Electronic Structure of Condensed Matter

Physics 598SCM  - Fall 2004 - Instructor: Richard M. Martin

Syllabus

(Last modified November 23, 2004 - Will be updated during the semester)

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Date 
# 
Lecture Topic 
Text 
Hmwk
Overview and Background
8/26
1
Electronic Structure and the Properties of Matter: Overview of status and challenges
Examples of extended band-like (weakly-correlated) and localized atomic-like (strongly-correlated) behavior: H, Na, Si, C60, MgB2, Cu, Ni, NiO, La2CuO4, Ce, ...
1,2
-
8/31 
2
Continue properties of matter; Theoretical background: Fundamental hamiltonian; Force theorem, Independent particle approximation (Hartree; Hartree-Fock; Density Matrices)
2,3 
1
9/2 
3
Crystal Symmetry and Bloch States
Atoms: Understanding formation of bands from atomic wavefunctions (part of Ch. 10)
4,10 
-
9/7 
4
Homogeneous electron gas: model system for understanding of electrons in condensed matter
5 
-
Density Functional Theory
9/9 
5
Hohenberg-Kohn Theorem, Kohn-Sham Ansatz:
Approach to the many-body problem using independent-particle methods
6,7 
2
9/14 
6
Solving the Kohn-Shams Eqs. -- LDA, GGAs, nonlocal functionals -- Tests on simple systems
8,9 
-
Independent Particle Approximation: The three basic methods
9/16 
7
Pseudopotentials: Theory and practical implementation
10,11 
-
9/21 
8
Plane Wave (and Grid) Calculations in Crystals:
Basic Understanding of Bands, Bloch theorem, Empirical pseudopotentials
12,N 
-
9/23 
9
Plane Wave Calculations in Crystals; self consistent DFT
Applications: crystals, surfaces, phonons, ...
13 
-
9/28 
9a
Examples of plane wave calculations with open source code ABINIT
13 
3
9/30 
10
Atom Centered Orbitals I: Tight-binding Bases:
Basic Understanding of Bands, molecules, clusters, nanotubes, ...
14,N
-
10/5 
11
Atom Centered Orbitals II: Gaussians, LCAO, ...
Applications: Crystals, large molecules, ....
15,16
3a
10/7 
12
Muffin Tin based methods: APW, KKR, MTO
Linearization: LAPW, LMTO -- Applications - transition metal compounds
16,17 
-
Predicting the properties of matter - Recent developments using independent particle methods
10/12 
13
Iterative methods: Efficient Plane Wave and Grid Calculations
L,M
-
10/14 
14
"Quantum Molecular Dynamics" (Car-Parrinello-type methods)
18
-
10/19 
15
Linear Response Theory: Phonons; "2n+1 theorem"
19
-
10/21 
16
Geometric Berry's phases: Electric Polarization, Wannier Functions, Quantitative Measure of Localization in an Insulator - introduction to "Order-N" (Ch. 23)
21,22
-
10/26 
17
Excitations: Time dependent density functional theory (TDDFT) - Failures of approximate functionals - Beyond Kohn-Sham . . .
20
-
Many-body methods for explicit treatment of interacting electrons 
10/28
18a
Introduction: The many-body hamiltonian - second quantization
- 
-
11/2 
18
Excitations of the many-electron system: Fermi Liquid Theory; Quasiparticles
- 
-
11/4 
19
Green's Functions, Self-energies; Quasiparticles
- 
-
11/9 
20
Lecture by L. Reining - TDDFT and many-body perturbation theory: the "GW" and "BSE" approximations
- 
-
11/11 
21
Lecture by L. Reining - TDDFT and many-body perturbation theory: the "GW" and "BSE" approximations - continued
- 
-
Strongly-Correlated Electron Systems
11/16 
22
Overview of Strongly Correlated Systems: Metal-Insulator Transitions; Local magnetic moments; Colossal Magnetoresistance; Hi-Tc superconductors.
Luttinger Theorem on Fermi Surface
- 
4
11/18
23
Prototype problems/models: Wigner transition in electron gas; Hubbard Model; Kondo/Anderson models
- 
-
11/22-26 
- 
No Lectures: Thanksgiving Break 
- 
-
11/30 
-
No class - Prof. Martin out of town
- 
-
12/2 
24
Kondo/Anderson impurity model; Large N limit; Anderson lattice, Heavy Fermions
- 
-
12/7 
25
Dynamical Mean Field Theory (DMFT)
Applications: Magnetic oxides, metal insulator transitions, rare earths, actinides
- 
-
12/9 
26
Hi-Tc Superconductors - Conclusions
- 
-
12/13 
MONDAY DEC. 13, 1-4:30 PM - Project Reports

Send reports of problems to:
Prof. Martin, rmartin@uiuc.edu
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