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PYU44T10 Condensed Matter Theory 

Michaelmas Term – 24 lectures/tutorials – 5 credits (S Sanvito)

Learning Outcomes
On successful completion of this module, students should be able to:

  • Demonstrate knowledge of the foundations of solid state Physics in terms of non-interacting electrons
  • Give a quantum mechanical description of the chemical bond for homonuclear and heteronuclear molecules
  • Describe the determination of simple band structure using the tight-binding method
  • Perform analytic calculations to solve elementary condensed-matter-related problems (simple molecule spectrum, band-structure of s-like 1D and 2D materials and of graphene)
  • Formulate a model based on the concepts learnt to explain simple condensed matter phenomena (e.g. the Peierls distortion)
  • Understand the difference between an interacting and a non-interacting problem and formulate a mean-field theory

Introduction: What Hamiltonian? Born-Oppenheimer Approximation; Tight-binding method for molecules; From molecules to solid; Going from 1D to 2D and 3D; C-graphite and C-nanotubes; Interfaces: charge transfer and screening; A proper calculation: the Coulomb potential back; Density Functional Theory; Kohn-Sham equations; The interacting problem; the Hubbard model for two sites and variable number of electrons; The mean field approximation.