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

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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

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PA4311 Quantum Theory of Solids Last time…

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PA4311 Quantum Theory of Solids Periodic structures and plane waves 223 course notes Solid state text books – e.g. Tanner, Introduction to the Physics of Electrons in Solids, Cambridge University press Hook and Hall, Solid State Physics 2 nd Ed., John Wiley and Sons Ashcroft and Mermin, Solid State Physics, Holt-Saunders

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PA4311 Quantum Theory of Solids graphene unit cell Crystal = Bravais lattice + basis

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PA4311 Quantum Theory of Solids 2D crystal – many choices for unit cell Hexagonal lattice, 2 atom basis Wigner-Seitz (primitive) Primitive Primitive centred Non-primitive

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PA4311 Quantum Theory of Solids wikipedia.org 3D crystal: zinc blende structure (diamond, Si, GaAs etc) www.seas.upenn.edu

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PA4311 Quantum Theory of Solids

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Wigner-Seitz cell in reciprocal space = Brillouin zone

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PA4311 Quantum Theory of Solids FCC Reciprocal lattice = BCC recip Léon Brillouin (1889-1969): most convenient primitive cell in reciprocal space is the Wigner-Seitz cell - edges of BZ are Bragg planes. Brillouin Zone

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PA4311 Quantum Theory of Solids Question 3.1

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

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PA4311 Quantum Theory of Solids Fourier representation of a periodic function

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PA4311 Quantum Theory of Solids Bloch theorem plane wave part

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PA4311 Quantum Theory of Solids Question 3.2

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