Towards compact phase-matched and waveguided nonlinear optics in atomically layered semiconductors

Nonlinear frequency conversion provides essential tools for light generation, photon entanglement, and manipulation. Transition metal dichalcogenides (TMDs) possess huge nonlinear susceptibilities and 3R-stacked TMD crystals further combine broken inversion symmetry and aligned layering, representing ideal candidates to boost the nonlinear optical gain with minimal footprint. Here, we report on the efficient frequency conversion of 3R-MoS2, revealing the evolution of its exceptional second-order nonlinear processes along the ordinary (in-plane) and extraordinary (out-of-plane) directions. By measuring second harmonic generation (SHG) of 3R-MoS2 with various thickness - from monolayer (~0.65 nm) to bulk (~1 {\mu}m) - we present the first measurement of the in-plane SHG coherence length (~530 nm) at 1520 nm and achieve record nonlinear optical enhancement from a van der Waals material, >10^4 stronger than a monolayer. It is found that 3R-MoS2 slabs exhibit similar conversion efficiencies of lithium niobate, but within propagation lengths >100-fold shorter at telecom wavelengths. Furthermore, along the extraordinary axis, we achieve broadly tunable SHG from 3R-MoS2 in a waveguide geometry, revealing the coherence length in such structure for the first time. We characterize the full refractive index spectrum and quantify both birefringence components in anisotropic 3R-MoS2 crystals with near-field nano-imaging. Empowered with these data we assess the intrinsic limits of the conversion efficiency and nonlinear optical processes in 3R-MoS2 attainable in waveguide geometries. Our analysis highlights the potential of 3R-stacked TMDs for integrated photonics, providing critical parameters for designing highly efficient on-chip nonlinear optical devices including periodically poled structures, resonators, compact optical parametric oscillators and amplifiers, and optical quantum circuits

Nanoscale Near-Field Tomography of Surface States on (Bi(0.5)b(0.5))(2)Te-3

Three-dimensional topological insulators (TIs) have attracted tremendous interest for their possibility to host massless Dirac Fermions in topologically protected surface states (TSSs), which may enable new kinds of high-speed electronics. However, recent reports have outlined the importance of band bending effects within these materials, which results in an additional two-dimensional electron gas (2DEG) with finite mass at the surface. TI surfaces are also known to be highly inhomogeneous on the nanoscale, which is masked in conventional far-field studies. Here, we use near-field microscopy in the mid infrared spectral range to probe the local surface properties of customtailored (Bi0.5Sb0.5)(2)Te-3 structures with nanometer precision in all three spatial dimensions. Applying nanotomography and nanospectroscopy, we reveal a few-nanometer-thick layer of high surface conductivity and retrieve its local dielectric function without assuming any model for the spectral response. This allows us to directly distinguish between different types of surface states. An intersubband transition within the massive 2DEG formed by quantum confinement in the bent conduction band manifests itself as a sharp, surface-bound, Lorentzian-shaped resonance. An additional broadband background in the imaginary part of the dielectric function may be caused by the TSS. Tracing the intersubband resonance with nanometer spatial precision, we observe changes of its frequency, likely originating from local variations of doping or/and the mixing ratio between Bi and Sb. Our results highlight the importance of studying the surfaces of these novel materials on the nanoscale to directly access the local optical and electronic properties via the dielectric function

Twist-tailoring Coulomb correlations in van der Waals homobilayers

The recent discovery of artificial phase transitions induced by stacking monolayer materials at magic twist angles represents a paradigm shift for solid state physics. Twist-induced changes of the single-particle band structure have been studied extensively, yet a precise understanding of the underlying Coulomb correlations has remained challenging. Here we reveal in experiment and theory, how the twist angle alone affects the Coulomb-induced internal structure and mutual interactions of excitons. In homobilayers of WSe2, we trace the internal 1s-2p resonance of excitons with phase-locked mid-infrared pulses as a function of the twist angle. Remarkably, the exciton binding energy is renormalized by up to a factor of two, their lifetime exhibits an enhancement by more than an order of magnitude, and the exciton-exciton interaction is widely tunable. Our work opens the possibility of tailoring quasiparticles in search of unexplored phases of matter in a broad range of van der Waals heterostructures. The crystallographic orientation of monolayers in van der Waals multi-layers controls their electronic and optical properties. Here the authors show how the twist angle affects Coulomb correlations governing the internal structure and the mutual interaction of excitons in homobilayers of WSe2

Ultrafast Nanoscopy of High-Density Exciton Phases in WSe2

The density-driven transition of an exciton gas into an electron–hole plasma remains a compelling question in condensed matter physics. In two-dimensional transition metal dichalcogenides, strongly bound excitons can undergo this phase change after transient injection of electron–hole pairs. Unfortunately, unavoidable nanoscale inhomogeneity in these materials has impeded quantitative investigation into this elusive transition. Here, we demonstrate how ultrafast polarization nanoscopy can capture the Mott transition through the density-dependent recombination dynamics of electron–hole pairs within a WSe2 homobilayer. For increasing carrier density, an initial monomolecular recombination of optically dark excitons transitions continuously into a bimolecular recombination of an unbound electron–hole plasma above 7 × 1012 cm–2. We resolve how the Mott transition modulates over nanometer length scales, directly evidencing the strong inhomogeneity in stacked monolayers. Our results demonstrate how ultrafast polarization nanoscopy could unveil the interplay of strong electronic correlations and interlayer coupling within a diverse range of stacked and twisted two-dimensional materials

Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures

Monolayers of transition-metal dichalcogenides feature exceptional optical properties that are dominated by tightly bound electron-hole pairs, called excitons. Creating van der Waals heterostructures by deterministically stacking individual monolayers can tune various properties via the choice of materials(1) and the relative orientation of the layers(2,3). In these structures, a new type of exciton emerges where the electron and hole are spatially separated into different layers. These interlayer excitons(4-6) allow exploration of many-body quantum phenomena(7,8) and are ideally suited for valleytronic applications(9). A basic model of a fully spatially separated electron and hole stemming from the K valleys of the monolayer Brillouin zones is usually applied to describe such excitons. Here, we combine photoluminescence spectroscopy and first-principles calculations to expand the concept of interlayer excitons. We identify a partially charge-separated electron-hole pair in MoS2/WSe2 heterostructures where the hole resides at the Gamma point and the electron is located in a K valley. We control the emission energy of this new type of momentum-space indirect, yet strongly bound exciton by variation of the relative orientation of the layers. These findings represent a crucial step towards the understanding and control of excitonic effects in van der Waals heterostructures and devices

Multi-terahertz nanotomography of van der Waals quantum materials

Van der Waals quantum materials exhibit fascinating emergent phenomena governed by topology, electronic correlations, or reduced dimensionality, and have revolutionized modern solid state physics by virtue of the versatility of two-dimensional crystals. In this thesis, we build on near-field microscopy in the terahertz (THz) and mid-infrared (or multi-THz) spectral windows and develop new tools to probe the unique properties of these systems on the relevant length, energy, and time scales. First, the distribution of nanoscale electromagnetic fields in multi-THz nanoscopy is quantified by numerically solving Maxwell’s equations and introducing a novel Fourier demodulation analysis that accounts for the tip tapping motion. Thereby, we visualize the light scattering process into the far field and determine the lateral resolution as well as the probing volume inside the sample, for the first time. Second, we employ these crucial insights into quantitative nanotomography to investigate topological insulators, which are expected to host massless Dirac fermions at their surfaces. A numerical retrieval of the local dielectric function of a few-nanometer-thick surface layer without any a priori assumptions about the spectral shape allows us to identify the contributions of two types of surface states: Band bending leads to an intersubband transition within a massive two-dimensional electron gas manifesting itself as a sharp resonance. Conversely, an additional, broadband absorption background may be caused by the topologically protected surface states. Tracing the dielectric response across a nanostructure reveals local variations of the energy of the intersubband transition, pointing towards nanoscale fluctuations of the doping or the Bi-to-Sb ratio. The subwavelength access to the dielectric function should find a wide range of applications and significantly improve the microscopic understanding of quantum materials. Finally, we use subcycle THz nanoscopy to gain a spatiotemporal access to photo-carrier dynamics in transition metal dichalcogenide bilayers – a prototypical platform for studying the ramifications of Coulomb correlations and reduced dimensionality in van der Waals quantum matter. Our experiments reveal pronounced inhomogeneities of the optoelectronic properties on the nanoscale and a drastic renormalization of the carrier lifetime as the excitation density or the relative orientation of adjacent monolayers is varied. These findings set the stage for controlling light-matter interaction in van der Waals crystals on the nanometer length- and femtosecond time scale

Quantifying nanoscale electromagnetic fields in near-field microscopy by Fourier demodulation analysis

Confining light to sharp metal tips has become a versatile technique to study optical and electronic properties far below the diffraction limit. Particularly near-field microscopy in the mid-infrared spectral range has found a variety of applications in probing nanostructures and their dynamics. Yet, the ongoing quest for ultimately high spatial resolution down to the single-nanometer regime and quantitative three-dimensional nano-tomography depends vitally on a precise knowledge of the spatial distribution of the near fields emerging from the probe. Here, we perform finite element simulations of a tip with realistic geometry oscillating above a dielectric sample. By introducing a novel Fourier demodulation analysis of the electric field at each point in space, we reliably quantify the distribution of the near fields above and within the sample. Besides inferring the lateral field extension, which can be smaller than the tip radius of curvature, we also quantify the probing volume within the sample. Finally, we visualize the scattering process into the far field at a given demodulation order, for the first time, and shed light onto the nanoscale distribution of the near fields, and its evolution as the tip-sample distance is varied. Our work represents a crucial step in understanding and tailoring the spatial distribution of evanescent fields in optical nanoscopy

Giant magnetic splitting inducing near-unity valley polarization in van der Waals heterostructures

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