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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 WSe

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.

Many-body interactions between excitons in a transition-metal dichalcogenide bilayer drive a transition into an electron-hole liquid at high densities. Using ultrafast polarization nanoscopy, we unveil spatiotemporal dynamics of this continuous Mott transition on the nanoscale.

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., This document is the Accepted Manuscript version of a Published Work that appeared in final form in ACS Photonics (copyright \copyright American Chemical Society) after peer review and technical editing by the publisher. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acsphotonics.9b01533

Two-dimensional transition metal dichalcogenides offer a fascinating platform for creating van der Waals heterojunctions with exciting physical properties. Because of their typical type-II band alignment, photoexcited electrons and holes can separate

Excitons play a dominant role in the optoelectronic properties of atomically thin van der Waals (vdW) semiconductors. These excitons are amenable to on-demand engineering with diverse control knobs, including dielectric screening, interlayer hybridization, and moiré potentials. However, external stimuli frequently yield heterogeneous excitonic responses at the nano- and meso-scales, making their spatial characterization with conventional diffraction-limited optics a formidable task. Here, we use a scattering-type scanning near-field optical microscope (s-SNOM) to acquire exciton spectra in atomically thin transition metal dichalcogenide microcrystals with previously unattainable 20 nm resolution. Our nano-optical data revealed material- and stacking-dependent exciton spectra of MoSe2, WSe2, and their heterostructures. Furthermore, we extracted the complex dielectric function of these prototypical vdW semiconductors. s-SNOM hyperspectral images uncovered how the dielectric screening modifies excitons at length scales as short as few nanometers. This work paves the way towards understanding and manipulation of excitons in atomically thin layers at the nanoscale., Excitons play an important role in the optical properties of 2D semiconductors, but their spatial characterization is usually constrained by the diffraction limit. Here, the authors report near-field optical spectroscopy of 2D transition metal dichalcogenides with 20 nm resolution, revealing their spatially dependent excitonic spectra and complex dielectric function.

By sampling terahertz waveforms emitted from InAs surfaces, we reveal how the entire, realistic geometry of typical near-field probes drastically impacts the broadband electromagnetic fields. In the time domain, these modifications manifest as a shift in the carrier-envelope phase and emergence of a replica pulse with a time delay dictated by the length of the cantilever. This interpretation is fully corroborated by quantitative simulations of terahertz emission nanoscopy based on the finite element method. Our approach provides a solid theoretical framework for quantitative nanospectroscopy and sets the stage for a reliable description of subcycle, near-field microscopy at terahertz frequencies.

In homobilayer systems, the twist angle θ has emerged as a powerful tuning knob for tailoring novel phase transitions in atomically thin layers stacked at magic twist angles [1] – a paradigm shift for condensed-matter physics. For twisted bilayers of transition metal dichalcogenides, topological phases [2] and even potential signatures of a superconducting state [3] have been discussed. Yet, a precise understanding of the underlying Coulomb correlations has remained challenging.

Phase-locked few-cycle mid-infrared pulses trace how the twist angle alone renormalizes the binding energy of excitons in twisted WSe2 homobilayers by a factor of two and tunes their lifetime by a factor of twenty.

We introduce a novel Fourier demodulation analysis to numerically simulate a realistic near-field microscopy scenario. The new concept allows us to access the experimentally elusive, nanoscale distributions of the demodulated electromagnetic fields in multi-THz nanoscopy. We quantify the achievable lateral resolution as well as the probing volume inside the sample and visualize the scattering process into the far field.

By probing internal 1s-2p transitions with phase-locked mid-infrared pulses, we reveal the internal structure and binding energy of photo-generated excitons in transition metal dichalcogenide bilayers. Furthermore, we trace how the twist angle precisely controls the ultrafast formation of interlayer excitons and tunes excitonic hybridization in hetero- and homobilayers, respectively.

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.

We combine a novel Fourier demodulation analysis with numerical simulations of nearfield microscopy. Thereby, we quantify the experimentally inaccessible, nanoscale electric field distributions from which we infer the fundamental limits of the spatial resolution.

We retrieve the local dielectric function of a fewnanometer-thick surface layer on the three-dimensional topological insulator (Bi 0.5 Sb 0.5 ) 2 Te 3 using mid-infrared nanotomography. Thereby, we identify the contributions of two types of surface states: Band bending leads to an intersubband transition within a massive two-dimensional electron gas, which gives rise to 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 changes to the resonance frequency of the intersubband transition, pointing towards nanoscale fluctuations of the doping or the Bi-to-Sb-ratio.

Three-dimensional topological insulators (TIs) have become an interesting platform for future high-speed electronics. The massless Dirac fermions in topologically protected surface states (TSSs) feature a chiral spin texture, which gives rise to inherently low scattering rates [1,2]. However, an additional two-dimensional electron gas (2DEG) with finite mass at TI surfaces can coexist under ambient conditions [3] owing to band bending effects.

Heterostructures of atomically thin van der Waals bonded monolayers have opened a unique platform to engineer Coulomb correlations, shaping excitonic, Mott insulating, or superconducting phases. In transition metal dichalcogenide heterostructures, electrons and holes residing in different monolayers can bind into spatially indirect excitons with a strong potential for optoelectronics, valleytronics, Bose condensation, superfluidity, and moir\'e-induced nanodot lattices. Yet these ideas require a microscopic understanding of the formation, dissociation, and thermalization dynamics of correlations including ultrafast phase transitions. Here we introduce a direct ultrafast access to Coulomb correlations between monolayers; phase-locked mid-infrared pulses allow us to measure the binding energy of interlayer excitons in WSe2/WS2 hetero-bilayers by revealing a novel 1s-2p resonance, explained by a fully quantum mechanical model. Furthermore, we trace, with subcycle time resolution, the transformation of an exciton gas photogenerated in the WSe2 layer directly into interlayer excitons. Depending on the stacking angle, intra- and interlayer species coexist on picosecond scales and the 1s-2p resonance becomes renormalized. Our work provides a direct measurement of the binding energy of interlayer excitons and opens the possibility to trace and control correlations in novel artificial materials., Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Materials. The final authenticated version is available online at https://doi.org/10.1038/s41563-019-0337-0

We retrieve the local dielectric function of a few-nm-thick surface layer on a threedimensional topological insulator by mid-infrared nano-tomography and find the coexistence of a massive electron gas and the topologically protected surface states.

In heterobilayers consisting of different transition-metal dichalcogenide (TMDC) monolayers, optically excited electron-hole pairs can be spatially separated into the adjacent layers due to a type-II band alignment. However, they remain Coulomb correlated and form interlayer excitons (ILEs), which recombine radiatively. While these ILEs are observed in several TMDC material combinations, their characters and properties depend on the specific system. Herein, some of these peculiarities are demonstrated by comparing studies performed on two different heterobilayer combinations: MoS2-WSe2 and MoSe2-WSe2.

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.

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 custom-tailored (Bi

Monolayers of transition metal dichalcogenides (TMDCs) feature exceptional optical properties that are dominated by excitons, tightly bound electron-hole pairs. Forming van der Waals heterostructures by deterministically stacking individual monolayers allows to tune various properties via choice of materials and relative orientation of the layers. In these structures, a new type of exciton emerges, where electron and hole are spatially separated. These interlayer excitons allow exploration of many-body quantum phenomena and are ideally suited for valleytronic applications. Mostly, a basic model of fully spatially-separated electron and hole stemming from the $K$ valleys of the monolayer Brillouin zones is applied to describe such excitons. Here, we combine photoluminescence spectroscopy and first principle calculations to expand the concept of interlayer excitons. We identify a partially charge-separated electron-hole pair in MoS$_2$/WSe$_2$ heterostructures residing at the $\Gamma$ and $K$ valleys. 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 TMDC heterostructures and devices., Comment: Nature Physics (2018), in press [main article (letter) and Supporting Information]

Two-dimensional transition-metal dichalcogenides (TMDCs) have recently emerged as a promising class of materials. A fascinating aspect of these atomically thin crystals is the possibility of combining different TMDCs into heterostructures. For several TMDC combinations, a staggered band alignment occurs, so that optically excited electron-hole pairs are spatially separated into different layers and form interlayer excitons (IEX). Here, we report on time-resolved, low-temperature photoluminescence (PL) of these IEX in a MoSe2-WSe2 heterostructure. In the time-resolved measurements, we observe indications of IEX diffusion in an inhomogeneous potential landscape. Excitation-density-dependent measurements reveal a dipolar, repulsive exciton-exciton interaction. PL measurements in applied magnetic fields show a giant valley-selective splitting of the IEX luminescence, with an effective g factor of about -15. This large value stems from the alignment of K+ and K- valleys of the constituent monolayers in our heterostructure, making intervalley transitions optically bright, so that contributions to the field-induced splitting arising from electron and hole valley magnetic moments add up. This giant splitting enables us to generate a near-unity valley polarization of interlayer excitons even under linearly polarized excitation by applying sufficiently large magnetic fields.

In this talk I will review terahertz scanning probe microscopy with a focus on recent developments that have made experiments with simultaneous ultrafast temporal resolution and atomic spatial resolution possible. Specifically, I will discuss the underlying principle of coupling terahertz radiation to sharp metallic tips, the connection between scattering-type scanning near-field optical microscopy (SNOM) and terahertz lightwave-driven scanning tunneling microscopy (THz-STM), and the key aspects of THz-STM that enable atomic spatial resolution. Finally, as an illustrative example, I will present ultrafast THz-STM snapshots and pump-probe measurements of electron densities in selected molecular orbitals of single molecules with sub-Angstrom spatial resolution [1].

Two-dimensional materials, such as graphene or hexagonal boron nitride, provide a versatile platform for tunable nanophotonics [1,2]. The hybridization of collective electronic motion with mid-infrared photons opens new paths towards plasmon-based nano-circuitry. In contrast to the semimetal graphene, semiconducting compounds hold promise for ultrafast control of polaritons with high contrast via interband excitation of carriers. Here, we demonstrate an ultrafast plasmonic switch based on the tunable bandgap semiconductor black phosphorus (BP) for femtosecond control of surface polaritons in the mid-infrared spectral range [3]. In our custom tailored SiO 2 /BP/SiO 2 heterostructure, a hybrid surface phonon-plasmon mode is created upon photo-activation featuring ultrafast switching times (∼50 fs) along with constant energy and momentum throughout its lifetime of ∼5 ps. We trace the polariton's creation, evolution and decay using scattering-type near-field optical microscopy which allows us to map out the unique properties of the mode in time, energy and space.

Surface polaritons, which emerge from the coupling between collective electronic motion with mid-infrared photons, have made two-dimensional materials a versatile platform for nanophotonics [1,2]. Apart from the well-studied plasmonic material graphene, semiconducting layered compounds and heterostructures hold new promise for high-contrast, ultrafast control of polaritons. Here, we report on tailored structures based on black phosphorus and SiO2 with favorable properties for ultrafast nanophotonics [3]. We use femtosecond mid-infrared near-field microscopy to photo-activate a hybrid surface phonon-plasmon polariton that is nonexistent in the unexcited sample and trace its mode structure in time, energy and space. We find that the mode shows excellent coherence and is strongly confined in energy and momentum throughout its lifetime of ~5 ps. These properties combined with the superior switching speed of ~50 fs render it a promising candidate for ultrafast nano-optical devices. © OSA 2017.

Atomically strong THz fields accelerate electrons in bulk semiconductors, new 2D materials, and atomically sharp tunneling junctions. By tracking this lightwave-driven charge transport with subcycle resolution, we explore dynamical Bloch oscillations as well as quasiparticle collisions and record the first single-molecule femtosecond movie.

Field-resolved detection of ultrafast pulses in the THz (0.1–10 THz) and multi-THz (10–100 THz) spectral range has provided key insights into the dynamics of low-energy collective excitations in condensed matter systems. However, the spatial resolution of these far-field studies is intrinsically limited to the scale of the probing wavelength by diffraction. Thus, the measured optical response is an average over sub-wavelength structures such as nanoparticles, nanocrystals, nanodomains, and microscopic defects. Apertureless scattering-type near-field scanning optical microscopy (s-NSOM) [1–4] bypasses this fundamental limit by utilizing the strong confinement of the optical near-field at the apex of a sharp metal tip. We have combined ultra-sensitive, field-resolved multi-THz spectroscopy with s-NSOM to access dynamic complex conductivities on the surfaces of nanostructures with 10nm spatial resolution. Electro-optic sampling of the scattered near-field pulses enables sub-cycle detection (10 fs temporal resolution) of waveforms consisting of less than one coherent photon per pulse. We have applied our versatile microscope to two nanostructures of similar shape but vastly different composition. First, carrier dynamics were studied in indium arsenide nanowires with sub-cycle temporal resolution [1], revealing the ultrafast (< 50 fs) formation of a carrier depletion layer at the nanowire surface. Second, we studied heterogeneous local dynamics in vanadium dioxide nanowires. Vanadium dioxide is a model system for insulator-to-metal phase transitions and is promising for technological applications. In our study, we found that substrate-induced strain drives a periodic modulation of the ultrafast photoconductivity along the nanowire. Finally, we have explored the ultimate limits of THz imaging resolution using a new technique called THz scanning tunnelling microscopy [3], where THz pulses drive femtosecond local currents across an atomic-scale tunnel junction.

Surface phonons of SiO2 can couple with photogenerated plasmon polaritons in black phosphorous to make coherent transient hybrid modes with constant energy and momentum The possibility of hybridizing collective electronic motion with mid-infrared light to form surface polaritons has made van der Waals layered materials a versatile platform for extreme light confinement1,2,3,4,5 and tailored nanophotonics6,7,8. Graphene9,10 and its heterostructures11,12,13,14 have attracted particular attention because the absence of an energy gap allows plasmon polaritons to be tuned continuously. Here, we introduce black phosphorus15,16,17,18,19 as a promising new material in surface polaritonics that features key advantages for ultrafast switching. Unlike graphene, black phosphorus is a van der Waals bonded semiconductor, which enables high-contrast interband excitation of electron–hole pairs by ultrashort near-infrared pulses. Here, we design a SiO2/black phosphorus/SiO2 heterostructure in which the surface phonon modes of the SiO2 layers hybridize with surface plasmon modes in black phosphorus that can be activated by photo-induced interband excitation. Within the Reststrahlen band of SiO2, the hybrid interface polariton assumes surface-phonon-like properties, with a well-defined frequency and momentum and excellent coherence. During the lifetime of the photogenerated electron–hole plasma, coherent hybrid polariton waves can be launched by a broadband mid-infrared pulse coupled to the tip of a scattering-type scanning near-field optical microscopy set-up. The scattered radiation allows us to trace the new hybrid mode in time, energy and space. We find that the surface mode can be activated within ∼50 fs and disappears within 5 ps, as the electron–hole pairs in black phosphorus recombine. The excellent switching contrast and switching speed, the coherence properties and the constant wavelength of this transient mode make it a promising candidate for ultrafast nanophotonic devices.

We combine ultrafast field-resolved terahertz spectroscopy with scattering-type near-field scanning optical microscopy to access sub-optical-cycle dynamics on the nanoscale. We trace the oscillating electric near field from a (10 nm)3 volume on the surface of an indium arsenide nanowire with 10 fs temporal resolution, revealing the formation of a depletion layer on the nanowire surface [1]. Furthermore, we apply ultrafast terahertz nanoscopy to strained vanadium dioxide nanobeams and observe a previously unseen correlation between the local steady-state phase-switching susceptibility and the ultrafast response to below threshold photoexcitation [2]. Our findings point towards a nanoscale periodic strain profile that is frozen into the VO 2 insulating state.

We perform an optical spectroscopy study to investigate the properties of different artificial MoS$_2$ bi- and trilayer stacks created from individual monolayers by a deterministic transfer process. These twisted bi- and trilayers differ from the common 2H stacking in mineral MoS$_2$ in the relative stacking angle of adjacent layers and the interlayer distance. The combination of Raman spectroscopy, second-harmonic-generation microscopy and photoluminescence measurements allows us to determine the degree of interlayer coupling in our samples. We find that even for electronically decoupled artificial structures, which show the same valley polarization degree as the constituent MoS$_2$ monolayers at low temperatures, there is a resonant energy transfer between individual layers which acts as an effective luminescence quenching mechanism.

Collinear laser fluorescence spectroscopy has been performed on the ground and isomeric states of $^{204,206}\mathrm{Fr}$ in order to determine their spins, nuclear moments, and changes in mean-squared charge radii. A new experimental technique has been developed as part of this work which much enhances the data collection rate while maintaining the high resolution. This has permitted the extension of this study to the two isomeric states in each nucleus. The investigation of nuclear $g$ factors and mean-squared charge radii indicates that the neutron-deficient Fr isotopes lie in a transitional region from spherical towards more collective structures.

Monolayer transition-metal dichalcogenides (TMDs) have recently emerged as fascinating novel materials. Like graphene, they can easily be exfoliated from bulk crystals. Unlike graphene, they have a large and direct band gap, making them attractive for potential applications in electronics or optoelectronics. They may also allow for novel device functionalities, as the spin and valley pseudospin degrees of freedom are directly coupled and stabilized by a large spin splitting in the conduction and valence bands. The optical properties of these two-dimensional crystals are dominated by tightly bound electron-hole pairs (excitons) and more complex quasiparticles such as charged excitons (trions) and biexcitons.

Tunneling between atomic layers strongly changes the polarizability of electron-hole pairs in van der Waals heterobilayers. By monitoring this dynamics with a near-field microscope, we record subcycle nano-movies of local tunneling processes even in insulators.

Van der Waals layered materials, such as graphene, hexagonal boron nitride, and transition metal dichalcogenides, have redefined the perspectives of future ultra-compact electronics and optics on the nanoscale. Specifically, the possibility of hybridizing collective electronic motion with mid-infrared photons in so-called surface polaritons has allowed for extreme light confinement and represents a key ingredient for tailored nanophotonics [1].