Cristina Bena (IPhT)

Thierry Jolicoeur (IPhT)

Topological materials have recently become one of the most studied subjects in solid state physics, in particular with the discovery of topological insulators and especially of Majorana fermions. Such states have been described as possible building blocks for quantum computers, hence the importance to study their properties and identify systems that can support them. Experimentally, many signatures are consistent with the formation of Majorana states, but there is still no definite proof of their existence.

In this series of lectures we will give a broad view of topological systems, including topological insulators, quantum Hall effect, and topological superconductors. We will discuss the properties of Majorana states and other topological edge states in both one-dimensional and two-dimensional systems, as well as the techniques to study the formation of these states and their properties.

The program of the lectures will include:

- Topology in solid state systems; Examples of topological materials and topological edge states (e.g. Majorana)
- Analytical and numerical techniques to derive the formation of edge states
- 2D electronic systems, Landau levels, integer and fractional quantum Hall effect
- The Laughlin wavefunction, more fractions composite fermions
- Multicomponent systems: spins and interlayer phase coherence, quantum Hall ferromagnetism
- The pfaffian state and its excitations