1. PA4311 Quantum Theory of Solids Quantum Theory of Solids Mervyn Roy (S6) www2.le.ac.uk/departments/physics/people/mervynroy

2. PA4311 Quantum Theory of Solids 1.Introduction and background 2.The many-electron wavefunction - Introduction to quantum chemistry (Hartree, HF, and CI methods) 3.Introduction to density functional theory (DFT) - Framework (Hohenberg-Kohn, Kohn-Sham) - Periodic solids, plane waves and pseudopotentials 4.Linear combination of atomic orbitals 5.Effective mass theory 6.ABINIT computer workshop (LDA DFT for periodic solids) Assessment: 70% final exam 30% coursework – mini ‘project’ report for ABINIT calculation www.abinit.org Course Outline

3. PA4311 Quantum Theory of Solids Last time…

4. PA4311 Quantum Theory of Solids conduction band valence band (heavy holes) doubly degenerate band (no spin orbit coupling)

5. PA4311 Quantum Theory of Solids Solving the single-electron Schrödinger equation

6. PA4311 Quantum Theory of Solids The central equation Tanner, section 4.6 Martin, section 12.1

7. PA4311 Quantum Theory of Solids Solution of the central equation

8. PA4311 Quantum Theory of Solids Empty lattice

9. PA4311 Quantum Theory of Solids

10. Weak periodic potential - appearance of band gaps at the BZ boundaries

11. PA4311 Quantum Theory of Solids Full solution