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The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder -- a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of VO2. We then apply our trained convolutional neural network architecture to new optical microscope images of a different VO2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way to using the model to control the pattern formation via, e.g., tailored hysteresis protocols. We also introduce a distribution-based confidence measure on the results of a multi-label classifier, which does not rely on adversarial training. In addition, we propose a new machine learning based criterion for diagnosing a physical system's proximity to criticality.

Among the family of transition metal dichalcogenides, 1T-TaS2 stands out for several peculiar physical properties including a rich charge density wave phase diagram, quantum spin liquid candidacy and low temperature Mott insulator phase. As 1T-TaS2 is thinned down to the few-layer limit, interesting physics emerges in this quasi 2D material. Here, using scanning near-field optical microscopy, we perform a spatial- and temperature-dependent study on the phase transitions of a few-layer thick microcrystal of 1T-TaS2. We investigate encapsulated air-sensitive 1T-TaS2 prepared under inert conditions down to cryogenic temperatures. We find an abrupt metal-to-insulator transition in this few-layer limit. Our results provide new insight in contrast to previous transport studies on thin 1T-TaS2 where the resistivity jump became undetectable, and to spatially resolved studies on non-encapsulated samples which found a gradual, spatially inhomogeneous transition. A statistical analysis suggests bimodal high and low temperature phases, and that the characteristic phase transition hysteresis is preserved down to a few-layer limit.

When two atomic layers are brought into contact at a relative twist angle, a large-scale pattern, called a moiré superlattice, emerges due to the (angular or lattice) mismatch between the layers. This has profound consequences in terms of the Hamiltonian of the system but was also considered in several publications as a means to extract the local strain tensor. While extracting the twist angle based on knowledge of the periodicity of the moiré is trivial in the case of a regular moiré pattern, in many examples in the literature, that is not the case. In particular, extracting the strain tensor and twist angle maps from a spatially varying moiré pattern is not straightforward. This article aims to provide a practical tool to extract the strain tensor and twist angle from an experimentally observable pattern. It further addresses the limitation of any such approach in the absence of additional experimental information beyond the moiré superlattice pattern.

The two natural allotropes of carbon, diamond and graphite, are extended networks of sp

The modeling of the near-field interaction in the scattering-type scanning near-field optical microscope (s-SNOM) is rapidly advancing, although an accurate yet versatile modeling framework that can be easily adapted to various complex situations is still lacking. In this work, we propose a time-efficient numerical scheme in the quasi-electrostatic limit to capture the tip-sample interaction in the near field. This method considers an extended tip geometry, which is a significant advantage compared to the previously reported method based on the point-dipole approximation. Using this formalism, we investigate, among others, nontrivial questions such as uniaxial and biaxial anisotropy in the near-field interaction, the relationship between various experimental parameters (e.g. tip radius, tapping amplitude, etc.), and the tip-dependent spatial resolution. The demonstrated method further sheds light on the understanding of the contrast mechanism in s-SNOM imaging and spectroscopy, while also representing a valuable platform for future quantitative analysis of the experimental observations.

The ability to create nanometer-scale lateral p-n junctions is essential for the next generation of two-dimensional (2D) devices. Using the charge-transfer heterostructure graphene/α-RuCl

Twisted van der Waals multilayers are widely regarded as a rich platform to access novel electronic phases, thanks to the multiple degrees of freedom such as layer thickness and twist angle that allow control of their electronic and chemical properties. Here, we propose that the stacking domains that form naturally due to the relative twist between successive layers act as an additional "knob" for controlling the behavior of these systems, and report the emergence and engineering of stacking domain-dependent surface chemistry in twisted few-layer graphene. Using mid-infrared near-field optical microscopy and atomic force microscopy, we observe a selective adhesion of metallic nanoparticles and liquid water at the domains with rhombohedral stacking configurations of minimally twisted double bi- and tri-layer graphene. Furthermore, we demonstrate that the manipulation of nanoparticles located at certain stacking domains can locally reconfigure the moir\'e superlattice in their vicinity at the {\mu}m-scale. In addition, we report first-principles simulations of the energetics of adhesion of metal atoms and water molecules on the stacking domains in an attempt to elucidate the origin of the observed selective adhesion. Our findings establish a new approach to controlling moir\'e-assisted chemistry and nanoengineering., Comment: 11 pages, 3 figures

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons—hybrids of infrared photons and lattice vibrations—form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide (MoO 3 ) and isotopically pure hexagonal boron nitride (h 11 BN). At a special frequency ω 0 , these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic-level repulsion and strong coupling.

We investigate transient nanotextured heterogeneity in vanadium dioxide (VO

The ability to perform nanometer-scale optical imaging and spectroscopy is key to deciphering the low-energy effects in quantum materials, as well as vibrational fingerprints in planetary and extraterrestrial particles, catalytic substances, and aqueous biological samples. These tasks can be accomplished by the scattering-type scanning near-field optical microscopy (s-SNOM) technique that has recently spread to many research fields and enabled notable discoveries. Herein, it is shown that the s-SNOM, together with scanning probe research in general, can benefit in many ways from artificial-intelligence (AI) and machine-learning (ML) algorithms. Augmented with AI- and ML-enhanced data acquisition and analysis, scanning probe optical nanoscopy is poised to become more efficient, accurate, and intelligent.

Polaritons in hyperbolic van der Waals materials-where principal axes have permittivities of opposite signs-are light-matter modes with unique properties and promising applications. Isofrequency contours of hyperbolic polaritons may undergo topological transitions from open hyperbolas to closed ellipse-like curves, prompting an abrupt change in physical properties. Electronically-tunable topological transitions are especially desirable for future integrated technologies but have yet to be demonstrated. In this work, we present a doping-induced topological transition effected by plasmon-phonon hybridization in graphene/α-MoO

Temperature-induced metal–insulator transition (MIT) in vanadium dioxide (VO2) has been under intense research interest for decades both theoretically and experimentally. Due to the complex nature of electron correlations, the underlying physics behind the MIT in VO2 has yet to be fully grasped. In this work, we utilize the fine resolution of the scattering-type scanning near-field optical microscope to investigate the MIT in an epitaxial VO2 thin film on the (100)R TiO2 substrate with mid-infrared light. Bidirectional tweed-like metal–insulator phase coexistence patterns are observed and understood under the Landau free energy paradigm. More interestingly, delayed metallic nucleation is observed near the surface cracks due to local strain relief. This research proposes ideas in investigating the temperature–pressure phase diagram and tuning the interplay between local strain and MIT in oxide thin films.

Two-dimensional (2D) materials can host stable, long-range magnetic phases in the presence of underlying magnetic anisotropy. The ability to realize the full potential of 2D magnets necessitates systematic investigation of the role of individual atomic layers and nanoscale inhomogeneity ($\textit{i.e.}$, strain) on the emergence and stability of both intra- and interlayer magnetic phases. Here, we report multifaceted spatial-dependent magnetism in few-layer CrSBr using magnetic force microscopy (MFM) and Monte Carlo-based magnetic simulations. We perform nanoscale visualization of the magnetic sheet susceptibility from raw MFM data and force-distance curves, revealing a characteristic onset of both intra- and interlayer magnetic correlations as a function of temperature and layer-thickness. We demonstrate that the presence of a single uncompensated layer in odd-layer terraces significantly reduces the stability of the low-temperature antiferromagnetic (AFM) phase and gives rise to multiple coexisting magnetic ground states at temperatures close to the bulk N\'eel temperature ($\textit{T}$$_N$). Furthermore, the AFM phase can be reliably suppressed using modest fields (~300 Oe) from the MFM probe, behaving as a nanoscale magnetic switch. Our prototypical study of few-layer CrSBr demonstrates the critical role of layer parity on field-tunable 2D magnetism and provides vital design criteria for future nanoscale magnetic devices. Moreover, we provide a roadmap for using MFM for nano-magnetometry of 2D materials, despite the ubiquitous absence of bulk zero-field magnetism in magnetized sheets., Comment: Main text: 30 pages, 4 figures. Supporting Information: 19 pages, 8 figures

We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The conversion is activated by applying a dc electric field that induces a density gradient or a current across the ribbon. Another scheme is degenerate four-wave mixing where the counter-propagating plasmons are emitted at the pump frequency. This third-order nonlinear process does not require a symmetry-breaking dc field. We suggest nano-optical experiments for measuring position-momentum entanglement of the emitted plasmon pairs. We estimate the critical pump fields at which the plasmon generation rates exceed their dissipation, leading to parametric instabilities., Comment: 11 pages, 8 figures

Tungsten ditelluride (WTe2) is an atomically layered transition metal dichalcogenide whose physical properties change systematically from monolayer to bilayer and few-layer versions. In this report, we use apertureless scattering-type near-field optical microscopy operating at Terahertz (THz) frequencies and cryogenic temperatures to study the distinct THz range electromagnetic responses of mono-, bi- and trilayer WTe2 in the same multi-terraced micro-crystal. THz nano-images of monolayer terraces uncovered weakly insulating behavior that is consistent with transport measurements. The near-field signal on bilayer regions shows moderate metallicity with negligible temperature dependence. Subdiffractional THz imaging data together with theoretical calculations involving thermally activated carriers favor the semimetal scenario with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \approx -10\,{{{\rm{meV}}}}$$\end{document}Δ≈−10meV over the semiconductor scenario for bilayer WTe2. Also, we observed clear metallic behavior of the near-field signal on trilayer regions. Our data are consistent with the existence of surface plasmon polaritons in the THz range confined to trilayer terraces in our specimens. Finally, data for microcrystals up to 12 layers thick reveal how the response of a few-layer WTe2 asymptotically approaches the bulk limit., The behaviour of Tungsten ditelluride (WTe2) in few-layer form is not yet fully characterized. Here the authors use a near-field terahertz microscopy technique to observe the electromagnetic responses of WTe2 flakes from one to several layers and to study their semimetallic/ semiconducting behavior.

The possibility of confining interlayer excitons in interfacial moiré patterns has recently gained attention as a strategy to form ordered arrays of zero-dimensional quantum emitters and topological superlattices in transition metal dichalcogenide heterostructures. Strain is expected to play an important role in the modulation of the moiré potential landscape, tuning the array of quantum dot-like zero-dimensional traps into parallel stripes of one-dimensional quantum wires. Here, we present real-space imaging of unstrained zero-dimensional and strain-induced one-dimensional moiré patterns along with photoluminescence measurements of the corresponding excitonic emission from WSe

The osmate pyrochlore Cd2Os2O7 supports an antiferromagnet insulator ground state with an all-in/all-out (AIAO) spin ordering at low temperature. Above 225 K, Cd2Os2O7 becomes a paramagnetic metal whereas the mechanism of this metal-to-insulator transition (MIT) remains elusive. In this letter, we use cryogenic near-field technique operating at terahertz frequencies to study the evolution of low-energy response across the MIT. We observed a systematic variation of the magnitude of nano-THz signal across the transition, consistent with the trend in the direct-current conductivity. Conducting domain walls that dominate the nano-scale landscape of the conductivity of a closely related AIAO system Nd2Ir2O7 are not apparent in Cd2Os2O7.

Significance The emergence of superconductivity in high-temperature cuprates arises out of a rich landscape of competing order. For example, stripe order can hoard the electrons needed to form Cooper pairs and establish superconductivity. Intriguingly, the complex interactions of such intertwined orders can be manipulated with light, where nonequilibrium dynamics alter the primacy of one order over another. Following photoexcitation of La2−xBaxCuO4 (x = 0.115) with near-infrared pulses, we observe a long-lived state that exhibits enhanced superconducting correlations well above the equilibrium superconducting transition temperature. Our analysis reveals that this metastable phase arises from a collapse of stripe order, providing an important demonstration of light-directed control in quantum materials., Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La2−xBaxCuO4 (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm2 results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La2−xBaxCuO4 is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

The ground-state properties of correlated electron systems can be extraordinarily sensitive to external stimuli, offering abundant platforms for functional materials. Using the multi-messenger combination of atomic force microscopy, cryogenic scanning near-field optical microscopy, magnetic force microscopy and ultrafast laser excitation, we demonstrate both 'writing' and 'erasing' of a metastable ferromagnetic metal phase in strained films of La

Unlike conventional plasmonic media, polaritonic van der Waals (vdW) materials hold promise for active control of light-matter interactions. The dispersion relations of elementary excitations such as phonons and plasmons can be tuned in layered vdW systems via stacking using functional substrates. In this work, infrared nanoimaging and nanospectroscopy of hyperbolic phonon polaritons are demonstrated in a novel vdW heterostructure combining hexagonal boron nitride (hBN) and vanadium dioxide (VO