Ultrahigh-resolution scanning microwave impedance microscopy of moiré lattices and superstructures

Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge

The Majorana fermion offers fascinating possibilities such as non-Abelian statistics and nonlocal robust qubits, and hunting it is one of the most important topics in current condensed matter physics. Most of the efforts have been focused on the Majorana bound state at zero energy in terms of scanning tunneling spectroscopy searching for the quantized conductance. On the other hand, a chiral Majorana edge channel appears at the surface of a three-dimensional topological insulator when engineering an interface between proximity-induced superconductivity and ferromagnetism. Recent advances in microwave spectroscopy of topological edge states open a new avenue for observing signatures of such Majorana edge states through the local optical conductivity. As a guide to future experiments, we show how the local optical conductivity and density of states present distinct qualitative features depending on the symmetry of the superconductivity, that can be tuned via the magnetization and temperature. In particular, the presence of the Majorana edge state leads to a characteristic nonmonotonic temperature dependence achieved by tuning the magnetization.

An Atomic-Scale Vector Network Analyzer

Electronic devices have been ever-shrinking toward atomic dimensions and have reached operation frequencies in the GHz range, thereby outperforming most conventional test equipment, such as vector network analyzers (VNA). Here the capabilities of a VNA on the atomic scale in a scanning tunneling microscope are implemented. Nonlinearities present in the voltage-current characteristic of atoms and nanostructures for phase-resolved microwave spectroscopy with unprecedented spatial resolution at GHz frequencies are exploited. The amplitude and phase response up to 9.3 GHz is determined, which permits accurate de-embedding of the transmission line and application of distortion-corrected waveforms in the tunnel junction itself. This enables quantitative characterization of the complex-valued admittance of individual magnetic iron atoms which show a lowpass response with a magnetic-field-tunable cutoff frequency.

Scanning Plasmon-Enhanced Microscopy for Simultaneous Optoelectrical Characterization

Scanning microscopy methods are crucial for the advancement of nanoelectronics. However, the vertical nanoprobes in such techniques suffer limitations such as the fragility at the tip-sample interface, complex instrumentation, and the lack of in operando functionality in several cases. Here, we introduce scanning plasmon-enhanced microscopy (SPEM) and demonstrate its capabilities on MoS2 and WSe2 nanosheets. SPEM combines a nanoparticle-on-mirror (NPoM) configuration with a portable conductive cantilever, enabling simultaneous optical and electrical characterization. This distinguishes it from other current techniques that cannot provide both characterizations simultaneously. It offers a competitive optical resolution of 600 nm with local enhancement of optical signal up to 20,000 times. A single gold nanoparticle with a 15 nm radius forms pristine, nondamaging van der Waals contact, which allows observation of unexpected p-type behavior of MoS2 at the nanoscale. SPEM reconstructs the NPoM method by eliminating the need for extensive statistical analysis and offering excellent nanoscale mapping resolution of any selected region. It surpasses other scanning techniques in combining precise optical and electrical characterization, interactive simplicity, tip durability, and reproducibility, positioning it as the optimal tool for advancing nanoelectronics.

Probing Polymorphic Stacking Domains in Mechanically Exfoliated Two-Dimensional Nanosheets Using Atomic Force Microscopy and Ultralow-Frequency Raman Spectroscopy

As one of the key features of two-dimensional (2D) layered materials, stacking order has been found to play an important role in modulating the interlayer interactions of 2D materials, potentially affecting their electronic and other properties as a consequence. In this work, ultralow-frequency (ULF) Raman spectroscopy, electrostatic force microscopy (EFM), and high-resolution atomic force microscopy (HR-AFM) were used to systematically study the effect of stacking order on the interlayer interactions as well as electrostatic screening of few-layer polymorphic molybdenum disulfide (MoS2) and molybdenum diselenide (MoSe2) nanosheets. The stacking order difference was first confirmed by measuring the ULF Raman spectrum of the nanosheets with polymorphic stacking domains. The atomic lattice arrangement revealed using HR-AFM also clearly showed a stacking order difference. In addition, EFM phase imaging clearly presented the distribution of the stacking domains in the mechanically exfoliated nanosheets, which could have arisen from electrostatic screening. The results indicate that EFM in combination with ULF Raman spectroscopy could be a simple, fast, and high-resolution method for probing the distribution of polymorphic stacking domains in 2D transition metal dichalcogenide materials. Our work might be promising for correlating the interlayer interactions of TMDC nanosheets with stacking order, a topic of great interest with regard to modulating their optoelectronic properties.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Machine Learning for Optical Scanning Probe Nanoscopy

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.

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.

Angular engineering strategy of an additional periodic phase for widely tunable phase-matched deep-ultraviolet second harmonic generation

Manipulation of the light phase lies at the heart of the investigation of light-matter interactions, especially for efficient nonlinear optical processes. Here, we originally propose the angular engineering strategy of the additional periodic phase (APP) for realization of tunable phase matching and experimentally demonstrate the widely tunable phase-matched second harmonic generation (SHG) which is expected for dozens of years. With an APP quartz crystal, the phase difference between the fundamental and frequency-doubled light is continuously angularly compensated under this strategy, which results the unprecedented and efficient frequency doubling at wavelengths almost covering the deep-UV spectral range from 221 to 332 nm. What's more, all the possible phase-matching types are originally realized simultaneously under the angular engineering phase-matching conditions. This work should not only provide a novel and practical nonlinear photonic device for tunable deep-UV radiation but also be helpful for further study of the light-matter interaction process.

Extracting the Strain Matrix and Twist Angle from the Moiré Superlattice in van der Waals Heterostructures

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.

Excitons and emergent quantum phenomena in stacked 2D semiconductors

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials.

Optical Responses of Chiral Majorana Edge States in Two-Dimensional Topological Superconductors

Majorana fermions exist on the boundaries of two-dimensional topological superconductors (TSCs) as charge-neutral quasiparticles. The neutrality makes the detection of such states challenging from both experimental and theoretical points of view. Current methods largely rely on transport measurements in which Majorana fermions manifest themselves by inducing electron-pair tunneling at the lead-contacting point. Here we show that chiral Majorana fermions in TSCs generate enhanced local optical response. The features of local optical conductivity distinguish them not only from trivial superconductors or insulators but also from normal fermion edge states such as those in quantum Hall systems. Our results provide a new applicable method to detect dispersive Majorana fermions and may lead to a novel direction of this research field.

Imaging Dual-Moiré Lattices in Twisted Bilayer Graphene Aligned on Hexagonal Boron Nitride Using Microwave Impedance Microscopy

Moiré superlattices (MSLs) formed in van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere. In this work, we directly image the moiré patterns in both monolayer and twisted bilayer graphene aligned on hexagonal boron nitride (hBN), using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ultrahigh spatial resolution (<2 nm). We observe two sets of MSLs with different periodicities in the trilayer stack. The smaller MSL breaks the 6-fold rotational symmetry and exhibits abrupt discontinuities at the boundaries of the larger MSL. Using a rigid atomic-stacking model, we demonstrate that the hBN layer considerably modifies the MSL of twisted bilayer graphene. We further analyze its effect on the reciprocal space spectrum of the dual-moiré system.

The limits of near field immersion microwave microscopy evaluated by imaging bilayer graphene moiré patterns

Near field scanning Microwave Impedance Microscopy can resolve structures as small as 1 nm using radiation with wavelengths of 0.1 m. Combining liquid immersion microscopy concepts with exquisite force control exerted on nanoscale water menisci, concentration of electromagnetic fields in nanometer-size regions was achieved. As a test material we use twisted bilayer graphene, because it provides a sample where the modulation of the moiré superstructure pattern can be systematically tuned from Ångstroms up to tens of nanometers. Here we demonstrate that a probe-to-pattern resolution of 10⁸ can be obtained by analyzing and adjusting the tip-sample distance influence on the dynamics of water meniscus formation and stability.

Here, the authors image twisted bilayer graphene using scanning microwave imaging microscopy, revealing structures with sizes down to 1 nm. They show that is possible by using spontaneously forming nanoscale water menisci that concentrates the microwave fields in small regions.