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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

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.

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.

We employ THz near-field microscopy to investigate ultrafast interlayer charge transfer in van der Waals heterostructures (HS) by tracing the resulting THz emission on the nanoscale. We further employ a novel concept of contact-free tunneling microscopy to monitor the interlayer electron-hole (e-h) pair population through its build up and decay, providing access to the ultrafast carrier dynamics with spatial resolution orders of magnitude better than the diffraction limit.

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.

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.

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

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.

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.

Long regarded as a model system for studying insulator-to-metal phase transitions, the correlated electron material vanadium dioxide (VO$_2$) is now finding novel uses in device applications. Two of its most appealing aspects are its accessible transition temperature ($\sim$341 K) and its rich phase diagram. Strain can be used to selectively stabilize different VO$_2$ insulating phases by tuning the competition between electron and lattice degrees of freedom. It can even break the mesoscopic spatial symmetry of the transition, leading to a quasi-periodic ordering of insulating and metallic nanodomains. Nanostructuring of strained VO$_2$ could potentially yield unique components for future devices. However, the most spectacular property of VO$_2$ - its ultrafast transition - has not yet been studied on the length scale of its phase heterogeneity. Here, we use ultrafast near-field microscopy in the mid-infrared to study individual, strained VO$_2$ nanobeams on the 10 nm scale. We reveal a previously unseen correlation between the local steady-state switching susceptibility and the local ultrafast response to below-threshold photoexcitation. These results suggest that it may be possible to tailor the local photo-response of VO$_2$ using strain and thereby realize new types of ultrafast nano-optical 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.

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].