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ETH Zrich - D-PHYS - Solid State Physics - Microstructure Research - Lectures - Group Theory for Solid State Physics FS 2016

Group Theory for Solid State Physics FS 2016

Selected Article

Nat. Comm 7, 13611 (2016)
Critical exponents and scaling invariance in the absence of a critical point
>>

Proc. R. Soc. A 472, 2195 (2016)
Thirty per cent contrast in secondary-electron imaging by scanning field-emission microscopy
>>
Phys. Rev. B 89, 014429 (2014)
Domain-wall free energy in Heisenberg ferromagnets
>>

Phys. Rev. B 87, 115436 (2013)
Scale invariance of a diodelike tunnel junction
>>

Manuscript

Lecture Notes
(last updated: 22.02.2016)
Lecturer: Prof. Dr. Danilo Pescia (pescia@solid.phys.ethz.ch)

Recommended Literature

Group Theory: Application to the Physics of Condensed Matter
(Published: 2008; Authors: Dresselhaus, Mildred S.; Dresselhaus, Gene; Jorio, Ado)
Lie-Gruppen und Lie-Algebren in der Physik
(Published: 2011; Author: Böhm, Manfred)

Extra Literature

Chapter 1 - Abstract Group Theory and Representation Theory of Groups
Point Groups in Solid State Physics I: Point Group Oh
(Published: 2013; Authors: A. Delibas et al.)
Chapter 3 - Continuous Groups and Symmetry Breaking Interactions
On One-Parameter Unitary Groups in Hilbert Space
(Published: 1932; Author: M. H. Stone)
The Harish-Chandra Character
(Published: 1980; Authors: M. F. Atiyah et al.)
Chapter 4 - Space Groups and their Representations
Space Groups and Their Representations
(Published: 1957; Author: George Koster)
The Plane Symmetry Groups: Their Recognition and Notation
(Published: 1978; Author: Schattenschneider, Doris)
Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals
(Published: 1936; Authors: L.P Bouckaert, R. Smoluchowski, E. Wigner)
Nonsymmorphic Symmetries and Their Consequences
(Published: 2012; Author: Bolin Liao)
Chapter 6 - Applications of Direct Products
Splitting of Terms in Crystals
(Published: 1929; Author: Hans Bethe)
An Anyon Primer
(by Sumathi Rao (retrieved: 27.04.2016))
Properties of the Thirty-Two Point Groups
(Published: 1963; Authors: G. F. Koster, J. O. Dimmock, R. G. Wheeler, H. Statz)
Photoemission of spin-polarized electrons from GaAs
(Published: 1976; Authors: Daniel T. Pierce and Felix Meier)
Experimental Symmetry Analysis of Electronic States by Spin-Dependent Photoemission
(Published: 1983; Authors: R. Allenspach, F. Meier, D. Pescia)
Optical spin orientation in crystals with diamond strucutre
(Published: 1984; Authors: R. Allenspach and D. Pescia)
Tables of Basis Functions for Double Point Groups
(Published: 1966; Authors: Y. Onodera and M. Okazaki)

Additional Material

Chapter 1 - Abstract Group Theory and Representation Theory of Groups
Common Point Groups
List of Point Groups
(by R. Balili et al. (retrieved: 02.04.2016))
Stereographic Projection
Chapter 3 - Continuous Groups and Symmetry Breaking Interactions
Linear Combinations of Spherical Harmonics up to l=3
(parter functions for the irr. repr. of Oh)
Chapter 4 - Space Groups and their Representations
The 3D Bravais Lattices
Irreducible Representations of the group of k of O7h
Chapter 6 - Applications of Direct Products
Clebsch-Gordan Coefficients, Spherical Harmonics, and d Functions
Character Table, Basis Functions and Multiplication Table for the Groups D3 and C3v
Character Table, Basis Functions and Multiplication Table for the Groups Oh and Td
Non-Relativistic Band Structure of GaAs and Ge
Relativistic Band Structure of GaAs
Relativistic Band Structure of Ge

Problem Sheets and Solutions

Assistant: Yves Forrer (yforrer@stud.phys.ethz.ch)
(Video-Solutions of the problems can be found here )
Chapter 1 - Abstract Group Theory and Representation Theory of Groups
Problem Sheet 1
Solution Sheet 1
(updated problem 7)
Problem Sheet 2
Solution Sheet 2
Chapter 2 - Group Theory and Eigenvalue Problems
Problem Sheet 3
Solution Sheet 3
Chapter 3 - Continuous Groups and Symmetry Breaking Interactions
Problem Sheet 4
Solution Sheet 4
Problem Sheet 5
Solution Sheet 5
Chapter 4 - Space Groups and Their Representations
Chapter 5 - Kronecker (Direct) Products
Chapter 6 - Applications of Direct Products
Problem Sheet 6
Solution Sheet 6

Oral Exam Information

Oral Exam Information
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