Topology is like geometry where I forget my glasses. I can see rough shapes, but no details, and can only distinguish shapes by their global properties – like whether they have a hole or not. We generally expect such properties to be robust against small local perturbations. This makes them interesting in a quantum mechanical context, as most quantum mechanical effects are famously fickle.
This project will investigate the robustness of topological properties under external perturbations, starting with disorder. The project will study how topological invariants disappear with realistic disorders, and for different types of topology.
The project is a collaboration between the department of physics and the centre for material science and quantum technology, and you will be co-supervised by experts in both.
Methods
The primary workhorse in this project will be density-functional theory (DFT), a standard method for computing material properties. You will use DFT to generate realistic disorder configurations for materials with varying topological properties, using the code doped. You will then study increasing order configuration, either in a simplified Wannierized model (obtained from DFT results) or at an approximate DFT level, by changing the supercell size.
This method requires good numerical skills, and an interest in material science. Additional interest in mathematics and topology is a plus, but is not necessary.
Milestones
- Identify realistic defect configurations in materials of interest.
- Compute their phase diagram and understand which are most stable under what circumstances
- Compute a Wannierized model and use local topological marker to compute their invariants
- Build periodic supercells of different sizes with defects and characterize their topology.
Courses relevant from the bachelor's degree:
Recommended courses for theoretical curriculum in the master's programme: