Lecturer: Dr Bartomeu Monserrat
This course introduces tight binding theory, a quantum mechanical model that describes the electronic band structure of crystalline solids by considering the interactions between localised orbitals. We will use various tight binding models of topological materials to illustrate the concepts. The course includes 12 lectures and two computing classes in which you will code your own tight binding model and is suitable for those with a physical sciences background.
Students should leave the course knowing:
- The basic theoretical framework known as second quantisation
- The basic theory behind tight binding theory
- How to code a tight binding model
- The key ideas underpinning topological materials
Lectures:
- Second quantisation
Identical quantum particles
Second quantisation formalism - Tight binding theory
Localised orbitals
Tight binding theory in real and reciprocal space
S-band in 1D - SSH model
2-band model
SSH model
Symmetry
Winding number
Edge-boundary correspondence - Berry phases
Berry phase
Berry curvature
Chern theorem - Graphene
2-band model
Low-energy physics
Symmetry - Haldane model
Inversion symmetry breaking
Time reversal symmetry breaking
Low-energy physics
Edge-boundary correspondence
Practicals:
- SSH model
Coding up a 1D tight binding model
Solving the 1D SSH model - Haldane model
Coding up a 2D tight binding model
Solving the 2D Haldane model
Prerequisities:
- Quantum mechanics
- Solid state physics
Recommended reading / References:
- David Vanderbilt, “Berry Phases in Electronic Structure”, Cambridge University Press