Deep-Ultraviolet and Helicity-Dependent Raman Spectroscopy for Carbon Nanotubes and 2D Materials.

Recent progress of Raman spectroscopy on carbon nanotubes and 2D materials is reviewed as a topical review. The Raman tensor with complex values is related to the chiral 1D/2D materials without mirror symmetry for the mirror in the propagating direction of light, such as chiral carbon nanotube and black phosphorus. The phenomenon of complex Raman tensor is observed by the asymmetric polar plot of helicity-dependent Raman spectroscopy using incident circularly-polarized lights. First-principles calculations of resonant Raman spectra directly give the complex Raman tensor that explains helicity-dependent Raman spectra and laser-energy-dependent relative intensities of Raman spectra. In deep-ultraviolet (DUV) Raman spectroscopy with 266 nm laser, since the energy of the photon is large compared with the energy gap, the first-order and double resonant Raman processes occur in general k points in the Brillouin zone. First-principles calculation is necessary to understand the DUV Raman spectra and the origin of double-resonance Raman spectra. Asymmetric line shapes appear for the G band of graphene for 266 nm laser and in-plane Raman mode of WS2 for 532 nm laser, while these spectra show symmetric line shapes for other laser excitation. The interference effect on the asymmetric line shape is discussed by fitting the spectra to the Breit-Wigner-Fano line shapes.

Interacting Phonons between Layers in Raman Spectra of Carbon Nanotubes inside Boron Nitride Nanotubes.

We present the resonant Raman spectra of a single-wall carbon nanotube inside a multiwall boron nitride nanotube (SWNT@BNNT). At EL = 1.58 eV, SWNT@BNNT exhibited resonant Raman spectra at 807 (ωBN) and 804 cm-1 (ωGr). Their intensities almost disappeared at EL = 2.33 eV. We assigned ωBN to the out-of-plane BN phonon mode that coupled with ωGr. At EL = 4.66 eV, the G+ and G- bands of the SWNT@BNNT red-shifted 3.8 cm-1 compared with the SWNT, suggesting the interwall interactions between the in-plane modes of SWNT and BNNT. Moreover, the E2g mode of the BNNT in SWNT@BNNT appeared at 1370.3 ± 0.1 cm-1, which is undistinguishable for EL < 3 eV because of the overlap with the D band frequency. The assignment of the present Raman spectra was confirmed through the first-principles calculations.

Engineering chirality at wafer scale with ordered carbon nanotube architectures.

Creating artificial matter with controllable chirality in a simple and scalable manner brings new opportunities to diverse areas. Here we show two such methods based on controlled vacuum filtration - twist stacking and mechanical rotation - for fabricating wafer-scale chiral architectures of ordered carbon nanotubes (CNTs) with tunable and large circular dichroism (CD). By controlling the stacking angle and handedness in the twist-stacking approach, we maximize the CD response and achieve a high deep-ultraviolet ellipticity of 40 ± 1 mdeg nm-1. Our theoretical simulations using the transfer matrix method reproduce the experimentally observed CD spectra and further predict that an optimized film of twist-stacked CNTs can exhibit an ellipticity as high as 150 mdeg nm-1, corresponding to a g factor of 0.22. Furthermore, the mechanical rotation method not only accelerates the fabrication of twisted structures but also produces both chiralities simultaneously in a single sample, in a single run, and in a controllable manner. The created wafer-scale objects represent an alternative type of synthetic chiral matter consisting of ordered quantum wires whose macroscopic properties are governed by nanoscopic electronic signatures and can be used to explore chiral phenomena and develop chiral photonic and optoelectronic devices.

Observing Axial Chirality of Chiral Single-Wall Carbon Nanotubes by Helicity-Dependent Raman Spectra.

Helicity-dependent Raman spectra of an isolated, chiral, single-wall carbon nanotube (SWNT) are reported using circularly polarized light. A polar plot of polarized Raman intensity for the radial breathing mode (RBM), which is excited by left-handed or right-handed circularly polarized light, shows asymmetric angle dependence relative to the nanotube axis direction, which reflects the axial chirality of a SWNT. The asymmetry in the polar plot of the RBM can be analyzed by a complex Raman tensor. The complex phase of each component of the Raman tensor has a maximum at chiral angle θ = 15° of a SWNT which is between two achiral SWNTs, that is, zigzag (θ = 0°) and armchair (θ = 30°) SWNTs. Considering the interaction between the chiral SWNT and the circularly polarized light, we discuss the origin of the complex phases excited by the opposite helicity of the circularly polarized light.

Nonlinear Optical Responses of Janus MoSSe/MoS2 Heterobilayers Optimized by Stacking Order and Strain.

Nonlinear optical responses in second harmonic generation (SHG) of van der Waals heterobilayers, Janus MoSSe/MoS2, are theoretically optimized as a function of strain and stacking order by adopting an exchange-correlation hybrid functional and a real-time approach in first-principles calculation. We find that the calculated nonlinear susceptibility, χ(2), in AA stacking (550 pm/V) becomes three times as large as AB stacking (170 pm/V) due to the broken inversion symmetry in the AA stacking. The present theoretical prediction is compared with the observed SHG spectra of Janus MoSSe/MoS2 heterobilayers, in which the peak SHG intensity of AA stacking becomes four times as large as AB stacking. Furthermore, a relatively large, two-dimensional strain (4%) that breaks the C3v point group symmetry of the MoSSe/MoS2, enhances calculated χ(2) values for both AA (900 pm/V) and AB (300 pm/V) stackings 1.6 times as large as that without strain.

Spatially Coherent Tip-Enhanced Raman Spectroscopy Measurements of Electron-Phonon Interaction in a Graphene Device.

Coherence length (Lc) of the Raman scattering process in graphene as a function of Fermi energy is obtained with spatially coherent tip-enhanced Raman spectroscopy. Lc decreases when the Fermi energy is moved into the neutrality point, consistent with the concept of the Kohn anomaly within a ballistic transport regime. Since the Raman scattering involves electrons and phonons, the observed results can be rationalized either as due to unusually large variation of the longitudinal optical phonon group velocity vg, reaching twice the value for the longitudinal acoustic phonon, or due to changes in the electron energy uncertainty, both properties being important for optical and transport phenomena that might not be observable by any other technique.

Vapor-Phase Indium Intercalation in van der Waals Nanofibers of Atomically Thin W6Te6 Wires.

One-dimensional (1D) conducting materials are of great interest as potential building blocks for integrated nanocircuits. Ternary 1D transition-metal chalcogenides, consisting of M6X6 wires with intercalated A atoms (M = Mo or W; X = S, Se, or Te; A = alkali or rare metals, etc.), have attracted much attention due to their 1D metallic behavior, superconductivity, and mechanical flexibility. However, the conventional solid-state reaction usually produces micrometer-scale bulk crystals, limiting their potential use as nanoscale conductors. Here we demonstrate a versatile method to fabricate indium (In)-intercalated W6Te6 (In-W6Te6) bundles with a nanoscale thickness. We first prepared micrometer-long, crystalline bundles of van der Waals W6Te6 wires using chemical vapor deposition and intercalated In into the crystal via a vapor-phase reaction. Atomic-resolution electron microscopy revealed that In atoms were surrounded by three adjacent W6Te6 wires. First-principles calculations suggested that their wire-by-wire stacking can transform through postgrowth intercalation. Individual In-W6Te6 bundles exhibited metallic behavior, as theoretically predicted. We further identified the vibrational modes by combining polarized Raman spectroscopy and nonresonant Raman calculations.

Complex Raman Tensor in Helicity-Changing Raman Spectra of Black Phosphorus under Circularly Polarized Light.

In anisotropic two-dimensional materials, complex values of Raman tensors are necessary to explain the abnormal linearly polarized Raman spectra. In this work, we measured the helicity-changing Raman spectra of few-layer black phosphorus (BP) excited by circularly polarized light. We observed that the polarized Raman intensities of the Ag modes show a deflection angle that depends on the sample orientation, thickness, and laser excitation energy. To understand the deflection, we calculated the resonant Raman spectra by first-principles calculations, which give complex Raman tensors as a function of laser excitation energy. In particular, the phase difference between the elements of the complex Raman tensor is relevant to the deflection angle. The calculated results of monolayer BP reproduce the experimental helicity-resolved Raman spectra of few-layer BP satisfactorily.

Selection rule for Raman spectra of two-dimensional materials using circularly-polarized vortex light.

Conservation of spin and orbital angular momenta of circularly-polarized vortex light is discussed for Raman spectra of two-dimensional materials. We first show the selection rule for optical absorption of two-dimensional materials as a function of the spin and orbital angular momentum of incident vortex light. In the case of two-dimensional materials, the Raman tensor for the incident vortex light does not change the symmetry of the phonon mode. Furthermore, the Raman active modes are classified by either "helicity-changing" or "helicity-conserved" Raman modes, in which the scattered photon of circularly polarized light either changes or does not change the helicity of the light, respectively. We show tables of selection rules for the Raman active modes of two-dimensional materials with 2, 3, 4, and 6 rotational symmetry for vortex light.

Resonance-Enhanced Excitation of Interlayer Vibrations in Atomically Thin Black Phosphorus.

The strength of interlayer coupling critically affects the physical properties of 2D materials such as black phosphorus (BP), where the electronic structure depends sensitively on layer thickness. Rigid-layer vibrations reflect directly the interlayer coupling strength in 2D van der Waals solids, but measurement of these characteristic frequencies is made difficult by sample instability and small Raman scattering cross sections in atomically thin elemental crystals. Here, we overcome these challenges in BP by performing resonance-enhanced low-frequency Raman scattering under an argon-protective environment. Interlayer breathing modes for atomically thin BP were previously unobservable under conventional (nonresonant) excitation but became strongly enhanced when the excitation energy matched the sub-band electronic transitions of few-layer BP, down to bilayer thicknesses. The measured out-of-plane interlayer force constant was found to be 10.1 × 1019 N/m3 in BP, which is comparable to graphene. Accurate characterization of the interlayer coupling strength lays the foundation for future exploration of BP twisted structures and heterostructures.

Effective impedance of two-dimensional metal with retardation effect.

Optical absorption with retardation effect is discussed for two-dimensional (2D) metal. The absorption is given by the induced Joule heat in the metal and it is proportional to Re(σ)/|ɛ|2in whichσandɛdenote conductivity and dielectric function, respectively. Here, we investigate the effective impedance in both retarded and non-retarded regions of surface plasmon by discussing the response of the current density to the electric fields. The absorption formula Re(σ)/|ɛ|2is compared with the formula Re(σ/ɛ) that is commonly used for the absorption in carbon nanotube. We show that Re(σ/ɛ) is equal to Re(σ)/|ɛ|2only in the non-retarded region. The physical reason for Re(σ/ɛ) ≠ Re(σ)/|ɛ|2in the retarded region is that the induced current density is not out-of-phase with the induced electric field, which is explained by the effective impedance for both regions. The opposite response of the current to the induced electric field distinguishes the retarded and non-retarded regions. The calculated optical absorption spectra by Re(σ)/|ɛ|2reproduce the absorption spectra by solving the Maxwell equation as a function of the angular frequency of light or incident angle relative to the 2D surface, which makes Re(σ)/|ɛ|2a general representation of absorption.

Temperature-dependent optical constants of monolayer [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]: spectroscopic ellipsometry and first-principles calculations.

The temperature-dependent ([Formula: see text]) optical constants of monolayer [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] were investigated through spectroscopic ellipsometry over the spectral range of 0.73-6.42 eV. At room temperature, the spectra of refractive index exhibited several anomalous dispersion features below 800 nm and approached a constant value of 3.5-4.0 in the near-infrared frequency range. With a decrease in temperature, the refractive indices decreased monotonically in the near-infrared region due to the temperature-dependent optical band gap. The thermo-optic coefficients at room temperature had values from [Formula: see text] to [Formula: see text] for monolayer transition metal dichalcogenides at a wavelength of 1200 nm below the optical band gap. The optical band gap increased with a decrease in temperature due to the suppression of electron-phonon interactions. On the basis of first-principles calculations, the observed optical excitations at 4.5 K were appropriately assigned. These results provide basic information for the technological development of monolayer transition metal dichalcogenides-based photonic devices at various temperatures.

Characterization of Excitonic Nature in Raman Spectra Using Circularly Polarized Light.

We propose a technique of Raman spectroscopy to characterize the excitonic nature and to evaluate the relative contribution of the two kinds of electron/exciton-phonon interactions that are observed in two-dimensional transition-metal dichalcogenides (TMDCs). In the TMDCs, the electron/exciton-phonon interactions mainly originate from the deformation potential (DP) or the Fröhlich interaction (FI) which give the mutually different Raman tensors. Using a circularly polarized light, the relative proportion of the DP and the FI can be defined by the ratio of helicity-polarized intensity that is observed by MoS2. By this analysis, we show that the excitonic FI interaction gradually increases with decreasing temperature, contributes equally to DP at ∼230 K, and dominates at lower temperatures. The excitonic effect in the Raman spectra is confirmed by modulating the dielectric environment for the exciton and by changing the laser power.

Step-like conductance of a silicene pseudospin junction.

A step-like conductance as a function of the Fermi energy is theoretically predicted for a junction made of silicene, in which the energy gap in the junction can be controlled by a perpendicular electric field. When the electric field is applied at the central area of the junction, the transmission probability of an electron becomes partially suppressed and the calculated conductance behaves a step-like function of the Fermi energy. Origins of the step-like conductance are (1) formation of a standing-wave of electron, (2) changing number of transport channels and (3) a rotation of out-of-plane pseudospin of the electron in silicene. We analytically show that the transmission probability of the electron through the junction depends on the direction of the pseudospin, in which the large rotation results in a vanishing conductance. When we switch-off the electric field, on the other hand, the pseudospin does not change the direction, which gives a finite conductance. Thus a switching device can be realized in the silicene pseudospin junction.

Origin of the Flat Band in Heavily Cs-Doped Graphene.

A flat energy dispersion of electrons at the Fermi level of a material leads to instabilities in the electronic system and can drive phase transitions. Here we show that the flat band in graphene can be achieved by sandwiching a graphene monolayer by two cesium (Cs) layers. We investigate the flat band by a combination of angle-resolved photoemission spectroscopy experiment and the calculations. Our work highlights that charge transfer, zone folding of graphene bands, and the covalent bonding between C and Cs atoms are the origin of the flat energy band formation. Analysis of the Stoner criterion for the flat band suggests the presence of a ferromagnetic instability. The presented approach is an alternative route for obtaining flat band materials to twisting bilayer graphene which yields thermodynamically stable flat band materials in large areas.

Non-vertical optical transition in near-field enhanced spectroscopy of graphene.

We theoretically investigate the optical transition of an electron in graphene that is excited by near-field around a conical Au tip. The interaction between the near-field and the electron is calculated by tight-binding method. In the case of near-field, the wavevector of the electron changes by the optical absorption from the valence band to the conduction band. We show that the change of the wavevector is inversely proportional to the localization width of the near-field, which is given as a function of the distance between the tip and graphene. We calculate the near-field absorption probability as a function of k in the Brillouin zone.

Deep-ultraviolet Raman scattering spectroscopy of monolayer WS2.

Raman scattering measurements of monolayer WS2 are reported as a function of the laser excitation energies from the near-infrared (1.58 eV) to the deep-ultraviolet (4.82 eV). In particular, we observed several strong Raman peaks in the range of 700∼850 cm-1 with the deep-ultraviolet laser lights (4.66 eV and 4.82 eV). Using the first-principles calculations, these peaks and other weak peaks were appropriately assigned by the double resonance Raman scattering spectra of phonons around the M and K points in the hexagonal Brillouin zone. The relative intensity of the first-order [Formula: see text] to A1g peak changes dramatically with the 1.58 eV and 2.33 eV laser excitations, while the comparable relative intensity was observed for other laser energies. The disappearance of the [Formula: see text] peak with the 1.58 eV laser light comes from the fact that valley polarization of the laser light surpasses the [Formula: see text] mode since the [Formula: see text] mode is the helicity-exchange Raman mode. On the other hand, the disappearance of the A1g peak with the 2.33 eV laser light might be due to the strain effect on the electron-phonon matrix element.

Resonance Raman Spectrum of Doped Epitaxial Graphene at the Lifshitz Transition.

We employ ultra-high vacuum (UHV) Raman spectroscopy in tandem with angle-resolved photoemission (ARPES) to investigate the doping-dependent Raman spectrum of epitaxial graphene on Ir(111). The evolution of Raman spectra from pristine to heavily Cs doped graphene up to a carrier concentration of 4.4 × 1014 cm-2 is investigated. At this doping, graphene is at the onset of the Lifshitz transition and renormalization effects reduce the electronic bandwidth. The optical transition at the saddle point in the Brillouin zone then becomes experimentally accessible by ultraviolet (UV) light excitation, which achieves resonance Raman conditions in close vicinity to the van Hove singularity in the joint density of states. The position of the Raman G band of fully doped graphene/Ir(111) shifts down by ∼60 cm-1. The G band asymmetry of Cs doped epitaxial graphene assumes an unusual strong Fano asymmetry opposite to that of the G band of doped graphene on insulators. Our calculations can fully explain these observations by substrate dependent quantum interference effects in the scattering pathways for vibrational and electronic Raman scattering.

Inversion domain boundaries in MoSe2 layers.

Structural defects, including point defects, dislocation and planar defects, significantly affect the physical and chemical properties of low-dimensional materials, such as layered compounds. In particular, inversion domain boundary is an intrinsic defect surrounded by a 60° grain boundary, which significantly influences electronic transport properties. We study atomic structures of the inversion domain grain boundaries (IDBs) in layered transition metal dichalcogenides (MoSe2 and MoS2) obtained by an exfoliation method, based on the aberration-corrected scanning transmission electron microscopy observation and density functional theory (DFT) calculation. The atomic-scale observation shows that the grain boundaries consist of two different types of 4-fold ring point shared and 8-fold ring edge shared chains. The results of DFT calculations indicate that the inversion domain grain boundary behaves as a metallic one-dimensional chain embedded in the semiconducting MoSe2 matrix with the occurrence of a new state within the band gap.

Hidden symmetries in N-layer dielectric stacks.

The optical properties of a multilayer system with arbitrary N layers of dielectric media are investigated. Each layer is one of two dielectric media, with a thickness one-quarter the wavelength of light in that medium, corresponding to a central frequency f 0. Using the transfer matrix method, the transmittance T is calculated for all possible 2 N sequences for small N. Unexpectedly, it is found that instead of 2 N different values of T at f 0 (T 0), there are only [Formula: see text] discrete values of T 0, for even N, and (N + 1) for odd N. We explain this high degeneracy in T 0 values by finding symmetry operations on the sequences that do not change T 0. Analytical formulae were derived for the T 0 values and their degeneracies as functions of N and an integer parameter for each sequence we call 'charge'. Additionally, the bandwidth at f 0 and filter response of the transmission spectra are investigated, revealing asymptotic behavior at large N.