We study a one-dimensional plasmonic system with nontrivial topology: a chain of metallic nanoparticles with alternating spacing, which in the limit of small particles is the plasmonic analogue to the Su-Schrieffer-Heeger model. Unlike prior studies we take into account long-range hopping with retardation and radiative damping, which is necessary for the scales commonly used in plasmonics experiments. This leads to a non-Hermitian Hamiltonian with frequency dependence that is notably not a perturbation of the quasistatic model. We show that the resulting band structures are significantly different, but that topological features such as quantized Zak phase and protected edge modes persist because the system has the same eigenmodes as a chirally symmetric system. We discover the existence of retardation-induced topological phase transitions, which are not predicted in the SSH model. We find parameters that lead to protected edge modes and confirm that they are highly robust under disorder, opening up the possibility of protected hotspots at topological interfaces that could have novel applications in nanophotonics. KEYWORDS: plasmonics, surface plasmons, topological insulator, edge states, hotspots, disorder, nanoparticle array P lasmonic systems take advantage of subwavelength field confinement and the resulting enhancement to create hotspots, with applications in medical diagnostics, sensing and metamaterials.1,2 Arrays of metallic nanoparticles support surface plasmons that delocalize over the structure and whose properties can be manipulated by tuning the dimensions of the particles and their spacing.3−6 In particular, 1D and 2D arrays have significant uses in band-edge lasing 7,8 and can be made to strongly interact with emitters.9,10 Configurations of nanoparticle dimers have been shown to exhibit interesting physical properties;11 in the following we consider a nanoparticle dimer array in the context of topological photonics.The rise of topological insulators, materials with an insulating bulk and conducting surface states that are protected from disorder, has inspired the study of analogous photonic and plasmonic systems.12−23 Topological photonics shows exciting potential for unidirectional plasmonic waveguides, 24 lasing, 25 and field enhancing hotspots with robust topological protection, which could prove useful for nanoparticle arrays on flexible substrates. 26 Plasmonic and photonic systems provide a powerful platform to examine topological insulators without the complication of interacting particles and with interesting additional properties like non-Hermiticity.27−32 The lack of Fermi level simplifies the excitation of states, and the tunability made available by the larger scale allows for the study of disorder and defects in greater depth than electronic systems.33−35 They also simplify the study of topology in finite systems. 36One of the simplest topologically nontrivial models is that of Su, Schrieffer, and Heeger (SSH), 37,38 which features a chain of atoms with staggered hoppin...

Topological photonic systems, with their ability to host states protected against disorder and perturbation, allow us to do with photons what topological insulators do with electrons. Topological photonics can refer to electronic systems coupled with light or purely photonic setups. By shrinking these systems to the nanoscale, we can harness the enhanced sensitivity observed in nanoscale structures and combine this with the protection of the topological photonic states, allowing us to design photonic local density of states and to push towards one of the ultimate goals of modern science: the precise control of photons at the nanoscale. This is paramount for both nano-technological applications and also for fundamental research in light matter problems. For purely photonic systems, we work with bosonic rather than fermionic states, so the implementation of topology in these systems requires new paradigms. Trying to face these challenges has helped in the creation of the exciting new field of topological nanophotonics, with far-reaching applications. In this prospective article we review milestones in topological photonics and discuss how they can be built upon at the nanoscale. I. OVERVIEWOne of the ultimate goals of modern science is the precise control of photons at the nanoscale. Topological nanophotonics offers a promising path towards this aim.A key feature of topological condensed matter systems is the presence of topologically protected surface states immune to disorder and impurities. These unusual properties can be transferred to nanophotonic systems, allowing us to combine the high sensitivity of nanoscale systems with the robustness of topological states. We expect that this new field of topological nanophotonics will lead to a plethora of new applications and increased physical insight.In this perspective, as presented schematically in FIG. 1, we begin (section II) by exploring topology in electronic systems. We aim this section towards readers who are new to the topic, so begin at an introductory level where no prior knowledge of topology is assumed.In section III we introduce light, first by discussing how topological electronic systems can interact with light (section III A), then move onto the topic of topological photonic analogues (section III B), in which purely photonic platforms are used to mimic the physics of topological condensed matter systems.In section IV we discuss various paths via which topological photonics can be steered into the nanoscale. Excellent and extensive reviews already exist on topological photonics [1][2][3][4], and many platforms showcasing unique strengths and limitations are currently being studied in the drive towards new applications in topological photonics such as cold atoms [5], liquid helium [6], polaritons [7], acoustic [8] and mechanical systems [9] but in this work * marie.rider16@imperial.ac.uk † www.GianniniLab.com FIG. 1. Schematic overview Schematic showing the topics covered in this perspective.we restrict ourselves to nanostructures. We discuss the effo...

The existence of topologically protected edge modes is often cited as a highly desirable trait of topological insulators. However, these edge states are not always present. A realistic physical treatment of long range hopping in a one-dimensional dipolar system can break the symmetry that protects the edge modes without affecting the bulk topological number, leading to a breakdown in bulk-edge correspondence. It is important to find a better understanding of where and how this occurs, as well as how to measure it. Here we examine the behaviour of the bulk and edge modes in a dimerised chain of metallic nanoparticles and in a simpler non-Hermitian next-nearest-neighbour model to provide some insight into the phenomena of bulk-edge breakdown. We construct bulk-edge correspondence phase diagrams for the simpler case and use these ideas to devise a measure of symmetry-breaking for the plasmonic system based on its bulk properties. This provides a parameter regime for which bulk-edge correspondence is preserved in the topological plasmonic chain, as well as a framework for assessing this phenomenon in other systems. arXiv:1902.00467v2 [cond-mat.mes-hall]

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Herein we demonstrate the dramatic effect of non-locality on the plasmons which contribute to the Casimir forces, with a graphene sandwich as a case study. The simplicity of this system allowed us to trace each contribution independently, as we observed that interband processes, although dominating the forces at short separations, are poorly accounted for in the framework of the Dirac cone approximation alone, and should be supplemented with other descriptions for energies higher than 2.5 eV. Finally, we proved that distances smaller than 200 nm, despite being extremely relevant to state-of-the-art measurements and nanotechnology applications, are inaccessible with closed-form response function calculations at present.