Symmetry-protected nodal phases in non-Hermitian systems

Non-Hermitian (NH) Hamiltonians have become an important asset for the effective description of various physical systems that are subject to dissipation. Motivated by recent experimental progress on realizing the NH counterparts of gapless phases such as Weyl semimetals, here we investigate how NH symmetries affect the occurrence of exceptional points (EPs), that generalize the notion of nodal points in the spectrum beyond the Hermitian realm. Remarkably, we find that the dimension of the manifold of EPs is generically increased by one as compared to the case without symmetry. This leads to nodal surfaces formed by EPs that are stable as long as a protecting symmetry is preserved, and that are connected by open Fermi volumes. We illustrate our findings with analytically solvable two-band lattice models in one and two spatial dimensions, and show how they are readily generalized to generic NH crystalline systems.Comment: Editors' Suggestio

Exceptional Topology of Non-Hermitian Systems

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits,s and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.Comment: 35 pages, 7 figure

Braid Protected Topological Band Structures with Unpaired Exceptional Points

We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e. the necessity of compensating the topological charge of a stable nodal point by an anti-dote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how noncommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions.Comment: 5+7 pages, 3+3 figure

Braid-protected topological band structures with unpaired exceptional points

We demonstrate the existence of topologically stable unpaired exceptional points (EPs), and construct simple non-Hermitian (NH) tight-binding models exemplifying such remarkable nodal phases. While fermion doubling, i.e., the necessity of compensating the topological charge of a stable nodal point by an antidote, rules out a direct counterpart of our findings in the realm of Hermitian semimetals, here we derive how nonommuting braids of complex energy levels may stabilize unpaired EPs. Drawing on this insight, we reveal the occurrence of a single, unpaired EP, manifested as a non-Abelian monopole in the Brillouin zone of a minimal three-band model. This third-order degeneracy represents a sweet spot within a larger topological phase that cannot be fully gapped by any local perturbation. Instead, it may only split into simpler (second-order) degeneracies that can only gap out by pairwise annihilation after having moved around inequivalent large circles of the Brillouin zone. Our results imply the incompleteness of a topological classification based on winding numbers, due to non-Abelian representations of the braid group intertwining three or more complex energy levels, and provide insights into the topological robustness of non-Hermitian systems and their non-Abelian phase transitions

2nd Project on Damage Stability for RoRo Passenger ships

Ro-ro passenger ship services constitute an important part of the European maritime infrastructure, and indeed play a crucial role for Sweden in connecting seaborne transport routes to and from our neighbouring countries. Moreover, northern European countries have been leading the development of, not only the ro-ro passenger ship concept as such, but also the development of relevant safety standards for this fleet. Understandably, it is therefore crucial for the Swedish maritime sector to take part of the legislative process that covers a significant share of the Swedish maritime infrastructure.Thus, in light of the IMO deliberations on the revisions of Chapter II-1 of the SOLAS Convention in general and proposals for an increased safety standard for passenger ships in particular, a first Triple-Helix project, partly funded by the Swedish Maritime Administration, was mobilized by the Swedish Shipowners’ Association, focusing on ro-ro passenger ship safety from a holistic perspective. The conclusions and findings of this Project can be found in the Report "Damage Stability Project for RoRo Passenger Ships – Final Report" [1.]. As the draft proposals for enhanced safety standards for passenger ships materialised into firm amendments to SOLAS Chapter II-1, which have now been adopted by the Marine Safety Committee of the International Maritime Organization during its 98th session, an extension of the Damage Stability Project was granted additional funding in the beginning of 2017 and consequently the 2nd Project on Damage Stability for Ro-Ro Passenger Ships (2nd RoPax DamStab Project) was mobilised. The aim of the 2nd RoPax DamStab Project has been to review and evaluate existing as well as future ro-ro passenger ship safety regulations from a theoretical perspective, with the objectives to: 1. provide in-depth knowledge about and facilitate the understanding of existing as well as future damage stability standards,2. facilitate understanding of ship type specific characteristics from a safety standard aspect, and3. assess the consequences for the ro-ro passenger ship fleet.This report outlines the work and findings of the 2nd RoPax DamStab Project as performed during the year of 2017