# Non-Hermitian topology for novel superconducting states

## Details

- Period: 2022-01-01 – 2025-12-31
- Funder: Swedish Research Council
- Type of funding: Starting Grant

## Beskrivning

Project title: Non-Hermitian topology for novel superconducting states

Main applicant: Jorge Luis Cayao Diaz, Division of Materials Theory

Grant amount: 4 000 000 SEK for the period 2022-2025

ABSTRACT: 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.

POPULAR ABSTRACT: Since its discovery, superconductivity has garnered widespread attention not only owing to its fundamental mechanisms but also due to its large number of applications for the emergent quantum technologies, making it one of the core areas in physics. This occurs because superconductivity is a unique manifestation of quantum mechanics on a truly macroscopic scale, which have already found unique applications in our daily life. The unusual properties of superconductors depend on their building blocks, the Cooper pairs, which are pairs of electrons that bound together below a critical temperature. Thus, the nature of a superconducting state depends on the type of Cooper pairs it hosts, where their understanding and control determine potential applications.

A very promising route for creating superconducting states with highly controllable properties and useful for applications involves the combination of conventional superconductors with non-superconducting materials. This is because non-superconducting materials modify the intrinsic Cooper pairs, giving rise to far more exotic Cooper pairs that then permit the creation of novel superconducting states.

Most of the research, on how to create new Cooper pairs, has been done in isolated systems, which, recently, has led to the prediction of topological superconductivity, a new type of superconductor that can be used for quantum computation free of decoherence. Because these predictions focus on isolated systems, the experimental realisation, which includes physical real systems necessarily coupled to their environment, does not agree with theory and is still a challenging task. The fact that physical systems are usually coupled to their environment makes them to behave as open systems, where energy is exchanged and gives rise to dissipation. Unlike isolated systems, which are described by Hermitian models that lead to real energies, open systems are instead described by non-Hermitian models that lead to complex energies. Very recently, it has been shown that dissipation in non-superconducting non-Hermitian systems enables the emergence of topological states with no analogue in Hermitian setups. Several properties have been exploited in these systems and found interesting application possibilities such as in high performance lasers, sensors, and topological dissipative devices. Despite the tremendous progress, however, most of the studies have focused on non-superconducting systems, leaving largely unexplored the field of non-Hermitian superconductivity. The intrinsic superconducting properties make superconductors far more promising than normal state materials, with prominent applications for real physical devices. The aim of this project is to theoretically explore, discover, and characterize entirely new superconducting states by novel combinations of conventional superconductivity and non-Hermitian effects. To achieve these goals, the project is organised into four inter-related subprojects where I will employ my previous experience to develop modern analytical and numerical methods to investigate the interplay of superconductivity and non-Hermitian physics. This will provide fundamental understanding of the emergent non-Hermitian 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.

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