PC5203, Advanced Solid State Physics, Aug 2021

Lecturer: Prof. Wang Jian-Sheng

Schedule: Monday 8:00-10:00am/Thursday 2:00-4:00pm on LumiNUS/zoom

Final exam: Tue 23 Nov 2021, 1:00-3:00pm, closed book, face-to-face, venue S12-04-02.

Reference Book: "Solid State Physics," Ashcroft/Mermin; "Many-Body Quantum Theory in Condensed Matter Phsyics, an introduction," H. Bruus and K. Flensberg, (Oxford Univ Press, 2004).

Offical Syllabus: This module aims to give graduate students additional training in the foundations of solid state physics and is intended to prepare them for research work and other graduate coursework modules. Topics to be covered include: translational symmetry and Bloch's theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock equations, APW, OPW, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors, insulators and metals, origin of ferromagnetism, models of Heisenberg, Stoner and Hubbard, Kondo effect. Students are expected to read from a range of recommended and reference texts, and will be given an opportunity to present their reading as part of the regular lessons.

Course Outline:

Week 1: 12 Aug, introduction

Week 2: 16,19 Aug, crystal symmetry, point and space groups, Bloch's theorem. Home work 1

Week 3: 23,26 Aug, lattice vibrations, ladder operators, phonon dispersion.

Week 4: 30 Aug, 2 Sep, second quantization, electrons, graphene tight-binding model, band structures. Home work 2

Week 5: 6,9 Sep, electron-electron interaction, electron-phonon interaction, Hartree-Fock method (reading notes on NEGF-fermionic)

Week 6: 13,16 Sep, many-body theory, Dyson expansion, Green's functions.

recess week, no classes

Week 7: 27,30 Sep, Hedin equations, GW method, midterm test on Thursday (Hedin-equations notes). Home work 3

Week 8: 4,7 Oct, electron-phonon interaction and SSH model, Peierls instability (SSH model topology).

Week 9: 11,14 Oct, electron transport, Landauer approach, thermoelectric effect.

Week 10: 18,21 Oct, electron transport, Boltzmann (and Kubo) approach (Boltzmann equation notes).

Week 11: 25,28 Oct, Berry phases in SSH model. Home work 4

Week 12: 1 Nov, Haldane model, linear response, integer quantum Hall effect, Chern number.

Week 13: 8,11 Nov, superconductivity, BCS theory (spinless superconductor).

Past semester final exam.

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