Lectures

WS 20/21

Theoretical Solid-State Physics RWTH Aachen The core of solid-state physics is the many-body problem. This lecture will introduce you to its essential theoretical aspects. E-mail: e.pavarini@fz-juelich.de Language: English Time and Place: Mondays, 10:30 to 12:00 and 12:30 to 14:00, on zoom Time and Place: Thursdays, from 10:30 to 12:30, on zoom Exam: Oral, February -- if too many, written proof Exercises: they will be uploaded each Thursday. they have to be handed in Thursday in a week (groups of 3 or 4) Exam Admission: at least half of the points in the exercises (groups of 3 or 4) Literature: J. Solyom, Fundamentals of the Physics of Solids, Springer, Vol I and II G. Grosso, G. Pastori-Parravicini, Solid State Physics, Academic press G. Czycholl, Theoretische Festkoerperphysik, Braunschweig Lecture Notes of the Autumn School on Correlated Electrons link here

LECTURE CONTENT -- WHERE TO FIND IT IN THE BOOKS

• introduction to the many-body problem
• hydrogen atom and atomic units
• from atoms to solid-state systems
• Born-Oppenheimen Anstatz and Born-Oppenheimer expansion
  • Czycholl Ch 2
• electron-phonon coupling and Jahn-Teller effect
  • Grosso Pastori-Parravicini Ch. VIII
• origin of the chemical bond
  • Solyom, Vol. 1 Ch 4
  • Grosso Pastori Parravicini Ch VI
• symmetries, structures, conservation laws, time-reversal symmetry
  • Grosso Pastori Parravicini Ch II
  • Solyom, Vol I, Ch. 5 and 6
  • my chapter on groups: download here
  • literature in my lecture on symmetries link
• density-functional theory (DFT): basics, successes and failures
  • Grosso Pastori Parravicini Ch IV,
  • intro to my correl11 chapter download here
  • Bob Jones chapter (historical) download here ]
• local-density approximation
  • Grosso Pastori Parravicini Ch IV, DFT material above
• second quantization
  • Grosso Pastori Parravicini Ch IV, Appendix B
  • Czycholl Ch. 5
  • Solyom Vol 2 Appendix H
  • Erik Koch, chapter correl13 download here
• the electronic hamiltonian in second quantization
  • Grosso Pastori Parravicini Ch IV; literature second quantization above
• Sommerfeld Expansions
  • Solyom, vol. 2, Ch 16
• tight-binding approach and electronic bands
  • Grosso Pastori Parravicini Ch V
• band metals and insulators
  • Grosso Pastori Parravicini Ch I,VI
• strongly-correlated systems and the Hubbard model
  • my chapter in correl17
  • my chapter in correl19
• Hartree-Fock and DFT+U [ correl17 ]
• Beyond Hartree-Fock: dynamical mean-field theory
  • correl19
• phonons: Solyom chapter 12 vol 1, Pastori Parravicini chapter IX
• magnetism and correlations
  • my chapter in correl15
• spin and orbital order
  • my chapter in correl16
• bosonic excitation: phonons; Goldstone and Higgs modes.

LECTURE MATERIAL WILL BE UPLOADED IN MOODLE. HERE IS AN OVERVIEW:

• Intro Hydrogen Atom slides (by J. Musshoff)
• How to plot spherical harmonics (by J. Musshoff) slides
• L1-L2: Born-Oppenheimer Ansatz and expansion. Stability of Matter.
• L3-L4: Born-Oppenheimer Ansatz expansion. Nature of the chemical bond. Jahn-Teller Theorem. Bravais Lattices. Van der Waals systems. Close packed structures.
• L5-L6: Ionic and covalent bond with examples.
• L7-L8: Metallic bond. What did we learn so far: Summary on the chemical bond. Symmetries and their consequences. Irreducible representations. Abelian Gruops. Translational group. The Bloch theorem and Bloch states.
• L9-L10: Symmetries and their consequences. Bravais lattice and Brillouin Zone. Point groups and Space of Groups. Identify a point group. Accidental degeneracy and nearly-degenerate bands. Effects of point symmetry on the k points. Star and group of the k point. Irreducibile Brillouin Zone.
• L11-L12: Symmetries and their consequences. Character tables, decomposition formula and projectors. Splitting of bands and symmetry. Splitting of atomic levels. Time-reversal symmetry and Kramers theorem.
• L13-L14: Symmetries: crystal momentum conservation, Laue diffraction, Bragg peaks and scattering. Double groups. Density-functional theory. Hohenberg-Kohn Theorem. Kohn-Sham equations. Local density approximation.
• L15-L16: DFT, Kohn-Sham equations, band-structure methods. Second quantization, field operators.
• L17-L18: Second quantization. Independent electrons. Sommerfeld expansion. Hubbard model.
• L19-L20: Hubbard model. Tight-binding approach. Mott transition. Hartree-Fock (FM).
• L21-L22: Hubbard model, Hartree Fock (AFM), large U limit and Green functions.
• L23-L24: Hubbard model, dynamical mean field. Phonons.
• L25: Phonons and melting. Summary and Exam Preparation