Non-Hermitian topology for novel superconducting states

In quantum mechanics, the conservation of energy is a basic postulate that permits to understand isolated systems in terms of real energies.

However, physical systems are usually coupled to their environment, where exchange of energy causes dissipation and leads to complex energies.

These open systems are described by non-Hermitian Hamiltonians and, very recently, it has been shown that their symmetry classification is broadened due to dissipation, giving rise to topological states with no analog in Hermitian setups.

Most of the research, however, has mainly focused on normal state systems, leaving largely unexplored superconductors, where their intrinsic particle-hole symmetry makes them even more promising for novel non-hermitian states.

The aim of this project is to theoretically  explore, discover, and characterize entirely new superconducting states by novel combinations of  superconducting order and non-Hermitian  topology.

To achieve these goals, the project is organised into four inter-related subprojects where I will employ my previous PhD and postdoc experience to develop modern  analytical and numerical methods for superconductivity, non-Hermitian topology, and symmetry classification.

This will provide fundamental understanding of the emergent superconductivity and will allow the design of detection schemes for potential applications. Thus, by linking the realms of superconductivity and non-Hermitian physics, this project opens a new field of research.