Fizeau drag in graphene plasmonics.

Dragging of light by moving media was predicted by Fresnel1 and verified by Fizeau's celebrated experiments2 with flowing water. This momentous discovery is among the experimental cornerstones of Einstein's special relativity theory and is well understood3,4 in the context of relativistic kinematics. By contrast, experiments on dragging photons by an electron flow in solids are riddled with inconsistencies and have so far eluded agreement with the theory5-7. Here we report on the electron flow dragging surface plasmon polaritons8,9 (SPPs): hybrid quasiparticles of infrared photons and electrons in graphene. The drag is visualized directly through infrared nano-imaging of propagating plasmonic waves in the presence of a high-density current. The polaritons in graphene shorten their wavelength when propagating against the drifting carriers. Unlike the Fizeau effect for light, the SPP drag by electrical currents defies explanation by simple kinematics and is linked to the nonlinear electrodynamics of Dirac electrons in graphene. The observed plasmonic Fizeau drag enables breaking of time-reversal symmetry and reciprocity10 at infrared frequencies without resorting to magnetic fields11,12 or chiral optical pumping13,14. The Fizeau drag also provides a tool with which to study interactions and nonequilibrium effects in electron liquids.

Unexpected catalytic activity of nanorippled graphene.

Graphite is one of the most chemically inert materials. Its elementary constituent, monolayer graphene, is generally expected to inherit most of the parent material's properties including chemical inertness. Here, we show that, unlike graphite, defect-free monolayer graphene exhibits a strong activity with respect to splitting molecular hydrogen, which is comparable to that of metallic and other known catalysts for this reaction. We attribute the unexpected catalytic activity to surface corrugations (nanoscale ripples), a conclusion supported by theory. Nanoripples are likely to play a role in other chemical reactions involving graphene and, because nanorippling is inherent to atomically thin crystals, can be important for two-dimensional (2D) materials in general.

Isotopic Control of the Boron-Vacancy Spin Defect in Hexagonal Boron Nitride.

We report on electron spin resonance (ESR) spectroscopy of boron-vacancy (V_{B}^{-}) centers hosted in isotopically engineered hexagonal boron nitride (hBN) crystals. We first show that isotopic purification of hBN with ^{15}N yields a simplified and well-resolved hyperfine structure of V_{B}^{-} centers, while purification with ^{10}B leads to narrower ESR linewidths. These results establish isotopically purified h^{10}B^{15}N crystals as the optimal host material for future use of V_{B}^{-} spin defects in quantum technologies. Capitalizing on these findings, we then demonstrate optically induced polarization of ^{15}N nuclei in h^{10}B^{15}N, whose mechanism relies on electron-nuclear spin mixing in the V_{B}^{-} ground state. This work opens up new prospects for future developments of spin-based quantum sensors and simulators on a two-dimensional material platform.

Optically Active Spin Defects in Few-Layer Thick Hexagonal Boron Nitride.

Optically active spin defects in hexagonal boron nitride (hBN) are promising quantum systems for the design of two-dimensional quantum sensing units offering optimal proximity to the sample being probed. In this Letter, we first demonstrate that the electron spin resonance frequencies of boron vacancy centers (V_{B}^{-}) can be detected optically in the limit of few-atomic-layer thick hBN flakes despite the nanoscale proximity of the crystal surface that often leads to a degradation of the stability of solid-state spin defects. We then analyze the variations of the electronic spin properties of V_{B}^{-} centers with the hBN thickness with a focus on (i) the zero-field splitting parameters, (ii) the optically induced spin polarization rate and (iii) the longitudinal spin relaxation time. This Letter provides important insights into the properties of V_{B}^{-} centers embedded in ultrathin hBN flakes, which are valuable for future developments of foil-based quantum sensing technologies.

Flat Bands and Giant Light-Matter Interaction in Hexagonal Boron Nitride.

Dispersionless energy bands in k space are a peculiar property gathering increasing attention for the emergence of novel electronic, magnetic, and photonic properties. Here, we explore the impact of electronic flat bands on the light-matter interaction. The van der Waals interaction between the atomic layers of hexagonal boron nitride induces flat bands along specific lines of the Brillouin zone. The macroscopic degeneracy along these lines leads to van Hove singularities with divergent joint density of states, resulting in outstanding optical properties of the excitonic states. For the direct exciton, we report a giant oscillator strength with a longitudinal-transverse splitting of 420 meV, a record value, confirmed by our ab initio calculations. For the fundamental indirect exciton, flat bands result in phonon-assisted processes of exceptional efficiency, that compete with direct absorption in reflectivity, and that make the internal quantum efficiency close to values typical of direct band gap semiconductors.

Author Correction: Ultralow-loss polaritons in isotopically pure boron nitride.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Isotope engineering of van der Waals interactions in hexagonal boron nitride.

Hexagonal boron nitride is a model lamellar compound where weak, non-local van der Waals interactions ensure the vertical stacking of two-dimensional honeycomb lattices made of strongly bound boron and nitrogen atoms. We study the isotope engineering of lamellar compounds by synthesizing hexagonal boron nitride crystals with nearly pure boron isotopes (10B and 11B) compared to those with the natural distribution of boron (20 at% 10B and 80 at% 11B). On the one hand, as with standard semiconductors, both the phonon energy and electronic bandgap varied with the boron isotope mass, the latter due to the quantum effect of zero-point renormalization. On the other hand, temperature-dependent experiments focusing on the shear and breathing motions of adjacent layers revealed the specificity of isotope engineering in a layered material, with a modification of the van der Waals interactions upon isotope purification. The electron density distribution is more diffuse between adjacent layers in 10BN than in 11BN crystals. Our results open perspectives in understanding and controlling van der Waals bonding in layered materials.

Ultralow-loss polaritons in isotopically pure boron nitride.

Conventional optical components are limited to size scales much larger than the wavelength of light, as changes to the amplitude, phase and polarization of the electromagnetic fields are accrued gradually along an optical path. However, advances in nanophotonics have produced ultrathin, so-called 'flat' optical components that beget abrupt changes in these properties over distances significantly shorter than the free-space wavelength. Although high optical losses still plague many approaches, phonon polariton (PhP) materials have demonstrated long lifetimes for sub-diffractional modes in comparison to plasmon-polariton-based nanophotonics. We experimentally observe a threefold improvement in polariton lifetime through isotopic enrichment of hexagonal boron nitride (hBN). Commensurate increases in the polariton propagation length are demonstrated via direct imaging of polaritonic standing waves by means of infrared nano-optics. Our results provide the foundation for a materials-growth-directed approach aimed at realizing the loss control necessary for the development of PhP-based nanophotonic devices.

Determining crystal phase purity in c-BP through X-ray absorption spectroscopy.

We employ X-ray absorption near-edge spectroscopy at the boron K-edge and the phosphorus L2,3-edge to study the structural properties of cubic boron phosphide (c-BP) samples. The X-ray absorption spectra are modeled from first-principles within the density functional theory framework using the excited electron core-hole (XCH) approach. A simple structural model of a perfect c-BP crystal accurately reproduces the P L2,3-edge, however it fails to describe the broad and gradual onset of the B K-edge. Simulations of the spectroscopic signatures in boron 1s excitations of intrinsic point defects and the hexagonal BP crystal phase show that these additions to the structural model cannot reproduce the broad pre-edge of the experimental spectrum. Calculated formation enthalpies show that, during the growth of c-BP, it is possible that amorphous boron phases can be grown in conjunction with the desired boron phosphide crystalline phase. In combination with experimental and theoretically obtained X-ray absorption spectra of an amorphous boron structure, which have a similar broad absorption onset in the B K-edge spectrum as the cubic boron phosphide samples, we provide evidence for the presence of amorphous boron clusters in the synthesized c-BP samples.

Negative refraction in hyperbolic hetero-bicrystals.

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons-hybrids of infrared photons and lattice vibrations-form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide (MoO3) and isotopically pure hexagonal boron nitride (h11BN). At a special frequency ω0, these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic-level repulsion and strong coupling.

Van der Waals isotope heterostructures for engineering phonon polariton dispersions.

Element isotopes are characterized by distinct atomic masses and nuclear spins, which can significantly influence material properties. Notably, however, isotopes in natural materials are homogenously distributed in space. Here, we propose a method to configure material properties by repositioning isotopes in engineered van der Waals (vdW) isotopic heterostructures. We showcase the properties of hexagonal boron nitride (hBN) isotopic heterostructures in engineering confined photon-lattice waves-hyperbolic phonon polaritons. By varying the composition, stacking order, and thicknesses of h10BN and h11BN building blocks, hyperbolic phonon polaritons can be engineered into a variety of energy-momentum dispersions. These confined and tailored polaritons are promising for various nanophotonic and thermal functionalities. Due to the universality and importance of isotopes, our vdW isotope heterostructuring method can be applied to engineer the properties of a broad range of materials.

Decoherence of V[Formula: see text] spin defects in monoisotopic hexagonal boron nitride.

Spin defects in hexagonal boron nitride (hBN) are promising quantum systems for the design of flexible two-dimensional quantum sensing platforms. Here we rely on hBN crystals isotopically enriched with either 10B or 11B to investigate the isotope-dependent properties of a spin defect featuring a broadband photoluminescence signal in the near infrared. By analyzing the hyperfine structure of the spin defect while changing the boron isotope, we first confirm that it corresponds to the negatively charged boron-vacancy center ([Formula: see text]). We then show that its spin coherence properties are slightly improved in 10B-enriched samples. This is supported by numerical simulations employing cluster correlation expansion methods, which reveal the importance of the hyperfine Fermi contact term for calculating the coherence time of point defects in hBN. Using cross-relaxation spectroscopy, we finally identify dark electron spin impurities as an additional source of decoherence. This work provides new insights into the properties of [Formula: see text] spin defects, which are valuable for the future development of hBN-based quantum sensing foils.

Graphene's non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects.

Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a "Doppler-like" shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

Planar refraction and lensing of highly confined polaritons in anisotropic media.

Refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, refraction between anisotropic media is a more exotic phenomenon which remains barely investigated, particularly at the nanoscale. Here, we visualize and comprehensively study the general case of refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and we do it with the use of nanoscale-confined polaritons in a natural medium: α-MoO3. The refracted polaritons exhibit non-intuitive directions of propagation as they traverse planar nanoprisms, enabling to unveil an exotic optical effect: bending-free refraction. Furthermore, we develop an in-plane refractive hyperlens, yielding foci as small as λp/6, being λp the polariton wavelength (λ0/50 compared to the wavelength of free-space light). Our results set the grounds for planar nano-optics in strongly anisotropic media, with potential for effective control of the flow of energy at the nanoscale.

Photopolymerization of self-assembled monolayers of diacetylenic alkylphosphonic acids on group-III nitride substrates.

This paper describes the fabrication and characterization of photopolymerizable alkylphosphonate self-assembled monolayers (SAMs) on group-III nitride substrates including GaN and Al(x)Ga(1-x)N (AlGaN; x = 0.2 and 0.25). Contact angle goniometry, visible absorption spectroscopy, and atomic force microscopy were used to assess the formation, desorption, and photopolymerization of SAMs of diacetylenic alkylphosphonic acids (CH(3)(CH(2))(n)-C[triple bond]C-C[triple bond]C-(CH(2))(m)PO(OH)(2); (m, n) = (3, 11), (6, 8), and (9, 5)). As with GaN substrates (Ito, T.; Forman, S. M.; Cao, C.; Li, F.; Eddy, C. R., Jr.; Mastro, M. A.; Holm, R. T.; Henry, R. L.; Hohn, K.; Edgar, J. H. Langmuir 2008, 24, 6630-6635), alkylphosphonic acids formed SAMs on UV/O(3)-treated AlGaN substrates from their toluene solutions in contrast to other primary substituted hydrocarbons with a terminal -COOH, -NH(2), -OH, or -SH group. Diacetylenic alkylphosphonate SAMs on group-III nitrides could be polymerized by UV irradiation (254 nm), as indicated by the appearance of a visible absorption band around 640 nm and also by their significantly reduced desorption from the surface in a 0.1 M aqueous NaOH solution. A longer UV irradiation time was required to maximize the photopolymerization of a SAM having a diacetylene group close to the terminal phosphonate moiety, probably because of the hindrance of the topochemical polymerization due to the limited flexibility of the cross-linking moieties on an atomically rough substrate surface.

Strong magnetophonon oscillations in extra-large graphene.

Van der Waals materials and their heterostructures offer a versatile platform for studying a variety of quantum transport phenomena due to their unique crystalline properties and the exceptional ability in tuning their electronic spectrum. However, most experiments are limited to devices that have lateral dimensions of only a few micrometres. Here, we perform magnetotransport measurements on graphene/hexagonal boron-nitride Hall bars and show that wider devices reveal additional quantum effects. In devices wider than ten micrometres we observe distinct magnetoresistance oscillations that are caused by resonant scattering of Landau-quantised Dirac electrons by acoustic phonons in graphene. The study allows us to accurately determine graphene's low energy phonon dispersion curves and shows that transverse acoustic modes cause most of phonon scattering. Our work highlights the crucial importance of device width when probing quantum effects and also demonstrates a precise, spectroscopic method for studying electron-phonon interactions in van der Waals heterostructures.

Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene.

At very small twist angles of ∼0.1°, bilayer graphene exhibits a strain-accompanied lattice reconstruction that results in submicron-size triangular domains with the standard, Bernal stacking. If the interlayer bias is applied to open an energy gap inside the domain regions making them insulating, such marginally twisted bilayer graphene is expected to remain conductive due to a triangular network of chiral one-dimensional states hosted by domain boundaries. Here we study electron transport through this helical network and report giant Aharonov-Bohm oscillations that reach in amplitude up to 50% of resistivity and persist to temperatures above 100 K. At liquid helium temperatures, the network exhibits another kind of oscillations that appear as a function of carrier density and are accompanied by a sign-changing Hall effect. The latter are attributed to consecutive population of the narrow minibands formed by the network of one-dimensional states inside the gap.

Photonic crystal for graphene plasmons.

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.

Reconfigurable infrared hyperbolic metasurfaces using phase change materials.

Metasurfaces control light propagation at the nanoscale for applications in both free-space and surface-confined geometries. However, dynamically changing the properties of metasurfaces can be a major challenge. Here we demonstrate a reconfigurable hyperbolic metasurface comprised of a heterostructure of isotopically enriched hexagonal boron nitride (hBN) in direct contact with the phase-change material (PCM) single-crystal vanadium dioxide (VO2). Metallic and dielectric domains in VO2 provide spatially localized changes in the local dielectric environment, enabling launching, reflection, and transmission of hyperbolic phonon polaritons (HPhPs) at the PCM domain boundaries, and tuning the wavelength of HPhPs propagating in hBN over these domains by a factor of 1.6. We show that this system supports in-plane HPhP refraction, thus providing a prototype for a class of planar refractive optics. This approach offers reconfigurable control of in-plane HPhP propagation and exemplifies a generalizable framework based on combining hyperbolic media and PCMs to design optical functionality.

Distinctive in-Plane Cleavage Behaviors of Two-Dimensional Layered Materials.

Mechanical exfoliation from bulk layered crystal is widely used for preparing two-dimensional (2D) layered materials, which involves not only out-of-plane interlayer cleavage but also in-plane fracture. Through a statistical analysis on the exfoliated 2D flakes, we reveal the in-plane cleavage behaviors of six representative layered materials, including graphene, h-BN, 2H phase MoS2, 1T phase PtS2, FePS3, and black phosphorus. In addition to the well-known interlayer cleavage, these 2D layered materials show a distinctive tendency to fracture along certain in-plane crystallography orientations. With theoretical modeling and analysis, these distinct in-plane cleavage behaviors can be understood as a result of the competition between the release of the elastic energy and the increase of the surface energy during the fracture process. More importantly, these in-plane cleavage behaviors provide a fast and noninvasive method using optical microscopy to identify the lattice direction of mechanical exfoliated 2D layered materials.