Masters defense: Georgios Georgogiannis

Title: Field Theoretical Modeling of Parafermion Devices for Quantum Transport.


Since the realization of zero-energy modes localized at the ends of a 1D topological p-wave superconductor, these zero-modes (Majorana modes) have been vigorously pursued, and many heterostructures to engineer them have been proposed. These theoretical proposals have motivated the development of hybrid systems which include topological insulators, spin-orbit coupled semiconductors, and integer quantum Hall edges all in combination with a superconductor. But Majorana modes are not the only exotic particles that can appear with topological properties at such heterostructures. As preliminary works have predicted, Fractional Quantum Hall/superconductor hybrids devices can host parafermions. Parafermions, unlike Majoranas, require electron-electron interactions to form, which result in richer non-Abelian braiding statistics. 

This thesis aims to construct a field theoretical model based on Bosonization and other analytical techniques to describe such Fractional Quantum Hall/superconductor hybrid devices. In particular, it aims to model the Crossed Andreev pairing between counter-propagating quantum Hall edge modes induced by the proximity with a superconductor with strong spin-orbit coupling (NbN), motivated by recent (by the time of writing) experimental results [Phys. Rev. X 12, 021057 (2022)].

First, it is studied the Integer Quantum Hall (non-Interacting) case by means of Perturbation Theory and the Feynman Path Integral where an estimation of the induced gap is given and next, by bosonizing the system it is studied the Interacting FQH system, and an estimation of the induced gap using the Renormalization Group analysis is provided.