Space group properties

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Presentation transcript:

Space group properties PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 20: Space group properties Chapter 10 in DDJ Non-symmorphic space groups Example -- diamond 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

2/27/2017 PHY 745 Spring 2017 -- Lecture 20

Non-lattice translation Space group Non-lattice translation Lattice translation Point operation 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

Effects of group operations on Bloch basis functions (symmorphic case) 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

Non-symmorphic space group Example -- diamond https://en.wikipedia.org/wiki/Diamond_cubic 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

Space group symmetry of diamond Maps to Oh point symmetry 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

From BSW paper Phys. Rev. 50, 58 (1936) 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

Effects of group operations on Bloch basis functions (general case) 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

From BSW paper Phys. Rev. 50, 58 (1936) 2/27/2017 PHY 745 Spring 2017 -- Lecture 20

PRL 16, 354 (1966) 2/27/2017 PHY 745 Spring 2017 -- Lecture 20