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The geometry of an inductor made of a long thin wire and having the highest possible Q-factor is found by numerical optimization. As frequency increases, the Q-factor first grows linearly and then according to a square-root law, while the cross-section of the optimal coil evolves from near-circular to sickle-shaped.

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.

Photonic crystals are commonly implemented in media with periodically varying optical properties. Photonic crystals enable exquisite control of light propagation in integrated optical circuits, and also emulate advanced physical concepts. However, common photonic crystals are unfit for in-operando on/off controls. We overcome this limitation and demonstrate a broadly tunable two-dimensional photonic crystal for surface plasmon polaritons. Our platform consists of a continuous graphene monolayer integrated in a back-gated platform with nano-structured gate insulators. Infrared nano-imaging reveals the formation of a photonic bandgap and strong modulation of the local plasmonic density of states that can be turned on/off or gradually tuned by the applied gate voltage. We also implement an artificial domain wall which supports highly confined one-dimensional plasmonic modes. Our electrostatically-tunable photonic crystals are derived from standard metal oxide semiconductor field effect transistor technology and pave a way for practical on-chip light manipulation., Traditional photonic crystals consist of periodic media with a pre-defined optical response. Here, the authors combine nanostructured back-gate insulators with a continuous layer of graphene to demonstrate an electrically tunable two-dimensional photonic crystal suitable for controlling the propagation of surface plasmon polaritons.

Non-equilibrium photoinduced plasmons in a high-mobility graphene monolayer are investigated at infrared wavelengths. The success of metal-based plasmonics for manipulating light at the nanoscale has been empowered by imaginative designs and advanced nano-fabrication. However, the fundamental optical and electronic properties of elemental metals, the prevailing plasmonic media, are difficult to alter using external stimuli. This limitation is particularly restrictive in applications that require modification of the plasmonic response at sub-picosecond timescales. This handicap has prompted the search for alternative plasmonic media1,2,3, with graphene emerging as one of the most capable candidates for infrared wavelengths. Here we visualize and elucidate the properties of non-equilibrium photo-induced plasmons in a high-mobility graphene monolayer4. We activate plasmons with femtosecond optical pulses in a specimen of graphene that otherwise lacks infrared plasmonic response at equilibrium. In combination with static nano-imaging results on plasmon propagation, our infrared pump–probe nano-spectroscopy investigation reveals new aspects of carrier relaxation in heterostructures based on high-purity graphene.

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.

Hexagonal boron nitride (h-BN) is a natural hyperbolic material, for which the dielectric constants are the same in the basal plane (epsilon^t = epsilon^x = epsilon^y) but have opposite signs (epsilon^t*epsilon^z < 0) from that in the normal plane (epsilon^z). Due to this property, finite-thickness slabs of h-BN act as multimode waveguides for 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. Remarkably, 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 structures can be classified as electromagnetic metamaterials since the resulting properties of these devices are not present in its constituent elements alone., 20 pages, 3 figures in Nature Nanotechnology 2015

Black phosphorous, a van der Waals layered semiconductor, is reported to reveal a plasmonic response that can be initiated by photoexcitation with femtosecond pulses.

All known superfluid and superconducting states of condensed matter are enabled by composite bosons (atoms, molecules, Cooper pairs) made of an even number of fermions. Temperatures where such macroscopic quantum phenomena occur are limited by the lesser of the binding energy and the degeneracy temperature of the bosons. High critical temperature cuprate superconductors set the present record of ~100 K. Here we propose a design for artificially structured materials to rival this record. The main elements of the structure are two monolayers of a transition metal dichalcogenide separated by an atomically thin spacer. Electrons and holes generated in the system would accumulate in the opposite monolayers and form bosonic bound states --- the indirect excitons. The resultant degenerate Bose gas of indirect excitons would exhibit macroscopic occupation of a quantum state and vanishing viscosity at high temperatures., Comment: 7 pages, 4 figures