This lecture covers fundamentals of solid state physics, 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.
Applications to the electronic states of low-dimensional materials and metallic microstructure interfaces are discussed to deepen the understanding.
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.
crystal structure, reciprocal lattice, Brillouin zone, electronic band structure, nearly free-electron model, tight-binding approximation, phonons, first-principles electronic-structure theory, Born-Oppenheimer approximation, Hartree-Fock approximation, density functional thoery
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
At the beginning of the class (not each class), solutions to exercise problems assigned during the previous class are reviewed.
|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, Low-dimensional system and nano-materials||Explain the tight-binding approximation of the valence band structure. Moreover, underatand how the NFE model and tight-binding approximation are applied to describe the electronic structure of low-dimensional materials.|
|Class 8||Review of the first half of the course (classes 1-7) and related exercises||Test level of understanding and self-evaluate achievement for classes 1-7.|
|Class 9||Bracket notation||Understand the bra-ket representation of state vectors and operators.|
|Class 10||Born-Oppenheimer approximation||Understand the Born-Oppenheimer approximation.|
|Class 11||Bose-Einstein statistics and phonons||Understand phonons through the language of Bose-Einstein statistics.|
|Class 12||Creation/annihilation operators and introduction to quantum many-body theory||Understand the basics of many-body quantum theory using the number representation through creation and annihilation operators.|
|Class 13||First-principles electronic-structure theory (Hartree-Fock approximation and wave-function theory)||Understand Hartree-Fock approximation and wave-function theory.|
|Class 14||First-principles electronic-structure theory (density functional theory)||Understand density functional theory.|
|Class 15||First-principles electronic-structure theory (examples for metallic microstructures, etc.)||Understand how first-principles calculations play roles in solid state physics through studying examples for such as applications to metallic microstructure interfaces.|
Lecture notes are distributed if necessary.
Kittel: Introduction to Solid State Physics,
Grosso, Parravicini: Solid State Physics,
Sakurai: Modern Quantum Mechanics,
Oshiyama et al.: Computations and Materials (in Japanese)
Learning achievement is evaluated by a final exam.
It is desirable that the students have learned basics of quantum mechanics.