Nano-photocurrent Mapping of Local Electronic Structure in Twisted Bilayer Graphene

Current-driven nonequilibrium electrodynamics in graphene revealed by nano-infrared imaging

Electrons in low-dimensional materials driven out of equilibrium by a strong electric field exhibit intriguing effects that have direct analogues in high-energy physics. In this work we demonstrate that two of these effects can be observed in graphene, leading to relevant implications for light-matter interactions at the nanoscale. For doped graphene, the Cherenkov emission of phonons caused by the fast flow of out-of-equilibrium electrons was found to induce direction-dependent asymmetric plasmon damping and an unexpected generation of photocurrent. For graphene close to charge neutrality, incident infrared photons were found to disrupt the creation-recombination balance of electron-hole pairs enabled by the condensed matter version of the Schwinger effect, resulting in an excess photocurrent that we term Schwinger photocurrent. Both Schwinger and Cherenkov photocurrents are different from other known light-to-current down conversions scenarios and thus expand the family of photoelectric effects in solid state devices. Through nano-infrared imaging methodology, we provide a more comprehensive view of current-driven nonequilibrium electrodynamics in graphene.

Landauer Resistivity Dipole at One-Dimensional Defect Revealed via near-Field Photocurrent Nanoscopy

The fundamental question of how to describe ohmic resistance at the nanoscale was answered by Landauer in his seminal picture of the Landauer resistivity dipole (LRD). While this picture is theoretically well understood, experimental studies remain scarce due to the need for noninvasive local probes. Here, we use the nanometer lateral resolution of near-field photocurrent imaging to thoroughly characterize a monolayer-bilayer graphene interface. Via systematic tuning of charge carrier density and current flow, we detected charge carrier accumulation around this nearly ideal one-dimensional defect due to the formation of the LRDs. We found that, at low doping levels, the photocurrent exhibits the same polarity as the applied source-drain voltage, reflecting carrier concentration changes induced by the LRDs. This signature disappears at higher charge carrier densities in agreement with the numerical calculations performed. Photocurrent nanoscopy can thus serve as a noninvasive technique to study local dissipation at hidden interfaces.

Infrared Spectroscopy for Diagnosing Superlattice Minibands in Twisted Bilayer Graphene near the Magic Angle

Twisted bilayer graphene (TBG) represents a highly tunable, strongly correlated electron system. However, understanding the single-particle band structure alone has been challenging due to a lack of spectroscopic measurements over a broad energy range. Here, we probe the band structure of TBG around the magic angle using infrared spectroscopy and reveal spectral features that originate from interband transitions. In combination with quantum transport, we connect spectral features over a broad energy range (10-700 meV) and track their evolution with the twist angle. We compare our data with calculations of the band structures obtained via the continuum model and find good agreement only when considering a variation of interlayer/intralayer tunneling parameters with the twist angle. Our analysis suggests that the magic angle also shifts due to lattice relaxation and is better defined for a wide angular range of 0.9-1.1°. Additionally, our measurements offer an optical fingerprint of the magic angle for screening heterostructures before nanofabrication.

Accelerated Nano-Optical Imaging through Sparse Sampling

The integration time and signal-to-noise ratio are inextricably linked when performing scanning probe microscopy based on raster scanning. This often yields a large lower bound on the measurement time, for example, in nano-optical imaging experiments performed using a scanning near-field optical microscope (SNOM). Here, we utilize sparse scanning augmented with Gaussian process regression to bypass the time constraint. We apply this approach to image charge-transfer polaritons in graphene residing on ruthenium trichloride (α-RuCl3) and obtain key features such as polariton damping and dispersion. Critically, nano-optical SNOM imaging data obtained via sparse sampling are in good agreement with those extracted from traditional raster scans but require 11 times fewer sampled points. As a result, Gaussian process-aided sparse spiral scans offer a major decrease in scanning time.

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Infrared nano-imaging of Dirac magnetoexcitons in graphene

Magnetic fields can have profound effects on the motion of electrons in quantum materials. Two-dimensional electron systems subject to strong magnetic fields are expected to exhibit quantized Hall conductivity, chiral edge currents and distinctive collective modes referred to as magnetoplasmons and magnetoexcitons. Generating these propagating collective modes in charge-neutral samples and imaging them at their native nanometre length scales have thus far been experimentally elusive. Here we visualize propagating magnetoexciton polaritons at their native length scales and report their magnetic-field-tunable dispersion in near-charge-neutral graphene. Imaging these collective modes and their associated nano-electro-optical responses allows us to identify polariton-modulated optical and photo-thermal electric effects at the sample edges, which are the most pronounced near charge neutrality. Our work is enabled by innovations in cryogenic near-field optical microscopy techniques that allow for the nano-imaging of the near-field responses of two-dimensional materials under magnetic fields up to 7 T. This nano-magneto-optics approach allows us to explore and manipulate magnetopolaritons in specimens with low carrier doping via harnessing high magnetic fields.

Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures

Ferroelectricity, a spontaneous and reversible electric polarization, is found in certain classes of van der Waals (vdW) materials. The discovery of ferroelectricity in twisted vdW layers provides new opportunities to engineer spatially dependent electric and optical properties associated with the configuration of moiré superlattice domains and the network of domain walls. Here, we employ near-field infrared nano-imaging and nano-photocurrent measurements to study ferroelectricity in minimally twisted WSe2. The ferroelectric domains are visualized through the imaging of the plasmonic response in a graphene monolayer adjacent to the moiré WSe2 bilayers. Specifically, we find that the ferroelectric polarization in moiré domains is imprinted on the plasmonic response of the graphene. Complementary nano-photocurrent measurements demonstrate that the optoelectronic properties of graphene are also modulated by the proximal ferroelectric domains. Our approach represents an alternative strategy for studying moiré ferroelectricity at native length scales and opens promising prospects for (opto)electronic devices.

Vertical Stress Induced Anomalous Spectral Shift of 13.17° Moiré Superlattice in Twist Bilayer Graphene

The electronic states of the twist bilayer graphene (TBG) moiré superlattice are usually regulated by the rotation angle, applied electric field, applied magnetic field, carrier concentration and applied stress, and thus exhibit novel physical properties. Squeezing, that is, applying vertical compressive stress to the graphene layers, has profound significance in regulating the photoelectric properties of the moiré superlattice and constructing optical nanodevices. This paper presents the photoelectric properties of a TBG moiré superlattice with a twist angle of 13.17° and tunability under vertical stress. Interlayer distance decreases nonlinearly with compressive stress from 0 to 10 GPa, giving rise to weakened interlayer coupling compared to a Bernal-stacked graphene bilayer and an enhanced repulsive effect between the layers. The calculated Bloch wave functions show a strong dependence on stress. With the increase in stress, the band gaps of the system present a nonlinear increase, which induces and enhances the interlayer charge transfer and leads to the redshift of the absorption spectrum of the moiré superlattice system. By analyzing the differences in the Bloch wave function and charge density differences, we explain the nature of the physical mechanism of photoelectric property change in a stress-regulated twist superlattice system. This study provides a theoretical basis for the identification of piezoelectric properties and the stress regulation of photoelectric devices based on TBG, and also provides a feasible method for regulating the performance of TBG.

Symmetry Breaking and Anomalous Conductivity in a Double-Moiré Superlattice

In a two-dimensional moiré superlattice, the atomic reconstruction of constituent layers could introduce significant modifications to the lattice symmetry and electronic structure at small twist angles. Here, we employ conductive atomic force microscopy to investigate a twisted trilayer graphene double-moiré superlattice. Two sets of moiré superlattices are observed. At neighboring domains of the large moiré, the current exhibits either 2- or 6-fold rotational symmetry, indicating delicate symmetry breaking beyond the rigid model. Moreover, an anomalous current appears at the "A-A" stacking site of the larger moiré, contradictory to previous observations on twisted bilayer graphene. Both behaviors can be understood by atomic reconstruction, and we also show that the measured current is dominated by the tip-graphene contact resistance that maps the local work function qualitatively. Our results reveal new insights of atomic reconstruction in novel moiré superlattices and opportunities for manipulating exotic quantum states on the basis of twisted van der Waals heterostructures.

Amine-Functionalized Carbon Nanodot Electrocatalysts Converting Carbon Dioxide to Methane

The electrochemical conversion of carbon dioxide (CO₂ ) to methane (CH₄ ), which can be used not only as fuel but also as a hydrogen carrier, has drawn great attention for use in supporting carbon capture and utilization. The design of active and selective electrocatalysts with exceptional CO₂ -to-CH₄ conversion efficiency is highly desirable; however, it remains a challenge. Here a molecular tuning strategy-in situ amine functionalization of nitrogen-doped graphene quantum dots (GQDs) for highly efficient CO₂ -to-CH₄ conversion is presented. Amine functionalized nitrogen-doped GQDs achieve a CH₄ Faradic efficiency (FE) of 63% and 46%, respectively, at CH₄ partial current densities of 170 and 258 mA cm^-2 , approximating to or even outperforming state-of-the-art Cu-based electrocatalysts. These GQDs also convert CO₂ to C₂ products mainly including C₂ H₄ and C₂ H₅ OH with a maximum FE of ≈10%. A systematic analysis reveals that the CH₄ yield varies linearly with amine group content, whereas the C₂ production rate is positively dependent on pyridinic N dopant content. This work provides insight into the rational design of carbon catalysts with CO₂ -to-CH₄ conversion efficiency at the industrially relevant level.

Deep Learning Analysis of Polaritonic Wave Images

Deep learning (DL) is an emerging analysis tool across the sciences and engineering. Encouraged by the successes of DL in revealing quantitative trends in massive imaging data, we applied this approach to nanoscale deeply subdiffractional images of propagating polaritonic waves in complex materials. Utilizing the convolutional neural network (CNN), we developed a practical protocol for the rapid regression of images that quantifies the wavelength and the quality factor of polaritonic waves. Using simulated near-field images as training data, the CNN can be made to simultaneously extract polaritonic characteristics and material parameters in a time scale that is at least 3 orders of magnitude faster than common fitting/processing procedures. The CNN-based analysis was validated by examining the experimental near-field images of charge-transfer plasmon polaritons at graphene/α-RuCl₃ interfaces. Our work provides a general framework for extracting quantitative information from images generated with a variety of scanning probe methods.

Rapid simulations of hyperspectral near-field images of three-dimensional heterogeneous surfaces

The scattering-type scanning near-field optical microscope (s-SNOM) has emerged as a powerful tool for resolving nanoscale inhomogeneities in laterally heterogeneous samples. However, most analytical models used to predict the scattering near-field signals are assuming homogenous landscapes (bulk materials), resulting in inconsistencies when applied to samples with more complex configurations. In this work, we combine the point-dipole model (PDM) to the finite-element method (FEM) to account for the lateral and vertical heterogeneities while keeping the computation time manageable. Full images, spectra, or hyperspectral line profiles can be simulated by calculating the self-consistent dipole radiation demodulated at higher harmonics of the tip oscillation, mimicking real experimental procedures. Using this formalism, we clarify several important yet puzzling experimental observations in near-field images on samples with rich typography and complex material compositions, heterostructures of two-dimensional material flakes, and plasmonic antennas. The developed method serves as a basis for future investigations of nano-systems with nontrivial topography.

Interface nano-optics with van der Waals polaritons

Polaritons are hybrid excitations of matter and photons. In recent years, polaritons in van der Waals nanomaterials-known as van der Waals polaritons-have shown great promise to guide the flow of light at the nanoscale over spectral regions ranging from the visible to the terahertz. A vibrant research field based on manipulating strong light-matter interactions in the form of polaritons, supported by these atomically thin van der Waals nanomaterials, is emerging for advanced nanophotonic and opto-electronic applications. Here we provide an overview of the state of the art of exploiting interface optics-such as refractive optics, meta-optics and moiré engineering-for the control of van der Waals polaritons. This enhanced control over van der Waals polaritons at the nanoscale has not only unveiled many new phenomena, but has also inspired valuable applications-including new avenues for nano-imaging, sensing, on-chip optical circuitry, and potentially many others in the years to come.

Formation of Moiré Superlattices via Surfactant/Nanosheet-Co-mediated Crystallization

Moiré superlattices (MSLs) of two-dimensional (2D) van der Waals materials have attracted considerable attention in recent years; however, studies of bottom-up growth of twisted MSL structures via solution-processed crystallization are rarely reported. Through facile one-pot solvothermal synthesis, here we demonstrate a nonclassical surfactant/nanosheet-co-mediated crystallization pathway for formation of MSL structures with two models of SnS₂ and SnSe₂. Our experimental results reveal that attractive interactions between 2D inorganic building blocks and surfactant organic molecules during the initial stage of crystallization are crucial to drive surfactant-covered nanosheets to crystallize into molecule-intercalated nanosheet aggregates. Under the high-pressure condition, further crystallograpic fusion can occur if the reaction time is prolonged, which alters the interactions of adjacent layers during the coalescence of small-grain-size 2D domains due to insertion of foreign molecules, leading to interlayer rotations. This work uncovers an interesting organic-inorganic cocrystallization growth mode and provides a novel pathway for large-scale fabrication of MSLs.

Hyperbolic enhancement of photocurrent patterns in minimally twisted bilayer graphene

Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene have been intensely studied. At small twist angle θ, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride substrate is optically hyperbolic. Our results illustrate the capabilities of the nano-photocurrent technique for probing nanoscale electronic inhomogeneities in two-dimensional materials.

Nano-imaging photoresponse in a moiré unit cell of minimally twisted bilayer graphene

Graphene-based moiré superlattices have recently emerged as a unique class of tuneable solid-state systems that exhibit significant optoelectronic activity. Local probing at length scales of the superlattice should provide deeper insight into the microscopic mechanisms of photoresponse and the exact role of the moiré lattice. Here, we employ a nanoscale probe to study photoresponse within a single moiré unit cell of minimally twisted bilayer graphene. Our measurements reveal a spatially rich photoresponse, whose sign and magnitude are governed by the fine structure of the moiré lattice and its orientation with respect to measurement contacts. This results in a strong directional effect and a striking spatial dependence of the gate-voltage response within the moiré domains. The spatial profile and carrier-density dependence of the measured photocurrent point towards a photo-thermoelectric induced response that is further corroborated by good agreement with numerical simulations. Our work shows sub-diffraction photocurrent spectroscopy is an exceptional tool for uncovering the optoelectronic properties of moiré superlattices.

Moiré metrology of energy landscapes in van der Waals heterostructures

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Plasmon-Enhanced Near-Field Chirality in Twisted van der Waals Heterostructures

It is shown that chiral plasmons, characterized by a longitudinal magnetic moment accompanying the longitudinal charge plasmon, lead to electromagnetic near-fields that are also chiral. For twisted bilayer graphene, we estimate that the near-field chirality of screened plasmons can be several orders of magnitude larger than that of the related circularly polarized light. The chirality also manifests itself in a deflection angle that is formed between the direction of the plasmon propagation and its Poynting vector. Twisted van der Waals heterostructures might thus provide a novel platform to promote enantiomer-selective physio-chemical processes in chiral molecules without the application of a magnetic field or external nanopatterning that break time-reversal, mirror plane, or inversion symmetry, respectively.