Lecture "Solid State Theory II" (515.474)

Band Structure Methods
SS 2014

First lecture (12.3.2014): General introduction to the course (pdf).
Second lecture (19.3.2014): DFT: Basic Concepts. Wave-function based methods. (pdf).
See also hand-written notes here: (pdf).
Third lecture (26.3.2014): DFT: Derivations. Hohenberg-Kohn Theorem and Kohn-Sham equations.
Meaning of the exchange and correlation energy. Homogeneous electron gas.
Hand-written notes here: (pdf).
Fourth lecture (2.4.2014): DFT: Practical Problems. Slides here: (pdf).
Fifth lecture (9.4.2014): Pseudopotential theory. Slides here: (pdf).
Sixth lecture (7.5.2014): Advanced Topics: Lattice Dynamics. Slides here: (pdf).
Seventh lecture (13.5.2014) First practical exercise: Band Structure and Equation of State of Silicon. (pdf).
Eigth lecture (21.5.2014) Advanced Topics> Lattice dynamics, linear response theory.
Hand-written notes here
Ninth lecture (23.5.2014) Second practical exercise: Phonon Dispersions of Silicon. (pdf).
Tenth lecture (28.5.2014) Discussion of Projects.
Eleventh lecture (4.6.2014) Localized basis sets: Tight Binding Method.
Exercise here.
Third Practical Exercise (10.6.2014) Maximally Localized Wannier Functions.
Twelth lecture (11.6.2014) Maximally Localized Wannier Functions; Augmented Methods.
Hand-written notes here.

For the first three lectures (DFT), the following links/references may be useful:

"A primer in Density Functional Theory" (here), chapter 1.
Ashcroft and Mermin, "Solid State Physics", Saunders College (NY): Chap. 17 (sect. 1 and 2).
Original Papers:
- "Inhomogeneous Electron Gas", P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). (here)
- "Self-Consistent Equations Including Exchange and Correlation Effects", W. Kohn and L. J. Sham, Phys. Rev.140, A1133 (1965). (here)

For pseudopotentials, I suggest to take a look at the slides of the lecture, and at the original papers:

"Norm-Conserving Pseudopotentials", D. R. Hamann, M. Schlueter, and C. Chiang Phys. Rev. Lett. 43, 1494 (1979). (here)
"Pseudopotentials that work: From H to Pu", G. B. Bachelet, D. R. Hamann, and M. Schlueter Phys. Rev. B 26, 4199 (1982). (here)

For linear response and lattice dynamics, the standard reference is:

"Phonons and related crystal properties from density-functional perturbation theory", S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001).(here)

For Wannier Functions and tight binding methods:

W. Harrison, Electronic Structure and the properties of Solids, Dover Books
N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
O.K. Andersen, T. Saha-Dasgupta, Muffin-tin orbitals of arbitrary order, Physical Review B 62, R16219 (2000).
J. C. Slater and G. F. Koster, Simplified LCAO Method for the Periodic Potential Problem, Phys. Rev. 94, 1498 (1954).