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.

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.

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.

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.

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 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.

Sensitive Phonon-Based Probe for Structure Identification of 1T' MoTe2.

In this work, by combining transmission electron microscopy and polarized Raman spectroscopy for the 1T' MoTe2 flakes with different thicknesses, we found that the polarization dependence of Raman intensity is given as a function of excitation laser wavelength, phonon symmetry, and phonon frequency, but has weak dependence on the flake thickness from few-layer to multilayer. In addition, the frequency of Raman peaks and the relative Raman intensity are sensitive to flake thickness, which manifests Raman spectroscopy as an effective probe for thickness of 1T' MoTe2. Our work demonstrates that polarized Raman spectroscopy is a powerful and nondestructive method to quickly identify the crystal structure and thickness of 1T' MoTe2 simultaneously, which opens up opportunities for the in situ probe of anisotropic properties and broad applications of this novel material.

Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus.

Orthorhombic black phosphorus (BP) and other layered materials, such as gallium telluride (GaTe) and tin selenide (SnSe), stand out among two-dimensional (2D) materials owing to their anisotropic in-plane structure. This anisotropy adds a new dimension to the properties of 2D materials and stimulates the development of angle-resolved photonics and electronics. However, understanding the effect of anisotropy has remained unsatisfactory to date, as shown by a number of inconsistencies in the recent literature. We use angle-resolved absorption and Raman spectroscopies to investigate the role of anisotropy on the electron-photon and electron-phonon interactions in BP. We highlight, both experimentally and theoretically, a nontrivial dependence between anisotropy and flake thickness and photon and phonon energies. We show that once understood, the anisotropic optical absorption appears to be a reliable and simple way to identify the crystalline orientation of BP, which cannot be determined from Raman spectroscopy without the explicit consideration of excitation wavelength and flake thickness, as commonly used previously.

Quantum Effects in the Thermoelectric Power Factor of Low-Dimensional Semiconductors.

We theoretically investigate the interplay between the confinement length L and the thermal de Broglie wavelength Λ to optimize the thermoelectric power factor of semiconducting materials. An analytical formula for the power factor is derived based on the one-band model assuming nondegenerate semiconductors to describe quantum effects on the power factor of the low-dimensional semiconductors. The power factor is enhanced for one- and two-dimensional semiconductors when L is smaller than Λ of the semiconductors. In this case, the low-dimensional semiconductors having L smaller than their Λ will give a better thermoelectric performance compared to their bulk counterpart. On the other hand, when L is larger than Λ, bulk semiconductors may give a higher power factor compared to the lower dimensional ones.

Large-Area Synthesis of High-Quality Uniform Few-Layer MoTe2.

The controlled synthesis of large-area, atomically thin molybdenum ditelluride (MoTe2) crystals is crucial for its various applications based on the attractive properties of this emerging material. In this work, we developed a chemical vapor deposition synthesis to produce large-area, uniform, and highly crystalline few-layer 2H and 1T' MoTe2 films. It was found that these two different phases of MoTe2 can be grown depending on the choice of Mo precursor. Because of the highly crystalline structure, the as-grown few-layer 2H MoTe2 films display electronic properties that are comparable to those of mechanically exfoliated MoTe2 flakes. Our growth method paves the way for the large-scale application of MoTe2 in high-performance nanoelectronics and optoelectronics.

Anomalous lattice vibrations of monolayer MoS2 probed by ultraviolet Raman scattering.

We present a comprehensive Raman scattering study of monolayer MoS2 with increasing laser excitation energies ranging from the near-infrared to the deep-ultraviolet. The Raman scattering intensities from the second-order phonon modes are revealed to be enhanced anomalously by only the ultraviolet excitation wavelength 354 nm. We demonstrate theoretically that such resonant behavior arises from a strong optical absorption that forms near the Γ point and ½ΓK of the band structure and an inter-valley resonant electronic scattering by the M-point phonons. These results advance our understanding of the double resonance Raman scattering process in low-dimensional semiconducting nanomaterials and provide a foundation for the technological development of monolayer MoS2 in the ultraviolet frequency range.

Ultrafast generation of fundamental and multiple-order phonon excitations in highly enriched (6,5) single-wall carbon nanotubes.

Using a macroscopic ensemble of highly enriched (6,5) single-wall carbon nanotubes, combined with high signal-to-noise ratio and time-dependent differential transmission spectroscopy, we have generated vibrational modes in an ultrawide spectral range (10-3000 cm(-1)). A total of 14 modes were clearly resolved and identified, including fundamental modes of A, E1, and E2 symmetries and their combinational modes involving two and three phonons. Through comparison with continuous wave Raman spectra as well as calculations based on an extended tight-binding model, we were able to identify all the observed peaks and determine the frequencies of the individual and combined modes. We provide a full summary of phonon frequencies for (6,5) nanotubes that can serve as a basic reference with which to refine our understanding of nanotube phonon spectra as well as a testbed for new theoretical models.

Observation of layer-breathing mode vibrations in few-layer graphene through combination Raman scattering.

We report the observation of layer-breathing mode (LBM) vibrations in few-layer graphene (FLG) samples of thickness from two to six layers, exhibiting both Bernal (AB) and rhombohedral (ABC) stacking order. The LBM vibrations are identified using a Raman combination band lying around 1720 cm(-1). From double resonance theory, we assign the feature as the LO+ZO' combination mode of the out-of-plane LBM (ZO') and the in-plane longitudinal optical mode (LO). The LOZO' Raman band is found to exhibit multiple peaks with a unique line shape for each layer thickness and stacking order. These complex line shapes of the LOZO'-mode arise both from the material-dependent selection of different phonons in the double-resonance Raman process and from the detailed structure of the different branches of LBM in FLG.

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.

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.

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.

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.

The fermi level dependent electronic properties of the smallest (2,2) carbon nanotube.

A metal-semiconductor transition in the smallest (2,2) single-wall carbon nanotube (SWNT) is predicted theoretically as a function of gate voltage. By hole-doping (or heavy electron-doping), the energy gap of a neutral (2,2) SWNT vanishes with structural change, and the (2,2) SWNT becomes metallic. The (2,2) tube assumes a doubly degenerate ground state around the charge neutral condition with an energy barrier, while this tube has only one nondegenerate metallic ground state over an energy window of -0.12 to +0.40 eV. Because of a high density of states at the Fermi energy for hole-doped (2,2) SWNTs, a possible superconducting transition is expected.