### Unconventional Superconductivity

**Lecturer**: Laura Classen

**Teaching Assistants**: Nikolaos Parthenios, Hannes Braun

**Lectures**: Thursday 14:00 - 16:00, Room PH 3344

**Tutorials**: Thursday 12:00- 14:00, Room PH 1121

The interaction between electrons in correlated quantum materials can give rise to new collective phases that cannot be understood based on single-particle properties. Superconductivity is one of the most fascinating examples. At its heart is the question about the glue that overcomes Coulomb repulsion and binds electrons into the pairs that form the superconducting condensate. In conventional superconductors, Bardeen-Cooper-Schrieffer (BCS) theory provides the answer in terms of electron-phonon interaction. However, many strongly-correlated quantum materials show evidence for an unconventional pairing mechanism that does not involve phonons. Examples include cuprates, iron-based superconductors or graphene heterostructures.

In this course, an introduction to the theoretical description of superconductivity from repulsive Coulomb interactions is given. It is shown how the renormalisation of the effective interaction can induce a pairing instability and yield a superconducting state with new symmetry or topology. The phenomenological treatment of an unconventional pairing state is introduced and examples for potential electronic pairing mechanisms in correlated quantum materials are discussed.

The following topics are covered:

- Cooper instability
- Generalised BCS mean-field theory
- Kohn-Luttinger mechanism
- Superconductivity in 2D quantum materials
- Landau free energy
- Topological superconductivity

**Literature**

- S. Maiti and A. Chubukov, lecture notes on "Superconductivity from repulsive interaction", AIP Conference Proceedings 1550,, 3 (2013), https://arxiv.org/abs/1305.4609
- M. Sigrist, lecture notes on "Introduction to unconventional superconductivity", AIP Conference Proceedings 789, 165 (2005), http://edu.itp.phys.ethz.ch/2007b/ws0506/us/summer_school.pdf
- M. Sigrist and K. Uedao, "Phenomenological theory of unconventional superconductivity", Rev. Mod. Phys. 63, 239 (1991)