Optical absorption is the most fundamental optical property characterizing light-matter interactions in materials and can be most readily compared with theoretical predictions. However, determination of optical absorption cross-section of individual nanostructures is experimentally challenging due to the small extinction signal using conventional transmission measurements. Recently, dramatic increase of optical contrast from individual carbon nanotubes has been successfully achieved with a polarization-based homodyne microscope, where the scattered light wave from the nanostructure interferes with the optimized reference signal (the reflected/transmitted light). Here we demonstrate high-sensitivity absorption spectroscopy for individual single-walled carbon nanotubes by combining the polarization-based homodyne technique with broadband supercontinuum excitation in transmission configuration. To our knowledge, this is the first time that high-throughput and quantitative determination of nanotube absorption cross-section over broad spectral range at the single-tube level was performed for more than 50 individual chirality-defined single-walled nanotubes. Our data reveal chirality-dependent behaviors of exciton resonances in carbon nanotubes, where the exciton oscillator strength exhibits a universal scaling law with the nanotube diameter and the transition order. The exciton linewidth (characterizing the exciton lifetime) varies strongly in different nanotubes, and on average it increases linearly with the transition energy. In addition, we establish an empirical formula by extrapolating our data to predict the absorption cross-section spectrum for any given nanotube. The quantitative information of absorption cross-section in a broad spectral range and all nanotube species not only provides new insight into the unique photophysics in one-dimensional carbon nanotubes, but also enables absolute determination of optical quantum efficiencies in important photoluminescence and photovoltaic processes.

Van der Waals (vdW) coupling is emerging as a powerful method to engineer and tailor physical properties of atomically thin two-dimensional (2D) materials. In graphene/graphene and graphene/boron-nitride structures it leads to interesting physical phenomena ranging from new van Hove singularities1-4 and Fermi velocity renormalization5, 6 to unconventional quantum Hall effects7 and Hofstadter's butterfly pattern8-12. 2D transition metal dichalcogenides (TMDCs), another system of predominantly vdW-coupled atomically thin layers13, 14, can also exhibit interesting but different coupling phenomena because TMDCs can be direct or indirect bandgap semiconductors15, 16. Here, we present the first study on the evolution of interlayer coupling with twist angles in as-grown MoS2 bilayers. We find that an indirect bandgap emerges in bilayers with any stacking configuration, but the bandgap size varies appreciably with the twist angle: it shows the largest redshift for AA- and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. The vibration frequency of the out-of-plane phonon in MoS2 shows similar twist angle dependence. Our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects, which leads to different interlayer separations between the two MoS2 layers in different stacking configurations.

Atomically thin two-dimensional (2D) layered materials, including graphene, boron nitride, and transition metal dichalcogenides (TMDs), can exhibit novel phenomena distinct from their bulk counterparts and hold great promise for novel electronic and optoelectronic applications. Controlled growth of such 2D materials with different thickness, composition, and symmetry are of central importance to realize their potential. In particular, the ability to control the symmetry of TMD layers is highly desirable because breaking the inversion symmetry can lead to intriguing valley physics, nonlinear optical properties, and piezoelectric responses. Here we report the first chemical vapor deposition (CVD) growth of spirals of layered MoS2 with atomically thin helical periodicity, which exhibits a chiral structure and breaks the three-dimensional (3D) inversion symmetry explicitly. The spirals composed of tens of connected MoS2 layers with decreasing areas: each basal plane has a triangular shape and shrinks gradually to the summit when spiraling up. All the layers in the spiral assume an AA lattice stacking, which is in contrast to the centrosymmetric AB stacking in natural MoS2 crystals. We show that the noncentrosymmetric MoS2 spiral leads to a strong bulk second-order optical nonlinearity. In addition, we found that the growth of spirals involves a dislocation mechanism, which can be generally applicable to other 2D TMD materials.

Van der Waals coupling is emerging as a powerful method to engineer physical properties of atomically thin two-dimensional materials. In coupled graphene-graphene and graphene-boron nitride layers, interesting physical phenomena ranging from Fermi velocity renormalization to Hofstadter's butterfly pattern have been demonstrated. Atomically thin transition metal dichalcogenides, another family of two-dimensional-layered semiconductors, can show distinct coupling phenomena. Here we demonstrate the evolution of interlayer coupling with twist angles in as-grown molybdenum disulfide bilayers. We find that the indirect bandgap size varies appreciably with the stacking configuration: it shows the largest redshift for AA- and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. Our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects that leads to different interlayer separations between the two molybdenum disulfide layers in different stacking configurations.

The complex optical susceptibility is the most fundamental parameter characterizing light-matter interactions and determining optical applications in any material. In one-dimensional (1D) materials, all conventional techniques to measure the complex susceptibility become invalid. Here we report a methodology to measure the complex optical susceptibility of individual 1D materials by an elliptical-polarization-based optical homodyne detection. This method is based on the accurate manipulation of interference between incident left- (right-) handed elliptically polarized light and the scattering light, which results in the opposite (same) contribution of the real and imaginary susceptibility in two sets of spectra. We successfully demonstrate its application in determining complex susceptibility of individual chirality-defined carbon nanotubes in a broad optical spectral range (1.6-2.7 eV) and under different environments (suspended and in device). This full characterization of the complex optical responses should accelerate applications of various 1D nanomaterials in future photonic, optoelectronic, photovoltaic, and bio-imaging devices.

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface¹. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device². Although related theoretical work began decades ago^1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.