Symmetry of lattice vibrations

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Presentation transcript:

Symmetry of lattice vibrations PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 22: Symmetry of lattice vibrations Chapter 11 in DDJ Lattice vibrations of LiF & elephants Lattice vibrations of diamond structured materials Some materials for this lecture were taken from an electronic version of DDJ. 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Enjoy your spring break Comments: Enjoy your spring break Please use part of the week of March 13 to prepare your presentations for the end of April. 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Example for LiF 6 branches 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Lattice vibrations in polar crystals couple to electromagnetic fields, adding “non analytic” term to the dynamical matrix: 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Resulting polarization density Brief digression concerning LO-TO phonon modes based on Grosso and Parravicini text q Resulting polarization density 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Coupling to an electric field Maxwell’s equations Longitudinal mode 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Longitudinal case continued 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Transverse modes 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

After several steps we get two modes Transverse modes After several steps we get two modes 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Ge (diamond structure) 6 branches 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Notation for Oh symmetry BSW Molecular G1 A1g G2 A2g G12 Eg G15’ T1g G25’ T2g G1’ A1u G2’ A2u G12’ Eu G15 T1u G25 T2u 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Symmetry of k=0 phonons in diamond structure Analysis of phonons for k>0 in diamond structure from Bouckaert, Smoluchowski, and WIgner: 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Ge (diamond structure) 6 branches 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

Phys. Rev. 158, 805-808 (1967) 3/03/2017 PHY 745 Spring 2017 -- Lecture 22

3/03/2017 PHY 745 Spring 2017 -- Lecture 22