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2023　Quantum theory of metals

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Academic unit or major
Graduate major in Materials Science and Engineering
Instructor(s)
Nakatsuji Kan  Gohda Yoshihiro 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(G1-103(G114))  Thr3-4(G1-103(G114))  
Group
-
Course number
MAT.M430
Credits
2
Academic year
2023
Offered quarter
3Q
Syllabus updated
2023/3/20
Lecture notes updated
-
Language used
Japanese
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Course description and aims

This lecture covers fundamentals in physics of metals, where electron theory as the basics of materials science is mainly discussed. The course teaches the electronic band theory from the basics which describes the electronic states of solids. The "nearly free-electron model" and the "tight-binding approximation" will be introduced as the simplest and most valuable models in the band theory. First-principles electron theory is discussed as one of the most important topics in advanced solid state physics. First-principles electron theory is cutting-edge non-empirical electron theory applied for numerical simulations. Hartree-Fock approximation is discussed, where the exchange effect coming from the Fermi-Dirac statistics is taken into account. Then, wave-function theory and density functional theory is introduced. These topics will help to understand quantum theory of metals.

Student learning outcomes

By completing this course, students will be able to:
1) Understand that the electronic states govern the material properties microscopically.
2) Understand the free-electron metallic states as the simplest itinerant electron system.
3) Understand that the electron states of solid crystals become Bloch states.
4) Understand that many-body effects among electrons reduce the Coulomb-repulsion energy.
5) Understand the basics of first-principles electron theory to describe electronic states non-empirically.

Keywords

crystal structure, reciprocal lattice, Brillouin zone, electronic band structure, nearly free-electron model, tight-binding approximation, phonons, first-principles electronic-structure theory, density functional theory, exchange interactions, metallic magnetism

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

At the beginning of the class (not each class), solutions to exercise problems assigned during the previous class are reviewed.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Fermi-Dirac statistics and free electron gas Explain how the energy of free-electron gas is described in Fermi-Dirac statistics.
Class 2 Space symmetry and crystal structures Explain the Bravais lattice and typical lattice structures.
Class 3 Reciprocal lattice and Brillouin zone Calculate the reciprocal lattice vectors of some typical lattices and draw the Brillouin zone.
Class 4 Bloch's theorem Understand that the wave functions of valence band electrons in crystals obey Bloch's theorem.
Class 5 Nearly free electron model Explain nearly free electron (NFE) model and the origin of the band gap.
Class 6 Fermi surface Understand the relationship between the shape of the Fermi surface and crystal and electronic structures.
Class 7 Tight-binding model Understand how the tight-binding approximation is applied to describe the electronic structure of materials.
Class 8 Structural phase transition Understand structural phase transition and the free energy.
Class 9 Bose-Einstein statistics and quantum harmonic oscillators Understand Bose-Einstein statistics and quantum harmonic oscillators.
Class 10 Phonons Understand phonons by statistical physics.
Class 11 Force constants and electronic states Understand relationship between force constants and electronic states.
Class 12 Effective spin-spin interactions Understand exchange interactions.
Class 13 Density functional theory Understand density functional theory.
Class 14 Ferromagnetism in metals Understand first-principles electron theory of ferromagnetism in metals

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Lecture notes are distributed if necessary.

Reference books, course materials, etc.

Kittel: Introduction to Solid State Physics,
R.M. Martin, Electronic structure,
Oshiyama et al.: Computations and Materials　(in Japanese),
A.A. Abrikosov: Fundamentals of the Theory of Metals.

Assessment criteria and methods

Learning achievement is evaluated by reports or a final exam.

Related courses

  • MAT.M409 ： Thermodynamics for Phase Equilibria
  • MAT.A203 ： Quantum Mechanics of Materials
  • MAT.M202 ： Statistical Mechanics(M)
  • MAT.M206 ： Electronic Structure and Physical Properties of Metals
  • MAT.C414 ： Introduction to Solid State Science

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is desirable that the students have learned basics of quantum mechanics.
Not available for those who are credited with MAT.M407-01 Advanced Solid State Physics a.

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