Non-Hermitian Hamiltonians provide a minimal description of dissipative systems. Non-Hermiticity leads to a wealth of novel phenomena such as the appearance of exceptional points or lines. Importantly, these new features have been harnessed in both quantum and classical experiments, including topological lasers or unidirectional invisibility.
In this talk, I will discuss some of the topological aspects of non-Hermitian systems. Due to generally present non-orthogonality of the orbitals in non-Hermitian Hamiltonians, the stability of topological edge modes to perturbations becomes unclear and requires a reinterpretation of the (Hermitian) bulk-boundary correspondence. In addition, a new set of topological invariants can be defined and directly linked to the non-Hermitian skin effect --- the exponential localization of all single-particle orbitals at one edge. Finally, I will show that shifting from the single-particle picture to the many-body physics in non-Hermitian models is not straightforward, even in the absence of interactions. The interplay between the Pauli exclusion principle and the skin effect leads us to conjecture a novel, fundamentally many-body, bulk-boundary principle.

Single-walled carbon nanotubes (SWCNTs) exhibit unique, remarkably diverse electronic and optical properties that depend critically on their exact chiral structure and are extremely sensitive to the local environment of the SWCNT, thereby making optical spectroscopy one of the most valuable methods to identify the different chiral species in a particular sample and at the same time probe their interactions with the local environment. In this presentation, I will provide an overview of how optical spectroscopy can be used to characterize the filling of SWCNTs [1-5], to investigate the interaction between encapsulated molecules and SWCNTs (e.g. energy transfer) [6] and to reveal new quasi-phase transitions within a single file of encapsulated water molecules.[7] I will also show an example of the versatility of the filling of SWCNTs with various solvents.[8] Moreover, examples of wavelength-dependent Raman characterizations of graphene nanoribbons and linear carbon chains grown inside the SWCNTs from precursor molecules will also be given.[9] The presentation will end with a discussion of the first results from a newly developed IR hyperspectral imaging setup, able to probe the chirality-specific interaction of chiral surfactants with SWCNT enantiomers.[10]


References:
[1] W. Wenseleers et al, Adv. Mater. 19, 2274 (2007)
[2] S. Cambré et al, Phys. Rev. Lett. 104, 207401 (2010)
[3] S. Cambré et al,, Angew. Chem. 50, 2764 (2011)
[4] S. Cambré et al, ACS Nano 6, 2649 (2012)
[5] S. Cambré et al, Nature Nanotechnol. 10, 248 (2015)
[6] S. van Bezouw et al, ACS Nano 12, 6881 (2018)
[7] X. Ma et al, Phys. Rev. Lett. 118, 027402 (2017)
[8] J. Campo et al, ACS nano 15, 113 (2021)
[9] H. Kuzmany et al, Carbon 171, 221 (2021) and M. Martinati et al, submitted
[10] M. Erkens et al, in preparation