Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons.

We report a nanoinfrared (IR) imaging study of the localized plasmon resonance modes of graphene nanoribbons (GNRs) using a scattering-type scanning near-field optical microscope (s-SNOM). By comparing the imaging data of GNRs that are aligned parallel and perpendicular to the in-plane component of the excitation laser field, we observed symmetric and asymmetric plasmonic interference fringes, respectively. Theoretical analysis indicates that the asymmetric fringes are formed due to the interplay between the localized surface plasmon resonance (SPR) mode excited by the GNRs and the propagative surface plasmon polariton (SPP) mode launched by the s-SNOM tip. With rigorous simulations, we reproduce the observed fringe patterns and address quantitatively the role of the s-SNOM tip on both the SPR and SPP modes. Furthermore, we have seen real-space signatures of both the dipole and higher-order SPR modes by varying the ribbon width.

Plasmons in graphene moiré superlattices.

Moiré patterns are periodic superlattice structures that appear when two crystals with a minor lattice mismatch are superimposed. A prominent recent example is that of monolayer graphene placed on a crystal of hexagonal boron nitride. As a result of the moiré pattern superlattice created by this stacking, the electronic band structure of graphene is radically altered, acquiring satellite sub-Dirac cones at the superlattice zone boundaries. To probe the dynamical response of the moiré graphene, we use infrared (IR) nano-imaging to explore propagation of surface plasmons, collective oscillations of electrons coupled to IR light. We show that interband transitions associated with the superlattice mini-bands in concert with free electrons in the Dirac bands produce two additive contributions to composite IR plasmons in graphene moiré superstructures. This novel form of collective modes is likely to be generic to other forms of moiré-forming superlattices, including van der Waals heterostructures.

Edge and Surface Plasmons in Graphene Nanoribbons.

We report on nano-infrared (IR) imaging studies of confined plasmon modes inside patterned graphene nanoribbons (GNRs) fabricated with high-quality chemical-vapor-deposited (CVD) graphene on Al2O3 substrates. The confined geometry of these ribbons leads to distinct mode patterns and strong field enhancement, both of which evolve systematically with the ribbon width. In addition, spectroscopic nanoimaging in the mid-infrared range 850-1450 cm(-1) allowed us to evaluate the effect of the substrate phonons on the plasmon damping. Furthermore, we observed edge plasmons: peculiar one-dimensional modes propagating strictly along the edges of our patterned graphene nanostructures.

Tunneling Plasmonics in Bilayer Graphene.

We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At subnanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nanoimaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tunneling. Moreover, we were able to shut off plasmons in bilayer graphene through gating within a wide voltage range. Theoretical modeling indicates that such a plasmon-off region is directly linked to a gapped insulating state of bilayer graphene, yet another implication of interlayer tunneling. Our work uncovers essential plasmonic properties in bilayer graphene and suggests a possibility to achieve novel plasmonic functionalities in graphene few-layers.

Sum-rule constraints on the surface state conductance of topological insulators.

We report the Drude oscillator strength D and the magnitude of the bulk band gap E_{g} of the epitaxially grown, topological insulator (Bi,Sb)_{2}Te_{3}. The magnitude of E_{g}, in conjunction with the model independent f-sum rule, allows us to establish an upper bound for the magnitude of D expected in a typical Dirac-like system composed of linear bands. The experimentally observed D is found to be at or below this theoretical upper bound, demonstrating the effectiveness of alloying in eliminating bulk charge carriers. Moreover, direct comparison of the measured D to magnetoresistance measurements of the same sample supports assignment of the observed low-energy conduction to topological surface states.

Soliton superlattices in twisted hexagonal boron nitride.

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.

Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial.

Hexagonal boron nitride (h-BN) is a natural hyperbolic material, in which the dielectric constants are the same in the basal plane (ε(t) ≡ ε(x) = ε(y)) but have opposite signs (ε(t)ε(z) < 0) in the normal plane (ε(z)). Owing to this property, finite-thickness slabs of h-BN act as multimode waveguides for the propagation of hyperbolic phonon polaritons--collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Here we show, by direct nano-infrared imaging, that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon polaritons. The hyperbolic plasmon-phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon-phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamaterial as the resulting properties of these devices are not present in its constituent elements alone.