Objectives

Solid material is an important part of nature. Understanding the physical properties of these materials has a pivotal role in physics and materials physics. The course will focus on crystalline materials including defects. The concept of many-body interaction and the approximation methods to solve the complex many-body interaction will be introduced in the first part of the course. This includes density functional theory, the second quantization, and field theory. In the second part of the course, the band structure in solids will be introduced by tight-binding approximation with an overview of several typical band structures of materials such as graphene, silicon, GaAs, Al, Cu, and Bi. Doped semiconductors and their applications will be introduced. The third part of the course will cover semiclassical transport in solids under electric and magnetic fields, which includes the Hall effect, magnetoresistance, and quantum Hall effect. The last part of the course will focus on the magnetism in solid materials. 

After this course, students will be able to: 

- Understand and read the band structure of solids

- Understand the basics of semiconducting devices

- Understand the electrical transport of electrons under electric and magnetic fields

- Understand the complexity and challenges of many-body interaction, in particular in solid materials

Prerequisites

Basic knowledge of quantum mechanics or quantum chemistry will be required for this course.  

Organization

27 one-and-a-quarter-hour lectures, 2 lectures per week. 

Grading

Grading is based on homework assignments (70%), and the final oral examination (30%).

Textbooks

There is no textbook for the course. Several books can be used for references. Reading materials will be provided in class. 

Solid State Physics and Condensed Matter Physics

Marvin L. Cohen and Steven G. Louie Fundamentals of Condensed Matter Physics, Cambridge University Press (2016), ISBN 978-0-521-51331-9 

John D. Joannopoulos and Efthimios Kaxiras, Quantum Theory of Materials, Cambridge University Press (2019),  ISBN 978-0-521-11711-1

Neil W. Ashcroft and N. David Cornell. Solid State Physics. Cengage India (2009), ISBN-13978-8131500521.

Kaxiras, E. Atomic and Electronic Structure of Solids. Cambridge University Press, 2003. ISBN: 9780521523394.

Piers Coleman. Introduction to Many-Body Physics. Cambridge University Press. ISBN-13978-0521864886

Henrik Bruus and Karsten Flensberg. Many-Body Quantum Theory in Condensed Matter Physics: An Introduction (Oxford Graduate Texts). Oxford University Press. ISBN-13978-0198566335

Theory and Symmetry 

F. Albert Cotton. Chemical Applications of Group Theory, 3rd Edition. Wiley-Interscience. 3rd edition

ISBN-13 978-0471510949

Mildred S. Dresselhaus, Gene Dresselhaus, Ado Jorio. Group Theory: Application to the Physics of Condensed Matter. Springer, ISBN-13978-3540328971

Magnetism

Stephen Blundell. Magnetism in Condensed Matter. Oxford University Press, ISBN 9780198505914

Michael Coey. Magnetism and Magnetic Materials. Cambridge University Press, ISBN 9780511845000

Berry phase in solids

David Vanderbilt. Berry Phases in Electronic Structure Theory. Cambridge University Press, ISBN 9781107157651

Basics of quantum mechanics

David J. Griffiths and Darrell F. Schroeter. Introduction to quantum mechanics. Cambridge University Press. ISBN 9781107189638

J. J. Sakurai and Jim Napolitano. Modern Quantum Mechanics. 3rd Edition 

Lectures

1. Introduction to many-body physics

2. Electronic structure of atoms

3. Single particle approximation (Hatree-Fock approximation)

4. Single particle approximation (Hatree-Fock approximation)

5. Free electrons

6. Free electrons with Hartree-Fock approximation

7. Hydrogen molecule with Hartree-Fock approximation

8. Density functional theory

9. Density functional theory-Practice (Quantum ATK)

10. Periodic potential

11. Reciprocal lattice

12. Nearly free electrons

13. Peierls distortion

14. Tight binding method

15. Tight binding method

16. Probing electronic band structures (ARPES)

17. Probing electronic band structures (STM)

18. Drude model

19. Intrinsic Semiconductors

20. Intrinsic Semiconductors

21. Doped Semiconductors

22. Semiconductor Junctions

23. General Hamiltonian under magnetic field and Landau levels

24. Density of states at Landau level, cyclic orbit, filling factor

25. Quantum Hall effect 

26. Diamagnetism and Paramagnetism

27. Magnetic order: Exchange coupling

Reference Courses

Prof. David Tong (University of Cambridge) https://www.damtp.cam.ac.uk/user/tong/solidstate.html

Prof. M. Sigrist ETH – Institute for Theoretical Physics – Solid State Theory – FS 2014

PD Dr. Vadim Geshkenbein ETH – Institute for Theoretical Physics – Solid State Theory – FS 2015

Objectives

Starting from the observation of wave-particle duality of matter, the exploration of quantum mechanics bloomed, giving rise to the foundation breaking to understand the ‘small world’ or the world of atoms. This course aims to introduce the basic and advanced quantum mechanics concepts from ‘first quantization’ to ‘second quantization’ and their applications to understand the quantum process in atoms, molecules, and solids. They include the understanding of atomic spectroscopy, energy levels in molecules, the band structure of solids, quantization in quantum wells, and photoluminescence in semiconductors, to name a few. Furthermore, the Berry phases in electronic structure theory and its related quantum Hall effect and topological materials will be introduced. The class is designed for graduate students with physics and materials science backgrounds, but it is not limited to ambitious students with other backgrounds. 

The course will provide a fundamental background for students to further study advanced concepts of magnetism, superconductivity, and topological materials. 

Prerequisites

Basic knowledge of quantum mechanics or quantum chemistry will be beneficial but it is not required.  

Organization

27 one-and-a-quarter-hour lectures, 2 lectures per week. 

Grading

Grading is homework assignments (70%), and the final examination (30%)

Textbooks

There is no textbook for the course. Several books can be used for references. Reading materials will be provided in class. 

Basics of quantum mechanics

David J. Griffiths and Darrell F. Schroeter. Introduction to quantum mechanics. Cambridge University Press. ISBN 9781107189638

Steven Weinberg. Lectures on Quantum Mechanics. Cambridge University Press. ISBN 978-1107111660

E. M. Lifshitz and L. D. Landau. Quantum Mechanics: Non-Relativistic Theory. Butterworth-Heinemann. ISBN 978-0750635394 

Richard P. Feynman, Robert B. Leighton, Matthew Sands. Lectures on Physics, Volume III. Pearson 2012

Jasprit Singh. Quantum mechanics: Fundamentals and Applications to Technology. John Wiley and Sons, ISBN: 978-3-527-61820-0

Basics of band structure and symmetry

Kaxiras, E. Atomic and Electronic Structure of Solids. Cambridge University Press, 2003. ISBN: 9780521523394.

Magnetism

Stephen Blundell. Magnetism in Condensed Matter. Oxford University Press, ISBN 9780198505914

Michael Coey. Magnetism and magnetic materials. Cambridge University Press, ISBN 9780511845000

Berry phase in solids

David Vanderbilt. Berry Phases in Electronic Structure Theory. Cambridge University Press, ISBN 9781107157651

Lectures

1. Introduction/Duality of particles and Waves

2. Larangian mechanics

3. Hamiltonian-Jacobi equation

4. Geometric optics and wave mechanics

5. Schrodinger equation

6. Hamiltonian and momentum operators

7. Hydrogen atom

8. Electronic structure of molecule

9. Band structure of solid

10. Band structure of solid

11. Angular Momentum and Spin

12. Angular Momentum and Spin

13. Combination of two spins

14. Identical Particles: Quantum Statistical Mechanics

15. Identical Particles: Exchange Force

16. Magnetic exchange coupling

17. Second quantization: Ideal and formulation

18. Second quantization: Ideal and formulation

19. Second quantization: Application

20. Second quantization: Application

21. Time-independent perturbation theory

22. Adiabatic approximation

23. Berry phase

24. Quantum superposition and entanglement 

25. Presentation

26. Presentation

27. Time-dependent perturbation theory

28. Recap

Objectives

The aim of this course is to introduce the basic concepts of quantum mechanics from ‘first quantization’ to second quantization. The band structure of solids will be introduced with the tight-binding approach. The concept of symmetry in molecules (point group) and solids (space group) will be introduced. Especially, the magnetic, superconducting properties of materials will be covered. The Berry phases in electronic structure theory and its related topological materials will be shortly introduced. The class is designed for last-year undergraduate and graduate students with physics and materials science backgrounds but it is not limited to ambitious students with other backgrounds.

The main focuses of the course are quantum mechanics, band structure of solids, and symmetry. This is the most important background for students can further reading by themselves for advanced concepts of magnetism, superconductivity, and topological materials.

본 수업의 목적은 'first quantization'부터 'second quantization'까지 양자역학의 기본 개념들을 소개하는 것이다. 고체의 밴드 구조는 밀접 결합 근사 (tight-binding approach)를 이용하여 다뤄질 것이다. 분자(point group)와 고체(space group)의 대칭성이 다뤄진다. 특히 물질의 자성과 초전도성이 다뤄질 것이다. 전자 구조 이론의 베리 위상과 관련된 위상학적 물질이 간략하게 소개될 것이다. 이 수업은 물리학 및 재료과학을 전공한 말년 학부생과 대학원생을 대상으로 진행되지만, 다른 전공을 가진 야심찬 학생들 또한 수강이 가능하다. 코스의 주요 초점은 양자역학, 고체의 밴드 구조, 대칭성이다. 이는 자성, 초전도성, 위상학적 물질과 같은 고급 개념들에 대해 학생들이 스스로 더 깊이 읽을 수 있도록 하는 가장 중요한 배경 지식이다.

Prerequisites

There is no prerequisite for this course. The basic knowledge of quantum mechanics or quantum chemistry will be benefit but it is not required.

Organization

15 three-hour lectures, one lecture per week.

Grading

Grading is based on attendance (20%), the homework assignments (40%) and the final examination (40%)

Textbooks

There is no textbook for the course. Several books can be used for references. Reading materials will be provided in class.

Basics of quantum mechanics

David J. Griffiths and Darrell F. Schroeter. Introduction to quantum mechanics. Cambridge University Press. ISBN 9781107189638

Jasprit Singh. Quantum mechanics: Fundamentals and Applications to Technology. John Wiley and Sons, ISBN: 978-3-527-61820-0

Basics of band structure and symmetry

Kaxiras, E. Atomic and Electronic Structure of Solids. Cambridge University Press, 2003. ISBN: 9780521523394.

F. Albert Cotton. Chemical applications of group theory. John Wiley and Sons, ISBN: 978-0-471-51094-9

Dresselhaus, Mildred S.; Dresselhaus, Gene; Jorio, Ado.  Group theory: Application to the Physics of Condensed Matter. Springer. ISBN 978-3-540-32899-5

Magnetism

Stephen Blundell. Magnetism in condensed Matter. Oxford University Press, ISBN 9780198505914

Ralph Skomski. Simple Models of magnetism. Oxford University Press. ISBN 9780199655397

Michael Coey. Magnetism and magnetic materials. Cambridge University Press, ISBN 9780511845000

Superconductivity

Stephen Blundell. Superconductivity: A Very Short Introduction. Oxford University Press, ISBN 9780199540907

Kun Yang, Steven Girvin. Modern Condensed Matter Physics.  Cambridge University Press, ISBN 9781107137394

Berry phase in solids

David Vanderbilt. Berry Phases in Electronic Structure Theory. Cambridge University Press, ISBN 9781107157651

 Lectures

1.       ‘First quantization’ of quantum mechanics

- The Schrodinger equation

- The statistical interpretation of wave functions

- Momentum

- The uncertainty principle

2.       Quantum mechanics

-          Time-independent Schrodinger equation

-          Infinite square well

-          Harmonic oscillator

-          Free particles

-          Operators

3.       Quantum mechanics

-          Hydrogen atoms

-          Angular momentum

-          Spin

4.       Quantum mechanics

-          Time-independent perturbation theory

-          Zeeman effect

-          Hyperfined Splitting

5.       Quantum mechanics

-          The variation principle

-          The adiabatic approximation

6.       Bonding in molecules and solids

-          Tight-binding models for molecules

7.       Bonding in molecules and solids

-          Tight-binding models for solids

8.       Symmetry

-          Symmetry in molecules and point group

9.       Symmetry

-          Applications of point group for molecules

10.   Symmetry

-          Symmetry in solids and Space group

-          Symmetry in reciprocal lattices

11.   Quantum mechanics

-          Second quantization

-          Quantization of the electromagnetic field

-          Phonons

-          Plasmons, magnons and polarons

12.   Magnetism

-          Isolated magnetic moments

-          Magnetic exchange interaction

13.   Magnetism

-          Control magnetism by electrical currents

-          Control magnetism by electrical gate-biases

14.   Superconductivity

-          Phenomenon of superconductivity

-          Microscope mechanism of superconductivity (BSC theory)

-          Phase diagram of different superconductivity

15.    Berry phase and topological materials

-          Berry phases

-          Band crossing and symmetry breaking

-          Topological insulators

-          Weyl semimetals

-          Dirac semimetals

-          Nodal line semimetals

Objectives

Density functional theory (DFT) becomes a standard approach to understand the material properties, from electronic band structures, phonon as well as transport phenomena. It is also useful to understand the chemical properties of materials.  This course will introduce key concepts of DFT and its practical use in different contexts. The course will start from a basic background of quantum physics and chemistry, Hartree-Fock to DFT approximations. The practical approach on how to use DFT code (e.g. Quantum Espresso) will be introduced. Some basics of using Linux operation system will be covered. After this course, students will establish a basic overview of how a DFT code works and abilities to further self-study. 

The class is designed for last-year undergraduate and graduate students with different backgrounds. 

(밀도범함수 (DFT) 이론은 물질의 전자, 포논 띠 구조 뿐만 아니라, 수송 정보까지 밝혀낼 수 있는 표준적인 접근법이 되었다. 이 수업은 밀도범함수 이론의 핵심 개념들을 소개하며, 상용 프로그램 (e.g., Quantum Espresso)을 통해 그것들을 실제로 적용해 볼 것이다. 기초적인 양자 물리학/화학에서부터 시작하여, Hartree-Fock 근사와 밀도범함수 이론까지 다루게 될 것이다. 리눅스 (Linux) 시스템의 기초적인 운용법 또한 다뤄질 것이다. 수강생들은 전반적으로 어떻게 밀도범함수 이론을 이용한 프로그램이 동작하는지 배우게 될 것이며, 추후 연구를 위한 능력을 기르게 될 것이다.

이 수업은 마지막 학년의 학부생과, 다양한 전공을 가진 대학원생들을 대상으로 한다.)       

Prerequisites

There is no prerequisite for this course. Students must bring their own laptop to class for last 4 hand-on lectures. 

Organization

15 three-hour lectures with five lectures replaced by a laboratory.

Five lab assignments, each for 2-3 weeks.

Grading

Attendance (20%), lab assignments (80%). There are no exams.

Textbooks

There is no textbook for the course. Several books can be used for references. Reading materials will be provided in class. 

Feliciano Giustino. Materials Modelling using Density Functional Theory. Oxford University Press ISBN 9780199662432

Attila Szabo and Neil S. Ostlund. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications. Inc. ISBN: 978-0486691862

David J. Griffiths and Darrell F. Schroeter. Introduction to quantum mechanics. Cambridge University Press. ISBN 9781107189638

Jensen, F. Introduction to Computational Chemistry. New York, NY: John Wiley & Sons, 1998. ISBN: 9780471984252

Kaxiras, E. Atomic and Electronic Structure of Solids. Cambridge, UK: Cambridge University Press, 2003. ISBN: 9780521523394

Martin, R. Electronic Structure: Basic Theory and Practical Methods. Cambridge, UK: Cambridge University Press, 2004. ISBN: 9780521782852

Simulation Software

The hands-on lab will introduce how to use Quantum Espresso code (https://www.quantum-espresso.org/). 

Lectures

1. Introduction to Computational Methods in Materials Science

2. Quantum Mechanics: Review

3. Electronic Structure of Atoms, Molecules, and Solids

4. Approximations for many-electron systems

5. The Hartree-Fock approximation

6. Density functional theory I: Basic concepts

7. Density Functional Theory II: Exchange-correlation functionals

8. Approximation in DFT codes 

9. Equilibrium structures of materials

10. Band structures of molecules and solids

11. Lab 1: Introduction to Linux 

12. Lab 2: Band Structure of Al, Si, NiO

13. Lab 3: van der Waal Interaction in 2D Materials

14. Lab 4: Vibration of molecules and solids

15. Project reports