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New mechanisms and materials for odd-frequency superconductivity

Periodic Reporting for period 3 - ODDSUPER (New mechanisms and materials for odd-frequency superconductivity)

Reporting period: 2021-02-01 to 2022-07-31

Odd-frequency superconductivity is a very unique superconducting state that is odd in time or, equivalently, frequency, which is opposite to the ordinary behavior of superconductivity. It has been realized to be the absolute key to understand the surprising physics of superconductor-ferromagnet (SF) structures and has also enabled the whole emerging field of superconducting spintronics. This project will discover and explore entirely new mechanisms and materials for odd-frequency superconductivity, to both generate a much deeper understanding of superconductivity and open for entirely new functionalities. Importantly, it will generalize and apply my initial discoveries of two new odd-frequency mechanisms, present in bulk multiband superconductors and in hybrid structures between topological insulators and conventional superconductors, respectively. In both cases odd-frequency superconductivity is generated without any need for ferromagnets or interfaces, completely different from the situation in SF structures. The result will be a significant expansion of the concept and importance of odd-frequency superconductivity to a very wide class of materials, ranging from multiband, bilayer, and nanoscale superconductors to topological superconductors. The project will also establish the connection between topology and odd-frequency pairing, which needs to be addressed in order to understand topological superconductors, as well as incorporate new materials and functionality into traditional SF structures. To achieve these goals the project will develop a novel methodological framework for large-scale and fully quantum mechanical studies with atomic level resolution, solving self-consistently for the superconducting state and incorporating quantum transport calculations.
The project has already made significant progress in discovering and exploring new mechanisms and materials for odd-frequency superconductivity. This has resulted so far in 21 peer-reviewed publications, including two review article that have summarized the current status on odd-frequency superconductivity in multiband superconductors and in one-dimensional hybrid structures, respectively, both areas at the core of the ERC project. The original research works have centered around fundamental understanding on where and how odd-frequency pairing appears, such as in hybrid systems or from impurity scattering, as well as explored entirely new materials and systems where we have discovered substantial odd-frequency pairing. Below are a few examples of our main results.
We have found pure odd-frequency pairing in Josephson junctions of topological Weyl nodal loop semimetals, which generates huge Josephson effects, even orders of magnitude larger than in more traditional odd-frequency superconducting systems. These junctions we have quantified as optimal odd-frequency junctions.
We have found dominating odd-frequency pairing in the known superconductor Cu-doped Bi2Se3, a result that challenges the current understanding of this material. We have also discovered an unexpected diamagnetic Meissner effect from the odd-frequency pairing in this material, which means the odd-frequency pairing is remains stable in the presence of a magnetic field. This result we have also extended to general two-band superconductors and demonstrated that for topological (normal-state) band structure odd-frequency pairing gives generically rise to a diamagnetic Meissner signal.
We have extended the classification of odd-frequency superconductivity to spin-3/2 systems, where orbital and spin degrees of freedom are strongly linked. We applied these results to known half-Heusler superconductors, establishing the likely presence of odd-frequency pairing.
We have extended the multiband mechanism for odd-frequency pairing to also include superconductors with pair density waves and applied the results to the underdoped cuprate superconductors, showing that odd-frequency is ubiquitous also in this family of superconductors.
We have investigated the possibilities for odd-frequency superconducting pairing in driven systems, and their establishing the possibility of Floquet engineering of bulk odd-frequency pairs. In addition, we have discovered how odd-frequency pairing can be the only superconducting pairing present at non-Hermitian exceptional points. These two last projects were not envisaged in the grant proposal but naturally grew out of our results within the project and very nicely fits within the overall aim of the project.
Several of the results listed above clearly classify as progress beyond the state-of-the-art and also not envisaged in the grant proposal, such as finding optimal odd-frequency junctions, Floquet engineering and non-Hermitian effects. For the rest of the project (1 year) we expect more results on odd-frequency superconductivity primarily within several areas.
We are expecting more results on odd-frequency superconductivity utilizing the same mechanism as in the multiband superconductors, but where the concept of band is widely extended. We are also continuing to our study vibrational defects, and generally, phonons can influence the superconducting pairing symmetries, both in order to gain fundamental understanding and to find new probes for odd-frequency superconductivity. For the latter we are also exploring other possibilities, for example, we already have very promising results on how quasiparticle interference (QPI) can be used to probe an odd frequency dependence. We are also extending our research into time-dependent systems beyond periodically driven Floquet systems, as odd-frequency pairing as an intrinsic dynamic feature of a system and as such will likely give rise to signatures in time-dependent quantities. Finally, further studies of non-Hermitian systems are also planned.
Non-Hermitian odd-frequency pairing (Phys Rev B 105, 094502 (2022))
Optimal odd-frequency Josephson junction using a Weyl nodal loop semimetal (npj Quantum Mater. 5, 42