-body perturbation theory and the band gap problem in semiconductors. Green function. From Mott insulators to correlated metals. Modeling many-body behavior. Dynamical mean-field theory.

4) Ab initio projects (incomplete list)
1. Graphene and nanotubes
2. BCS superconductivity
3. Surfaces
4. Piezoelectric systems
5. GW semiconductors

Anonymous students’ evaluations (2016-17)

1) Overall Grade :
60% very good, 40% good
2) The format of this course has been helpful to the way I learn :
100% Agree
3) This course has stimulated my interest in learning about this subject outside of class :
20% Strongly agree, 80% Agree
4) The supporting materials in this course are relevant and contribute to my learning :
40% Strongly agree, 40% Agree, 20% Neither agree nor disagree
5) The pace of this course allows time for my reflection and learning :
20% Strongly agree, 80% Agree
6) Did you find interesting/useful the "Ab initio projects" part ?
60% Strongly agree, 40% Agree
7) Did you find pertinent the "Exam by project" approach ?
40% Strongly agree, 60% Agree

Some free comments :
" Interesting and novel course. A good balance between theoretical notions and their application in the project."

" The scope of the course was somewhat ambitious. Understanding the theory behind DFT and DMFT and implementing these ideas on the laptop would have been impossible, especially in a language I have never used. Luckily, all code was always given and our task was to tweak it and learn about it in a "trial-and-error" fashion. The pace of the course was somewhat odd, especially at the beginning, when I felt it was hard to solve the weekly assignments. This caused some stress but luckily the best part was yet to come : the project part was perhaps when I learnt mostly about the coding aspects of the course. It was great being able to solve a very recent research problem on our own (albeit with some help). I am very proud on the outcome of the course : I leave the course having a better feeling of what research is in this area and with the necessary knowledge to start solving difficult problems using this very useful tool."

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Prochain Séminaire de la FIP :
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Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr