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Metals are canonical plasmonic media at infrared and optical wavelengths, allowing one to guide and manipulate light at the nanoscale. A special form of optical waveguiding is afforded by highly anisotropic crystals revealing the opposite signs of the dielectric functions along orthogonal directions. These media are classified as hyperbolic and include crystalline insulators, semiconductors, and artificial metamaterials. Layered anisotropic metals are also anticipated to support hyperbolic waveguiding. However, this behavior remains elusive, primarily because interband losses arrest the propagation of infrared modes. Here, we report on the observation of propagating hyperbolic waves in a prototypical layered nodal-line semimetal ZrSiSe. The observed waveguiding originates from polaritonic hybridization between near-infrared light and nodal-line plasmons. Unique nodal electronic structures simultaneously suppress interband loss and boost the plasmonic response, ultimately enabling the propagation of infrared modes through the bulk of the crystal.

Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene have been intensely studied. At small twist angle θ, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride substrate is optically hyperbolic. Our results illustrate the capabilities of the nano-photocurrent technique for probing nanoscale electronic inhomogeneities in two-dimensional materials., Here, the authors use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at domain walls separating micron-scale AB and BA stacking regions in twisted bilayer graphene, and observe hyperbolic enhancement of the photocurrent pattern.

Hyperbolic Cooper-pair polaritons (HCP) in cuprate superconductors are of fundamental interest due to their potential for providing insights into the nature of unconventional superconductivity. Here, we critically assess an experimental approach using near-field imaging to probe HCP in Bi

Van-der Waals (vdW) atomically layered crystals can act as optical waveguides over a broad range of the electromagnetic spectrum ranging from Terahertz to visible. Unlike common Si-based waveguides, vdW semiconductors host strong excitonic resonances that may be controlled using non-thermal stimuli including electrostatic gating and photoexcitation. Here, we utilize waveguide modes to examine photo-induced changes of excitons in the prototypical vdW semiconductor, WSe2, prompted by femtosecond light pulses. Using time-resolved scanning near-field optical microscopy we visualize the electric field profiles of waveguide modes in real space and time and extract the temporal evolution of the optical constants following femtosecond photoexcitation. By monitoring the phase velocity of the waveguide modes, we detect incoherent A-exciton bleaching along with a coherent optical Stark shift in WSe2. The authors use time-resolved scanning near-field optical microscopy to probe the ultrafast excitonic processes and their impact on waveguide operation in transition metal dichalcogenide crystals. They observe significant modulation of the complex index by monitoring waveguide modes on the fs time scale, and identify both coherent and incoherent manipulations of WSe2 excitonic resonances.

We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results provide a fast and robust method for mapping the electronic structure of TBG and suggest that similar methods can be broadly applied to probe electronic inhomogeneities of moir\'e superlattices in other van der Waals heterostructures.

Interlayer excitons are bound states of electrons and holes confined in separate two-dimensional layers. Due to their repulsive dipolar interaction, interlayer excitons can form a correlated liquid. If another electron-hole bilayer is present, excitons from different bilayers can exhibit mutual attraction. We study such a quadrilayer system by a hypernetted chain formalism. We compute ground state energies, pair correlation functions, and collective mode velocities as functions of the exciton densities. We estimate the critical density for the transition to a paired biexciton phase. For a strongly unbalanced (unequal density) system, the excitons in the more dilute bilayer behave as polarons. We compute energies and effective masses of such exciton-polarons.

Topological spin textures are field arrangements that cannot be continuously deformed to a fully polarized state. In particular, merons are topological textures characterized by half-integer topological charge ±1/2 and vortex-like swirling patterns at large distances. Merons have been studied previously in the context of cosmology, fluid dynamics, condensed matter physics and plasmonics. Here, we visualized optical spin angular momentum of phonon polaritons that resembles nanoscale meron spin textures. Phonon polaritons, hybrids of infrared photons and phonons in hexagonal boron nitride, were excited by circularly polarized light incident on a ring-shaped antenna and imaged using infrared near-field techniques. The polariton field reveals a half-integer topological charge determined by the handedness of the incident beam. Our phonon polaritonic platform opens up new pathways to create, control, and visualize topological textures.

The ability to perform nanometer-scale optical imaging and spectroscopy is key to deciphering the low-energy effects in quantum materials, as well as vibrational fingerprints in planetary and extraterrestrial particles, catalytic substances, and aqueous biological samples. These tasks can be accomplished by the scattering-type scanning near-field optical microscopy (s-SNOM) technique that has recently spread to many research fields and enabled notable discoveries. Herein, it is shown that the s-SNOM, together with scanning probe research in general, can benefit in many ways from artificial-intelligence (AI) and machine-learning (ML) algorithms. Augmented with AI- and ML-enhanced data acquisition and analysis, scanning probe optical nanoscopy is poised to become more efficient, accurate, and intelligent.

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with $$\Delta \approx -10\,{{{\rm{meV}}}}$$ Δ ≈ − 10 meV over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit.

An indirect exciton is a bound state of an electron and a hole in spatially separated layers. Two-dimensional indirect excitons can be created optically in heterostructures containing double quantum wells or atomically thin semiconductors. We study theoretically transmission of such bosonic quasiparticles through nano-constrictions. We show that quantum transport phenomena, e.g., conductance quantization, single-slit diffraction, two-slit interference, and the Talbot effect, are experimentally realizable in systems of indirect excitons. We discuss similarities and differences between these phenomena and their counterparts in electronic devices., (v2) Updated title, text, and references; 12 pages, 9 figures

Natural hyperbolic materials with dielectric permittivities of opposite signs along different principal axes can confine long-wavelength electromagnetic waves down to the nanoscale, well below the diffraction limit. Confined electromagnetic waves coupled to phonons in hyperbolic dielectrics including hexagonal boron nitride (hBN) and α-MoO3 are referred to as hyperbolic phonon polaritons (HPPs). HPP dissipation at ambient conditions is substantial, and its fundamental limits remain unexplored. Here, we exploit cryogenic nanoinfrared imaging to investigate propagating HPPs in isotopically pure hBN and naturally abundant α-MoO3 crystals. Close to liquid-nitrogen temperatures, losses for HPPs in isotopic hBN drop significantly, resulting in propagation lengths in excess of 8 μm, with lifetimes exceeding 5 ps, thereby surpassing prior reports on such highly confined polaritonic modes. Our nanoscale, temperature-dependent imaging reveals the relevance of acoustic phonons in HPP damping and will be instrumental in mitigating such losses for miniaturized mid-infrared technologies operating at liquid-nitrogen temperatures., Research at Columbia is supported by Vannevar Bush Faculty Fellowship ONR-VB: N00014-19-1-2630. We thank A. Sternbach and S. Zhang for helpful discussions. Exfoliation and transfer of hBN onto desired substrates and electron beam lithography of gold disks were performed by J.T.M. and supported by the National Science Foundation (DMR1904793). Additional structure fabrication was supported by the Center on Precision-Assembled Quantum Materials, funded through the U.S. National Science Foundation (NSF) Materials Research Science and Engineering Centers (award no. DMR-2011738). Initial simulations and experimental design from Vanderbilt were provided by J.D.C. in collaboration with the Columbia team (D.N.B. and G.N.) and was supported by the Office of Naval Research (N00014-18-1-2107). The hBN phonon band structure calculation was performed by R.C. and L.A. and supported by the Spanish MINECO/FEDER grant (MAT2015-71035- R). Cryogenics nano-optics experiments at Columbia were solely supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. D.N.B is the Gordon and Betty Moore Foundation’s EPiQS Initiative Investigator no. 9455.

Author(s): Chen, X; Yao, Z; Xu, S; McLeod, AS; Gilbert Corder, SN; Zhao, Y; Tsuneto, M; Bechtel, HA; Martin, MC; Carr, GL; Fogler, MM; Stanciu, SG; Basov, DN; Liu, M | Abstract: The underlying physics behind an experimental observation often lacks a simple analytical description. This is especially the case for scanning probe microscopy techniques, where the interaction between the probe and the sample is nontrivial. Realistic modeling to include the exact details of the probe is widely acknowledged as a challenge. Due to various complexity constraints, the probe is often only approximated in a simplified geometry, leading to a source for modeling inconsistencies. On the other hand, a well-trained artificial neural network based on real data can grasp the hidden correlation between the signal and the sample properties, circumventing the explicit probe modeling process. In this work we show that, via a combination of model calculation and experimental data acquisition, a physics-infused hybrid neural network can predict the probe-sample interaction in the widely used scattering-type scanning near-field optical microscope. This hybrid network provides a long-sought solution for accurate extraction of material properties from tip-specific raw data. The methodology can be extended to other scanning probe microscopy techniques as well as other data-oriented physical problems in general.

When light-matter polaritons travel in periodic media, they acquire properties akin to Bloch quasi-particles in crystals., Efficient control of photons is enabled by hybridizing light with matter. The resulting light-matter quasi-particles can be readily programmed by manipulating either their photonic or matter constituents. Here, we hybridized infrared photons with graphene Dirac electrons to form surface plasmon polaritons (SPPs) and uncovered a previously unexplored means to control SPPs in structures with periodically modulated carrier density. In these periodic structures, common SPPs with continuous dispersion are transformed into Bloch polaritons with attendant discrete bands separated by bandgaps. We explored directional Bloch polaritons and steered their propagation by dialing the proper gate voltage. Fourier analysis of the near-field images corroborates that this on-demand nano-optics functionality is rooted in the polaritonic band structure. Our programmable polaritonic platform paves the way for the much-sought benefits of on-the-chip photonic circuits.

Lighting a route for hyperbolic dispersion The propagation of light within a material is usually well defined, with the propagation described by scattering and dispersion. In artificially designed metamaterials and in anisotropic layered materials, the dispersion can be hyperbolic, giving rise to subwavelength confinement of the light. Sternbach et al. show that the hyperbolic dispersion can be optically switched on and off on demand in the layered transition metal dichalcogenide tungsten diselenide (see the Perspective by Deng and Chen). Illuminating the material with ultrafast pulses of sub-bandgap light creates a transient waveguide, resulting in hyperbolic dispersion in the material. The ability to tune the dispersion characteristics on demand using optical pumping is an effective approach for developing ultrafast switching photonic devices and controlling the propagation of light on the nanoscale. Science , this issue p. 617 ; see also p. 572

We studied both experimentally and theoretically attractive dipolar interaction in bilayers of indirect excitons (IXs) with built-in dipole moments and found monotonic IX energy reduction with density and spatial attraction between IX clouds.

Dragging of light by moving dielectrics was predicted by Fresnel and verified by Fizeau's celebrated experiments with flowing water. This momentous discovery is among the experimental cornerstones of Einstein's special relativity and is well understood in the context of relativistic kinematics. In contrast, experiments on dragging photons by an electron flow in solids are riddled with inconsistencies and so far eluded agreement with the theory. Here we report on the electron flow dragging surface plasmon polaritons (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 launched against the drifting carriers. Unlike the Fizeau effect for light, the SPP drag by electrical currents defies the simple kinematics interpretation and is linked to the nonlinear electrodynamics of the Dirac electrons in graphene. The observed plasmonic Fizeau drag enables breaking of time-reversal symmetry and reciprocity at infrared frequencies without resorting to magnetic fields or chiral optical pumping., Comment: 11 pages, 3 figures

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl3, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl3 interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl3 at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: EF = 0.6 eV (n = 2.7 × 1013 cm–2). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl3 giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping., Research at Columbia was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. J.Z., L.X., and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056 - 390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19) and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL). J.Z., L.X., and A.R. would like to acknowledge Nicolas Tancogne-Dejean for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. Work at ORNL was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant JPMXP0112101001, JSPS KAKENHI Grant JP20H00354, and the CREST (JPMJCR15F3), JST. S.E.N. was supported by the Division of Scientific User Facilities of the U.S. DOE Basic Energy Sciences. M.M.F. acknowledges support from the Office of Naval Research Grant N00014-18-1-2722. D.N.B. is the Vannevar Bush Faculty ONR-VB: N00014-19-1-2630 and Moore investigator in Quantum Materials EPIQS program #9455. A.S.M acknowledges support from award 80NSSC19K1210 under the NASA Laboratory Analysis of Returned Samples program.

We explore attractive dipolar interaction in indirect excitons (IXs). For one layer of IXs in a single pair of coupled quantum wells (CQW), the out-of-plane IX electric dipoles lead to repulsive dipolar interaction between IXs. The attractive dipolar interaction between IXs is realized in a 2-CQW heterostructure with two IX layers in two separated CQW pairs. We found both in experimental measurements and theoretical simulations that increasing density of IXs in one layer causes a monotonic energy reduction for IXs in the other layer. We also found an in-plane shift of a cloud of IXs in one layer towards a cloud of IXs in the other layer. This behaviour is qualitatively consistent with attractive dipolar interaction. The measured IX energy reduction and IX cloud shift are higher than the values given by the correlated liquid theory.

Tungsten ditelluride (WTe_2) is a transition metal dichalcogenide whose physical properties depend critically on the number of layers. In this paper, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to identify distinct THz range electromagnetic behavior of WTe_2 mono-, bi- and tri-layer terraces in the same micro-crystals. We observed clear metallic behavior of the near-field signal on tri-layer regions. Our data are consistent with the existence of surface plasmon polaritons (SPP) in the THz range confined to tri-layer terraces in our specimens. The near-field signal on bi-layer regions surprisingly shows moderately metallicity, but with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations considering thermally activated carriers favor the semimetal scenario over the semiconductor scenario for bi-layer WTe_2. THz images for monolayer terraces uncovered weakly insulating behavior consistent with transport data.

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \approx -10\,{{{\rm{meV}}}}$$\end{document}Δ≈−10meV over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit., The behaviour of Tungsten ditelluride (WTe2) in few-layer form is not yet fully characterized. Here the authors use a near-field terahertz microscopy technique to observe the electromagnetic responses of WTe2 flakes from one to several layers and to study their semimetallic/ semiconducting behavior.

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.

We theoretically study the low energy electromagnetic response of BCS type superconductors focusing on propagating collective modes that are observable with THz near field optics. The interesting frequency and momentum range is $\omega < 2\Delta$ and $q < 1/\xi$ where $\Delta$ is the gap and $\xi$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and Carlson-Goldman modes using THz near field technique, although none of these modes couple linearly to far field radiation. Coupling of THz near field radiation to the amplitude mode requires particle-hole symmetry breaking while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-THz frequency range. In a system of two superconducting layers with nanometer scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well defined resonance peaks in the near-field THz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two dimensional superconductors, realized for example in samples of high T$_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the THz near field radiation., Comment: 12 pages, 7 figures

Significance The 3D nodal points in Dirac and/or Weyl semimetals are in the vanguard of quantum materials research. A hallmark of these systems is the linear band dispersion. This latter electronic stricture gives rise to unconventional transport and optical phenomena. Here, we demonstrate that solids with dispersive nodal lines in the electronic structure share many common aspects with the response of 3D nodal-points systems. We investigated N b A s 2 using a combination of optical and magneto-optical techniques and have identified electromagnetic signature of dispersive nodal lines. This particular compound has allowed us to inquire the impact of spin-orbit coupling on the universal characteristic of nodal metals.

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.

Mid-infrared nanoimaging and spectroscopy of two-dimensional (2D) materials have been limited so far to scattering-type scanning near-field optical microscopy (s-SNOM) experiments, where light from the sample is scattered by a metallic-coated atomic force microscope (AFM) tip interacting with the material at the nanoscale. These experiments have recently allowed imaging of plasmon polaritons in graphene as well as hyperbolic phonon polaritons in hexagonal boron nitride (hBN). Here we show that the high mechanical sensitivity of an AFM cantilever can be exploited for imaging hyperbolic phonon polaritons in hBN. In our imaging process, the lattice vibrations of hBN micrometer-sized flakes are locally enhanced by the launched phonon polaritons. These enhanced vibrations are coupled to the AFM tip in contact with the sample surface and recorded during scanning. Imaging resolution of Δ/20 is shown (Δ being the polaritonic fringes' separation distance), comparable to the best resolution in s-SNOM. Importantly, this detection mechanism is free from light background, and it is in fact the first photonless detection of phonon polaritons.

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.

Using magneto-infrared spectroscopy, we have explored the charge dynamics of (Bi,Sb)$_2$Te$_3$ thin films on InP substrates. From the magneto-transmission data we extracted three distinct cyclotron resonance (CR) energies that are all apparent in the broad band Faraday rotation (FR) spectra. This comprehensive FR-CR data set has allowed us to isolate the response of the bulk states from the intrinsic surface states associated with both the top and bottom surfaces of the film. The FR data uncovered that electron- and hole-type Dirac fermions reside on opposite surfaces of our films, which paves the way for observing many exotic quantum phenomena in topological insulators., 5 pages, accepted by Nano Lett (2016)

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.

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.

Significance The emergence of superconductivity in high-temperature cuprates arises out of a rich landscape of competing order. For example, stripe order can hoard the electrons needed to form Cooper pairs and establish superconductivity. Intriguingly, the complex interactions of such intertwined orders can be manipulated with light, where nonequilibrium dynamics alter the primacy of one order over another. Following photoexcitation of La2−xBaxCuO4 (x = 0.115) with near-infrared pulses, we observe a long-lived state that exhibits enhanced superconducting correlations well above the equilibrium superconducting transition temperature. Our analysis reveals that this metastable phase arises from a collapse of stripe order, providing an important demonstration of light-directed control in quantum materials., Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La2−xBaxCuO4 (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm2 results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La2−xBaxCuO4 is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature

Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La 2−x Ba x CuO 4 (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm 2 results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La 2−x Ba x CuO 4 is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system whose transport features a universal hydrodynamic description, even at room temperature. This quantum critical "Dirac fluid" is expected to have a shear viscosity close to a minimum bound, with an inter-particle scattering rate saturating at the Planckian time $\hbar/(k_B T)$. While electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene, a "smoking gun" of viscous behavior remains elusive. In this work, we directly image viscous Dirac fluid flow in graphene at room temperature via measurement of the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy (NV) centers in diamond. Scanning single-spin and wide-field magnetometry reveals a parabolic Poiseuille profile for electron flow in a graphene channel near the charge neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in an Ohmic conductor. Via combined imaging-transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly-ideal electron fluid in neutral graphene at room temperature. Our results pave the way to study hydrodynamic transport in quantum critical fluids relevant to strongly-correlated electrons in high-$T_c$ superconductors. This work also highlights the capability of quantum spin magnetometers to probe correlated-electronic phenomena at the nanoscale., Comment: Author list and title have been updated in published version

We report on a nanoinfrared (IR) imaging study of ultraconfined plasmonic hotspots inside graphene nanobubbles formed in graphene/hexagonal boron nitride (hBN) heterostructures. The volume of these plasmonic hotspots is more than one-million-times smaller than what could be achieved by free-space IR photons, and their real-space distributions are controlled by the sizes and shapes of the nanobubbles. Theoretical analysis indicates that the observed plasmonic hotspots are formed due to a significant increase of the local plasmon wavelength in the nanobubble regions. Such an increase is attributed to the high sensitivity of graphene plasmons to its dielectric environment. Our work presents a novel scheme for plasmonic hotspot formation and sheds light on future applications of graphene nanobubbles for plasmon-enhanced IR spectroscopy.

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.

Phonon polaritons in van der Waals materials reveal significant confinement accompanied with long propagation length: important virtues for tasks pertaining to the control of light and energy flow at the nanoscale. While previous studies of phonon polaritons have relied on relatively thick samples, here reported is the first observation of surface phonon polaritons in single atomic layers and bilayers of hexagonal boron nitride (hBN). Using antenna-based near-field microscopy, propagating surface phonon polaritons in mono- and bilayer hBN microcrystals are imaged. Phonon polaritons in monolayer hBN are confined in a volume about one million times smaller than the free-space photons. Both the polariton dispersion and their wavelength-thickness scaling law are altered compared to those of hBN bulk counterparts. These changes are attributed to phonon hardening in monolayer-thick crystals. The data reported here have bearing on applications of polaritons in metasurfaces and ultrathin optical elements.

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. While high optical losses still plague many approaches, phonon polariton materials have demonstrated long lifetimes for localized modes in comparison to plasmon-polariton based nanophotonics. Our work predicts a further 14-fold increase in the optic phonon lifetime and we experimentally report a ~3-fold improvement through isotopic enrichment of hexagonal boron nitride (hBN). We establish commensurate increases in the phonon polariton propagation length via direct imaging of polaritonic standing waves by means of infrared nano-optics. Our results provide the foundation for a materials-growth-directed approach towards realizing the loss control necessary for the development of phonon polariton based nanophotonic devices.

Hexagonal boron nitride (hBN) is a natural hyperbolic material that supports both volume-confined hyperbolic polaritons (HPs) and sidewall-confined hyperbolic surface polaritons (HSPs). In this work, we demonstrate efficient excitation, control and steering of HSPs in hBN through engineering the geometry and orientation of hBN sidewalls. By combining infrared (IR) nano-imaging and numerical simulations, we investigate the reflection, transmission and scattering of HSPs at the hBN corners with various apex angles. We show that the sidewall-confined nature of HSPs enables a high degree of control over their propagation by designing the geometry of hBN nanostructures.

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.

The Pancharatnam–Berry phase is a geometric phase acquired over a cycle of parameters in the Hamiltonian governing the evolution of the system. Here, we report on the observation of the Pancharatnam–Berry phase in a condensate of indirect excitons (IXs) in a GaAs-coupled quantum well structure. The Pancharatnam–Berry phase is directly measured by detecting phase shifts of interference fringes in IX interference patterns. Correlations are found between the phase shifts, polarization pattern of IX emission, and onset of IX spontaneous coherence. The evolving Pancharatnam–Berry phase is acquired due to coherent spin precession in IX condensate and is observed with no decay over lengths exceeding 10 μm indicating long-range coherent spin transport., Geometric phases in matter are of fundamental interest. Here the authors observe the Pancharatnam–Berry phase in matter waves by imaging light interference patterns from cold gases of indirect excitons and find long-range coherent spin transport in the system.

Indirect excitons (IXs) are explored both for studying quantum Bose gases in semiconductor materials and for the development of excitonic devices. IXs were extensively studied in III–V and II–VI semiconductor heterostructures where IX range of existence has been limited to low temperatures. Here, we present the observation of IXs at room temperature in van der Waals transition metal dichalcogenide (TMD) heterostructures. This is achieved in TMD heterostructures based on monolayers of MoS2 separated by atomically thin hexagonal boron nitride. The IXs we realize in the TMD heterostructure have lifetimes orders of magnitude longer than lifetimes of direct excitons in single-layer TMD and their energy is gate controlled. The realization of IXs at room temperature establishes the TMD heterostructures as a material platform both for a field of high-temperature quantum Bose gases of IXs and for a field of high-temperature excitonic devices., Indirect excitons, composed of a spatially separated electron and hole, could find applications in excitonic devices for signal processing and communication, however they are normally detected at low temperatures. Here, the authors observe room-temperature indirect excitons in van der Waals transition metal dichalcogenide heterostructures.

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory., 5 pages, 4 figures

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor $\sigma^{(3)}$ whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for $\sigma^{(3)}$ for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments., Comment: 10 pages, 5 figures

We report on the observation of the Pancharatnam-Berry phase in a condensate of indirect excitons realized in a GaAs coupled quantum well structure. Our measurements indicate long range coherent spin transport.