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Plasmon polaritons are hybrid excitations of light and mobile electrons that can confine the energy of long-wavelength radiation at the nanoscale. Plasmon polaritons may enable many enigmatic quantum effects, including lasing 1 , topological protection2,3 and dipole-forbidden absorption 4 . A necessary condition for realizing such phenomena is a long plasmonic lifetime, which is notoriously difficult to achieve for highly confined modes 5 . Plasmon polaritons in graphene—hybrids of Dirac quasiparticles and infrared photons—provide a platform for exploring light–matter interaction at the nanoscale6,7. However, plasmonic dissipation in graphene is substantial 8 and its fundamental limits remain undetermined. Here we use nanometre-scale infrared imaging to investigate propagating plasmon polaritons in high-mobility encapsulated graphene at cryogenic temperatures. In this regime, the propagation of plasmon polaritons is primarily restricted by the dielectric losses of the encapsulated layers, with a minor contribution from electron–phonon interactions. At liquid-nitrogen temperatures, the intrinsic plasmonic propagation length can exceed 10 micrometres, or 50 plasmonic wavelengths, thus setting a record for highly confined and tunable polariton modes. Our nanoscale imaging results reveal the physics of plasmonic dissipation and will be instrumental in mitigating such losses in heterostructure engineering applications. The fundamental limits to plasmon damping in graphene are determined using nanoscale infrared imaging at cryogenic temperatures, and plasmon polaritons are observed to propagate over 10 micrometres in high-mobility encapsulated graphene.

We review recent discoveries of the intriguing plasmonic phenomena at a variety of electronic boundaries (EBs) in graphene including a line of charges in graphene induced by a carbon nanotube gate, grain boundaries in chemical vapor deposited graphene films, an interface between graphene and moire patterned graphene, an interface between graphene and bilayer graphene, and others. All these and other EBs cause plasmonic impedance mismatch at the two sides of the boundaries. Manifestations of this effect include plasmonic fringes that stem from plasmon reflections and interference. Quantitative analysis and modeling of these plasmonic fringes uncovered intriguing properties and underlying physics of the EBs. Potential plasmonic applications associated with these EBs are also briefly discussed.

Properties of atomic van der Waals heterostructures are profoundly influenced by interlayer coupling, which critically depends on stacking of the proximal layers. Rotational misalignment or lattice mismatch of the layers gives rise to a periodic modulation of the stacking, the moiré superlattice. Provided the superlattice period extends over many unit cells, the coupled layers undergo lattice relaxation, leading to the concentration of strain at line defects – solitons - separating large area commensurate domains. We visualize such long-range periodic superstructures in thin crystals of hexagonal boron nitride using atomic-force microscopy and nano-infrared spectroscopy. The solitons form sub-surface hexagonal networks with periods of a few hundred nanometers. We analyze the topography and infrared contrast of these networks to obtain spatial distribution of local strain and its effect on the infrared-active phonons of hBN., Solitons may develop when strain forms at line defects separating commensurate domains in misaligned or lattice-mismatched van der Waals heterostructures. Here, the authors use atomic-force microscopy and nano-infrared spectroscopy to image solitons in thin hBN crystals in the form of long-range periodic superstructures, creating sub-surface hexagonal networks with periods of a few hundred nanometers.

We present a comprehensive study of the reflection of normally incident plasmon waves from a low-conductivity 1D junction in a 2D conductive sheet. Rigorous analytical results are derived in the limits of wide and narrow junctions. Two types of phenomena determine the reflectance, the cavity resonances within the junction and the capacitive coupling between the leads. The resonances give rise to alternating strong and weak reflection but are vulnerable to plasmonic damping. The capacitive coupling, which is immune to damping, induces a near perfect plasmon reflection in junctions narrower than $1/10$ of the plasmon wavelength. Our results are important for infrared 2D plasmonic circuits utilizing slot antennas, split gates or nanowire gates. They are also relevant for the implementation of nanoscale terahertz detectors, where optimal light absorption coincides with the maximal junction reflectance.

Twisting a route for surface plasmons Graphene is an atomically thin material that supports highly confined plasmon polaritons, or nano-light, with very low loss. The properties of graphene can be made richer by introducing and then rotating a second layer so that there is a slight angle between the atomic registry. Sunku et al. show that the moiré patterns that result from such twisted bilayer graphene also provide confined conducting channels that can be used for the directed propagation of surface plasmons. Controlling the structure thereby provides a pathway to control and route surface plasmons for a nanophotonic platform. Science , this issue p. 1153

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local ac conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contain additional confined bands which produce a structure-specific contrast of the local conductivity. The calculated plasmonic interference profiles are in quantitative agreement with our experiments., Comment: 14 pages, 5 figures

We show that surface plasmons of a two-dimensional Dirac metal such as graphene can be reflected by line-like perturbations hosting one-dimensional electron states. The reflection originates from a strong enhancement of the local optical conductivity caused by optical transitions involving these bound states. We propose that the bound states can be systematically created, controlled, and liquidated by an ultranarrow electrostatic gate. Using infrared nanoimaging, we obtain experimental evidence for the locally enhanced conductivity of graphene induced by a carbon nanotube gate, which supports this theoretical concept., Comment: 14 pages, 12 figures, submitted to PRL

Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe, as well as the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials such as aluminum oxide (by itself or covered with graphene) reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with the radiative damping included perturbatively., Comment: 25 pages, 15 figures. Minor changes to improve presentation