Lattice reconstruction in twisted bilayer graphene

Twisted bilayer graphene (TBG) provides a tunable platform to study emergent properties that are absent in single-layer graphene by the van der Waals (vdW) interlayer interaction. The vdW interlayer interaction can also lead to notable lattice reconstruction at the interface, promoting interlayer commensurability while minimizing intralayer lattice distortion. The lattice reconstruction in TBG is a pivotal phenomenon that significantly influences the optical and electronic properties. Currently, the study of lattice reconstruction in TBG attracts much attention in condensed matter physics. In this article, we review the experimental advances in the field of TBG lattice reconstruction. The formation and atomic-scale characterization within reconstructed TBG are overviewed comprehensively. In addition, lattice reconstruction-induced electronic modulations are introduced. Moreover, coexistence and transition between reconstructed and unreconstructed phases within a critical transition regime are described. Furthermore, we discuss the prospects of tunable reconstruction within TBG and other 2D material heterostructures.

Dynamical control of nanoscale light-matter interactions in low-dimensional quantum materials

Tip-enhanced nano-spectroscopy and -imaging have significantly advanced our understanding of low-dimensional quantum materials and their interactions with light, providing a rich insight into the underlying physics at their natural length scale. Recently, various functionalities of the plasmonic tip expand the capabilities of the nanoscopy, enabling dynamic manipulation of light-matter interactions at the nanoscale. In this review, we focus on a new paradigm of the nanoscopy, shifting from the conventional role of imaging and spectroscopy to the dynamical control approach of the tip-induced light-matter interactions. We present three different approaches of tip-induced control of light-matter interactions, such as cavity-gap control, pressure control, and near-field polarization control. Specifically, we discuss the nanoscale modifications of radiative emissions for various emitters from weak to strong coupling regime, achieved by the precise engineering of the cavity-gap. Furthermore, we introduce recent works on light-matter interactions controlled by tip-pressure and near-field polarization, especially tunability of the bandgap, crystal structure, photoluminescence quantum yield, exciton density, and energy transfer in a wide range of quantum materials. We envision that this comprehensive review not only contributes to a deeper understanding of the physics of nanoscale light-matter interactions but also offers a valuable resource to nanophotonics, plasmonics, and materials science for future technological advancements.

Ferroelectric Domain and Switching Dynamics in Curved In2Se3: First-Principles and Deep Learning Molecular Dynamics Simulations

Despite its prevalence in experiments, the influence of complex strain on material properties remains understudied due to the lack of effective simulation methods. Here, the effects of bending, rippling, and bubbling on the ferroelectric domains are investigated in an In2Se3 monolayer by density functional theory and deep learning molecular dynamics simulations. Since the ferroelectric switching barrier can be increased (decreased) by tensile (compressive) strain, automatic polarization reversal occurs in α-In2Se3 with a strain gradient when it is subjected to bending, rippling, or bubbling deformations to create localized ferroelectric domains with varying sizes. The switching dynamics depends on the magnitude of curvature and temperature, following an Arrhenius-style relationship. This study not only provides a promising solution for cross-scale studies using deep learning but also reveals the potential to manipulate local polarization in ferroelectric materials through strain engineering.

Gold Nanodrum Resonators

Nanodrum resonators have been fabricated using nanometer-thick gold films as the drumheads. The fabrication method is favorable for large-area array manufacture of arbitrary shapes. The drum resonators exhibit fundamental mode vibration frequencies in the MHz regime. We use the stretched-plate model to describe the natural vibrations of the drum. The Q factor of the fundamental mode increases as the thickness of the drum increases and decreases as the drum diameter goes up. The highest Q factor of the fundamental mode reaches 290 at room temperature and atmospheric pressure. Based on the deduced material properties we estimate that the resonator has a mass sensitivity of 1.11 × 10-22 g/Hz.

Topological Flat Bands in Strained Graphene: Substrate Engineering and Optical Control

The discovery of correlated phases in twisted moiré superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing substrates for tailored properties is hindered by the incomplete understanding of the relationship between the substrate's shapes and the electronic properties of the deposited materials. By analyzing effective models of graphene under periodic deformations with generic crystalline profiles, we identify strong C2z symmetry breaking as the critical substrate geometric feature for emerging energy gaps and quasi-flat bands. We find continuous strain profiles producing connected pseudomagnetic field landscapes are important for band topology. We show that the resultant electronic and topological properties from a substrate can be controlled with circularly polarized light, which also offers unique signatures for identifying the band topology imprinted by strain. Our results can guide experiments on strain engineering for exploring interesting transport and topological phenomena.

In-situ atomic level observation of the strain response of graphene lattice

Strain is inevitable in two-dimensional (2D) materials, regardless of whether the film is suspended or supported. However, the direct measurement of strain response at the atomic scale is challenging due to the difficulties of maintaining both flexibility and mechanical stability at low temperature under UHV conditions. In this work, we have implemented a compact nanoindentation system with a size of [Formula: see text] 160 mm[Formula: see text] [Formula: see text] 5.2 mm in a scanning tunneling microscope (STM) sample holder, which enables the reversible control of strain and gate electric field. A combination of gearbox and piezoelectric actuator allowed us to modulate the depth of the indentation continuously with nanometer precision. The 2D materials were transferred onto the polyimide film. Pd clamp was used to enhance the strain transfer from the polyimide from to the 2D layers. Using this unique technique, strain response of graphene lattice were observed at atomic precision. In the relaxed graphene, strain is induced mainly by local curvature. However, in the strained graphene with tented structure, the lattice parameters become more sensitive to the indentor height change and stretching strain is increased additionally. Moreover, the gate controllability is confirmed by measuring the dependence of the STM tip height on gate voltage.

Enhanced Crystallinity of Covalent Organic Frameworks Formed Under Physical Confinement by Exfoliated Graphene

The polymerization of 1,4-benzenediboronic acid (BDBA) on mica to form a covalent organic framework (COF-1) reveals a dramatic increase in crystallinity when physically confined by exfoliated graphene. COF-1 domains formed under graphene confinement are highly geometric in shape and on the order of square micrometers in size, while outside of the exfoliated flakes, the COF-1 does not exhibit long-range mesoscale structural order, according to atomic force microscopy imaging. Micro-Fourier transform infrared spectroscopy confirms the presence of COF-1 both outside and underneath the exfoliated graphene flakes, and density functional theory calculations predict that higher mobility and self-assembly are not causes of this higher degree of crystallinity for the confined COF-1 domains. The most likely origin of the confined COF-1's substantial increase in crystallinity is from enhanced dynamic covalent crystallization due to the water confined beneath the graphene flake.

Electron transport properties of graphene quantum dots with non-centro-symmetric Gaussian deformation

A theoretical investigation on electron transport properties of rectangular graphene quantum dots (GQDs) with non-centro-symmetric out-of-plane Gaussian deformation of elliptic type is presented. Different levels of deformation are explored to estimate system geometry optimal for potential electronic applications. Electronic properties of deformed GQDs are studied in terms of local density of states (LDOS), band-gap opening and equilibrium ballistic conductance. In particular, it was observed that the symmetry of spatial LDOS structure is directly linked with the symmetry of properly defined local strain field (LSF) map, for a wide energy range. The relationship confirms qualitatively predictions obtained on the basis of the concept of a pseudomagnetic field, used in continuum models of graphene, including strain induced effects. The conductance spectra of deformed GQD as a device connected to semi-infinite graphene armchair nanoribbons as reservoirs are studied in a frame of tight-binding (TB) model in combination with non-equilibrium Green's-functions technique (NEGF).

Coupling nanobubbles in 2D lateral heterostructures

Two-dimensional transition metal dichalcogenides provide flexible platforms for nanophotonic engineering due to their exceptional mechanical and optoelectronic properties. For example, continuous band gap tunability has been achieved in 2D TMDs by elastic strain engineering. Localized elastic deformations in nanobubbles behave as "artificial atoms" with a spatially varying band gap resulting in funnelling of excitons and photocarriers. Here we present a new method of nanobubble fabrication in monolayer 2D lateral heterostructures using high temperature superacid treatment. We fabricated MoS₂ and WS₂ nanobubbles and performed near-field imaging with nanoscale resolution using tip-enhanced photoluminescence (TEPL) spectroscopy. TEPL nanoimaging revealed the coupling between MoS₂ and WS₂ nanobubbles with a large synergistic PL enhancement due to the plasmonic tip, hot electrons, and exciton funnelling. We investigated the contributions of different enhancement mechanisms, and developed a quantum plasmonic model, in good agreement with the experiments. Our work opens new avenues in exploration of novel nanophotonic coupling schemes.

Ultrasharp Lateral p-n Junctions in Modulation-Doped Graphene

We demonstrate ultrasharp (≲10 nm) lateral p-n junctions in graphene using electronic transport, scanning tunneling microscopy, and first-principles calculations. The p-n junction lies at the boundary between differentially doped regions of a graphene sheet, where one side is intrinsic and the other is charge-doped by proximity to a flake of α-RuCl₃ across a thin insulating barrier. We extract the p-n junction contribution to the device resistance to place bounds on the junction width. We achieve an ultrasharp junction when the boundary between the intrinsic and doped regions is defined by a cleaved crystalline edge of α-RuCl₃ located 2 nm from the graphene. Scanning tunneling spectroscopy in heterostructures of graphene, hexagonal boron nitride, and α-RuCl₃ shows potential variations on a sub 10 nm length scale. First-principles calculations reveal that the charge-doping of graphene decays sharply over just nanometers from the edge of the α-RuCl₃ flake.

The Magnetic Genome of Two-Dimensional van der Waals Materials

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Large-area nanoengineering of graphene corrugations for visible-frequency graphene plasmons

Quantum confinement of the charge carriers of graphene is an effective way to engineer its properties. This is commonly realized through physical edges that are associated with the deterioration of mobility and strong suppression of plasmon resonances. Here, we demonstrate a simple, large-area, edge-free nanostructuring technique, based on amplifying random nanoscale structural corrugations to a level where they efficiently confine charge carriers, without inducing significant inter-valley scattering. This soft confinement allows the low-loss lateral ultra-confinement of graphene plasmons, scaling up their resonance frequency from the native terahertz to the commercially relevant visible range. Visible graphene plasmons localized into nanocorrugations mediate much stronger light-matter interactions (Raman enhancement) than previously achieved with graphene, enabling the detection of specific molecules from femtomolar solutions or ambient air. Moreover, nanocorrugated graphene sheets also support propagating visible plasmon modes, as revealed by scanning near-field optical microscopy observation of their interference patterns.

Developing Graphene-Based Moiré Heterostructures for Twistronics

Graphene-based moiré heterostructures are strongly correlated materials, and they are considered to be an effective platform to investigate the challenges of condensed matter physics. This is due to the distinct electronic properties that are unique to moiré superlattices and peculiar band structures. The increasing research on strongly correlated physics via graphene-based moiré heterostructures, especially unconventional superconductors, greatly promotes the development of condensed matter physics. Herein, the preparation methods of graphene-based moiré heterostructures on both in situ growth and assembling monolayer 2D materials are discussed. Methods to improve the quality of graphene and optimize the transfer process are presented to mitigate the limitations of low-quality graphene and damage caused by the transfer process during the fabrication of graphene-based moiré heterostructures. Then, the topological properties in various graphene-based moiré heterostructures are reviewed. Furthermore, recent advances regarding the factors that influence physical performances via a changing twist angle, the exertion of strain, and regulation of the dielectric environment are presented. Moreover, various unique physical properties in graphene-based moiré heterostructures are demonstrated. Finally, the challenges faced during the preparation and characterization of graphene-based moiré heterostructures are discussed. An outlook for the further development of moiré heterostructures is also presented.

Oscillations of the Spacing between van Hove Singularities Induced by sub-Ångstrom Fluctuations of Interlayer Spacing in Graphene Superlattices

Physical properties of two-dimensional van der Waals (vdWs) structures depend sensitively on both stacking orders and interlayer interactions. Yet, in most cases studied to date, the interlayer interaction is considered to be a "static" property of the vdWs structures. Here we demonstrate that applying a scanning tunneling microscopy (STM) tip pulse on twisted bilayer graphene (TBG) can induce sub-Ångstrom fluctuations of the interlayer separation in the TBG, which are equivalent to dynamic vertical external pressure of about 10 GPa on the TBG. The sub-Ångstrom fluctuations of the interlayer separation result in large oscillations of the energy separations between two van Hove singularities (VHSs) in the TBG. The period of the oscillations of the VHSs spacing is extremely long, about 500-1000 sec, attributing to tip-induced local stress in the atomic-thick TBG. Our result provides an efficient method to tune and measure the physical properties of the vdWs structures dynamically.

Mechanisms of Spontaneous Curvature Inversion in Compressed Graphene Ripples for Energy Harvesting Applications via Molecular Dynamics Simulations

Electrically conductive, highly flexible graphene membranes hold great promise for harvesting energy from ambient vibrations. For this study, we built numerous three-dimensional graphene ripples, with each featuring a different amount of compression, and performed molecular dynamics simulations at elevated temperatures. These ripples have a convex cosine shape, then spontaneously invert their curvature to concave. The average time between inversion events increases with compression. We use this to determine how the energy barrier height depends on strain. A typical convex-to-concave curvature inversion process begins when the ripple's maximum shifts sideways from the normal central position toward the fixed outer edge. The ripple's maximum does not simply move downward toward its concave position. When the ripple's maximum moves toward the outer edge, the opposite side of the ripple is pulled inward and downward, and it passes through the fixed outer edge first. The ripple's maximum then quickly flips to the opposite side via snap-through buckling. This trajectory, along with local bond flexing, significantly lowers the energy barrier for inversion. The large-scale coherent movement of ripple atoms during curvature inversion is unique to two-dimensional materials. We demonstrate how this motion can induce an electrical current in a nearby circuit.

Electric-Field Control of a Single-Atom Polar Bond

We expose the polar covalent bond between a single Au atom terminating the apex of an atomic force microscope tip and a C atom of graphene on SiC(0001) to an external electric field. For one field orientation, the Au─C bond is strong enough to sustain the mechanical load of partially detached graphene, while for the opposite orientation, the bond breaks easily. Calculations based on density-functional theory and nonequilibrium Green's function methods support the experimental observations by unveiling bond forces that reflect the polar character of the bond. Field-induced charge transfer between the atomic orbitals modifies the polarity of the different electronegative reaction partners and the Au─C bond strength.

Numerical quasiconformal transformations for electron dynamics on strained graphene surfaces

The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly obtained, but the resulting Dirac equation is intricate for general surface deformations. Two different strategies are introduced to simplify this problem: the diagonal metric approximation and the change of variables to isothermal coordinates. These coordinates are obtained from quasiconformal transformations characterized by the Beltrami equation, whose solution gives the mapping between both coordinate systems. To implement this second strategy, a least-squares finite-element numerical scheme is introduced to solve the Beltrami equation. The Dirac equation is then solved via an accurate pseudospectral numerical method in the pseudo-Hermitian representation that is endowed with explicit unitary evolution and conservation of the norm. The two approaches are compared and applied to the scattering of electrons on Gaussian shaped graphene surface deformations. It is demonstrated that electron wave packets can be focused by these local strained regions.

Strain Investigation on Spin-Dependent Transport Properties of γ-Graphyne Nanoribbon Between Gold Electrodes

Strain engineering has become one of the effective methods to tune the electronic structures of materials, which can be introduced into the molecular junction to induce some unique physical effects. The various γ-graphyne nanoribbons (γ-GYNRs) embedded between gold (Au) electrodes with strain controlling have been designed, involving the calculation of the spin-dependent transport properties by employing the density functional theory. Our calculated results exhibit that the presence of strain has a great effect on transport properties of molecular junctions, which can obviously enhance the coupling between the γ-GYNR and Au electrodes. We find that the current flowing through the strained nanojunction is larger than that of the unstrained one. What is more, the length and strained shape of the γ-GYNR serves as the important factors which affect the transport properties of molecular junctions. Simultaneously, the phenomenon of spin-splitting occurs after introducing strain into nanojunction, implying that strain engineering may be a new means to regulate the electron spin. Our work can provide theoretical basis for designing of high performance graphyne-based devices in the future.

Mutually Reinforced Polymer-Graphene Bilayer Membranes for Energy-Efficient Acoustic Transduction

Graphene holds promise for thin, ultralightweight, and high-performance nanoelectromechanical transducers. However, graphene-only devices are limited in size due to fatigue and fracture of suspended graphene membranes. Here, a lightweight, flexible, transparent, and conductive bilayer composite of polyetherimide and single-layer graphene is prepared and suspended on the centimeter scale with an unprecedentedly high aspect ratio of 10⁵ . The coupling of the two components leads to mutual reinforcement and creates an ultrastrong membrane that supports 30 000 times its own weight. Upon electromechanical actuation, the membrane pushes a massive amount of air and generates high-quality acoustic sound. The energy efficiency is ≈10-100 times better than state-of-the-art electrodynamic speakers. The bilayer membrane's combined properties of electrical conductivity, mechanical strength, optical transparency, thermal stability, and chemical resistance will promote applications in electronics, mechanics, and optics.

Tunable Lattice Reconstruction, Triangular Network of Chiral One-Dimensional States, and Bandwidth of Flat Bands in Magic Angle Twisted Bilayer Graphene

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θ_{c}. Experimentally, the θ_{c} is demonstrated to be very close to the magic angle (θ≈1.08°). Here we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunneling microscopy (STM). Our experiment demonstrates that both structures are stable in the TBG around the magic angle. By using a STM tip, we show that the two structures can be changed to each other and a triangular network of chiral one-dimensional states hosted by domain boundaries can be switched on and off. Consequently, the bandwidth of the flat band, which plays a vital role in the emergent strongly correlated states in the magic angle TBG, is tuned. This provides an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

Effect of carbon doping on electromechanical response of boron nitride nanosheets

The electromechanical response of hexagonal-boron nitride nanosheets (h-BNSs) was studied via molecular dynamics simulations (MDS) with a three-body Tersoff potential force field using a charge-dipole (C-D) potential model. Carbon (C)-doped h-BNSs with triangular, trapezoidal and circular pores were considered. The elastic and piezoelectric coefficients of h-BNSs under tension and shear loading conditions were determined. The induced polarization in h-BNSs was found to depend on the local arrangement of C atoms around B and N atoms, and the polarization increases if C atoms are surrounded by N atoms. This is attributed to the generation of higher dipole moments due to C-N bonds compared with C-B bonds. At ∼5.5% C-doping concentration, the axial piezoelectric coefficient of doped h-BNSs with triangular and trapezoidal pores increased by 18.5% and 3.5%, respectively, while it reduced by 22.5% in the case of circular pores compared to pristine h-BNS. The shear piezoelectric coefficient of C-doped h-BNSs with triangular and trapezoidal pores increased by 20.5% and 1%, respectively, while it reduced by 7% in case of circular pores. Young's moduli of C-doped h-BNSs with triangular, trapezoidal and circular pores increased by 9%, 7.5% and 5.5%, respectively, due to the C-C bonds being stronger than all other bonds. The respective improvements in shear moduli are 8.5%, 5% and 5%. The elastic and piezoelectric properties of armchair h-BNSs were found to be higher than zigzag h-BNSs. The results also reveal that the piezoelectric coefficient increases as doping increases; it reaches its maximum value around 0.41 C m^-2 at 12.6% C-doping concentration and then starts decreasing. The present work shows that we can engineer the electromechanical response of h-BNSs via novel pathways such as different types and size of pores as well as C-doping concentration to suit a particular nanoelectromechanical systems (NEMS) application.

Fluctuation-induced current from freestanding graphene

At room temperature, micron-sized sheets of freestanding graphene are in constant motion, even in the presence of an applied bias voltage. We quantify the out-of-plane movement by collecting the displacement current using a nearby small-area metal electrode and present an Ito-Langevin model for the motion coupled to a circuit containing diodes. Numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero. However, there is power dissipated by the load resistor, and its time average is exactly equal to the power supplied by the thermal bath. The exact power formula is similar to Nyquist's noise power formula, except that the rate of change of diode resistance significantly boosts the output power, and the movement of the graphene shifts the power spectrum to lower frequencies. We have calculated the equilibrium average of the power by asymptotic and numerical methods. Excellent agreement is found between experiment and theory.

Graphene Hybrid Structures for Integrated and Flexible Optoelectronics

Graphene (Gr) has many unique properties including gapless band structure, ultrafast carrier dynamics, high carrier mobility, and flexibility, making it appealing for ultrafast, broadband, and flexible optoelectronics. To overcome its intrinsic limit of low absorption, hybrid structures are exploited to improve the device performance. Particularly, van der Waals heterostructures with different photosensitive materials and photonic structures are very effective for improving photodetection and modulation efficiency. With such hybrid structures, Gr hybrid photodetectors can operate from ultraviolet to terahertz, with significantly improved R (up to 10⁹ A W^-1 ) and bandwidth (up to 128 GHz). Furthermore, integration of Gr with silicon (Si) complementary metal-oxide-semiconductor (CMOS) circuits, the human body, and soft tissues is successfully demonstrated, opening promising opportunities for wearable sensors and biomedical electronics. Here, the recent progress in using Gr hybrid structures toward high-performance photodetectors and integrated optoelectronic applications is reviewed.

Flat Bands and Mechanical Deformation Effects in the Moiré Superlattice of MoS2-WSe2 Heterobilayers

It has recently been shown that quantum-confined states can appear in epitaxially grown van der Waals material heterobilayers without a rotational misalignment (θ = 0°), associated with flat bands in the Brillouin zone of the moiré pattern formed due to the lattice mismatch of the two layers. Peaks in the local density of states and confinement in a MoS₂/WSe₂ system was qualitatively described only considering local stacking arrangements, which cause band edge energies to vary spatially. In this work, we report the presence of large in-plane strain variation across the moiré unit cell of a θ = 0° MoS₂/WSe₂ heterobilayer and show that inclusion of strain variation and out-of-plane displacement in density functional theory calculations greatly improves their agreement with the experimental data. We further explore the role of a twist angle by showing experimental data for a twisted MoS₂/WSe₂ heterobilayer structure with a twist angle of θ = 15°, which exhibits a moiré pattern but no confinement.

New imaging modes for analyzing suspended ultra-thin membranes by double-tip scanning probe microscopy

Scanning probe microscopy (SPM) techniques are amongst the most important and versatile experimental methods in surface- and nanoscience. Although their measurement principles on rigid surfaces are well understood and steady progress on the instrumentation has been made, SPM imaging on suspended, flexible membranes remains difficult to interpret. Due to the interaction between the SPM tip and the flexible membrane, morphological changes caused by the tip can lead to deformations of the membrane during scanning and hence significantly influence measurement results. On the other hand, gaining control over such modifications can allow to explore unknown physical properties and functionalities of such membranes. Here, we demonstrate new types of measurements that become possible with two SPM instruments (atomic force microscopy, AFM, and scanning tunneling microscopy, STM) that are situated on opposite sides of a suspended two-dimensional (2D) material membrane and thus allow to bring both SPM tips arbitrarily close to each other. One of the probes is held stationary on one point of the membrane, within the scan area of the other probe, while the other probe is scanned. This way new imaging modes can be obtained by recording a signal on the stationary probe as a function of the position of the other tip. The first example, which we term electrical cross-talk imaging (ECT), shows the possibility of performing electrical measurements across the membrane, potentially in combination with control over the forces applied to the membrane. Using ECT, we measure the deformation of the 2D membrane around the indentation from the AFM tip. In the second example, which we term mechanical cross-talk imaging (MCT), we disentangle the mechanical influence of a scanning probe tip (e.g. AFM) on a freestanding membrane by means of independently recording the response of the opposing tip. In this way we are able to separate the tip-induced membrane deformation topography from the (material-dependent) force between the tip and the membrane. Overall, the results indicate that probing simultaneously both surfaces of ultra-thin membranes, such as suspended 2D materials, could provide novel insights into the electronic properties of the materials.

Tunable magnetism of a single-carbon vacancy in graphene

Creating a single-carbon vacancy introduces (quasi-)localized states for both σ and π electrons in graphene. Theoretically, interactions between the localized σ electrons and quasilocalized π electrons of a single-carbon vacancy in graphene are predicted to control its magnetism. However, experimentally confirming this prediction through manipulating the interactions remains an outstanding challenge. Here we report the manipulation of magnetism in the vicinity of an individual single-carbon vacancy in graphene by using a scanning tunnelling microscopy (STM) tip. Our spin-polarized STM measurements, complemented by density functional theory calculations, indicate that the interactions between the localized σ and quasilocalized π electrons could split the π electrons into two states with opposite spins even when they are well above the Fermi level. Via the STM tip, we successfully manipulate both the magnitude and direction of magnetic moment of the π electrons with respect to that of the σ electrons. Three different magnetic states of the single-carbon vacancy, exhibiting magnetic moments of about 1.6 μ_B, 0.5 μ_B, and 0 μ_B respectively, are realized in our experiment.

Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene

A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report a definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moiré patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic fields can be fine-tuned by both the rotation angle and heterostrain. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.

Strain Engineering of 2D Materials: Issues and Opportunities at the Interface

Triggered by the growing needs of developing semiconductor devices at ever-decreasing scales, strain engineering of 2D materials has recently seen a surge of interest. The goal of this principle is to exploit mechanical strain to tune the electronic and photonic performance of 2D materials and to ultimately achieve high-performance 2D-material-based devices. Although strain engineering has been well studied for traditional semiconductor materials and is now routinely used in their manufacturing, recent experiments on strain engineering of 2D materials have shown new opportunities for fundamental physics and exciting applications, along with new challenges, due to the atomic nature of 2D materials. Here, recent advances in the application of mechanical strain into 2D materials are reviewed. These developments are categorized by the deformation modes of the 2D material-substrate system: in-plane mode and out-of-plane mode. Recent state-of-the-art characterization of the interface mechanics for these 2D material-substrate systems is also summarized. These advances highlight how the strain or strain-coupled applications of 2D materials rely on the interfacial properties, essentially shear and adhesion, and finally offer direct guidelines for deterministic design of mechanical strains into 2D materials for ultrathin semiconductor applications.

Programmable graphene nanobubbles with three-fold symmetric pseudo-magnetic fields

Graphene nanobubbles (GNBs) have attracted much attention due to the ability to generate large pseudo-magnetic fields unattainable by ordinary laboratory magnets. However, GNBs are always randomly produced by the reported protocols, therefore, their size and location are difficult to manipulate, which restricts their potential applications. Here, using the functional atomic force microscopy (AFM), we demonstrate the ability to form programmable GNBs. The precision of AFM facilitates the location definition of GNBs, and their size and shape are tuned by the stimulus bias of AFM tip. With tuning the tip voltage, the bubble contour can gradually transit from parabolic to Gaussian profile. Moreover, the unique three-fold symmetric pseudo-magnetic field pattern with monotonous regularity, which is only theoretically predicted previously, is directly observed in the GNB with an approximately parabolic profile. Our study may provide an opportunity to study high magnetic field regimes with the designed periodicity in two dimensional materials.

Asymmetric 3D Elastic-Plastic Strain-Modulated Electron Energy Structure in Monolayer Graphene by Laser Shocking

Graphene has a great potential to replace silicon in prospective semiconductor industries due to its outstanding electronic and transport properties; nonetheless, its lack of energy bandgap is a substantial limitation for practical applications. To date, straining graphene to break its lattice symmetry is perhaps the most efficient approach toward realizing bandgap tunability in graphene. However, due to the weak lattice deformation induced by uniaxial or in-plane shear strain, most strained graphene studies have yielded bandgaps <1 eV. In this work, a modulated inhomogeneous local asymmetric elastic-plastic straining is reported that utilizes GPa-level laser shocking at a high strain rate (dε/dt) ≈ 10⁶ -10⁷ s^-1 , with excellent formability, inducing tunable bandgaps in graphene of up to 2.1 eV, as determined by scanning tunneling spectroscopy. High-resolution imaging and Raman spectroscopy reveal strain-induced modifications to the atomic and electronic structure in graphene and first-principles simulations predict the measured bandgap openings. Laser shock modulation of semimetallic graphene to a semiconducting material with controllable bandgap has the potential to benefit the electronic and optoelectronic industries.

The qPlus sensor, a powerful core for the atomic force microscope

Atomic force microscopy (AFM) was introduced in 1986 and has since made its way into surface science, nanoscience, chemistry, biology, and material science as an imaging and manipulating tool with a rising number of applications. AFM can be employed in ambient and liquid environments as well as in vacuum and at low and ultralow temperatures. The technique is an offspring of scanning tunneling microscopy (STM), where the tunneling tip of the STM is replaced by using a force sensor with an attached tip. Measuring the tiny chemical forces that act between the tip and the sample is more difficult than measuring the tunneling current in STM. Therefore, even 30 years after the introduction of AFM, progress in instrumentation is substantial. Here, we focus on the core of the AFM, the force sensor with its tip and detection mechanism. Initially, force sensors were mainly micro-machined silicon cantilevers, mainly using optical methods to detect their deflection. The qPlus sensor, originally based on a quartz tuning fork and now custom built from quartz, is self-sensing by utilizing the piezoelectricity of quartz. The qPlus sensor allows us to perform STM and AFM in parallel, and the spatial resolution of its AFM channel has reached the subatomic level, exceeding the resolution of STM. Frequency modulation AFM (FM-AFM), where the frequency of an oscillating cantilever is altered by the gradient of the force that acts between the tip and the sample, has emerged over the years as the method that provides atomic and subatomic spatial resolution as well as force spectroscopy with sub-piconewton sensitivity. FM-AFM is precise; because of all physical observables, time and frequency can be measured by far with the greatest accuracy. By design, FM-AFM clearly separates conservative and dissipative interactions where conservative forces induce a frequency shift and dissipative interactions alter the power needed to maintain a constant oscillation amplitude of the cantilever. As it operates in a noncontact mode, it enables simultaneous AFM and STM measurements. The frequency stability of quartz and the small oscillation amplitudes that are possible with stiff quartz sensors optimize the signal to noise ratio. Here, we discuss the operating principles, the assembly of qPlus sensors, amplifiers, limiting factors, and applications. Applications encompass unprecedented subatomic spatial resolution, the measurement of forces that act in atomic manipulation, imaging and spectroscopy of spin-dependent forces, and atomic resolution of organic molecules, graphite, graphene, and oxides.

Folding 2D Structures into 3D Configurations at the Micro/Nanoscale: Principles, Techniques, and Applications

Compared to their 2D counterparts, 3D micro/nanostructures show larger degrees of freedom and richer functionalities; thus, they have attracted increasing attention in the past decades. Moreover, extensive applications of 3D micro/nanostructures are demonstrated in the fields of mechanics, biomedicine, optics, etc., with great advantages. However, the mainstream micro/nanofabrication technologies are planar ones; therefore, they cannot be used directly for the construction of 3D micro/nanostructures, making 3D fabrication at the micro/nanoscale a great challenge. A promising strategy to overcome this is to combine the state-of-the-art planar fabrication techniques with the folding method to produce 3D structures. In this strategy, 2D components can be easily produced by traditional planar techniques, and then, 3D structures are constructed by folding each 2D component to specific orientations. In this way, not only will the advantages of existing planar techniques, such as high precision, programmable patterning, and mass production, be preserved, but the fabrication capability will also be greatly expanded without complex and expensive equipment modification/development. The goal here is to highlight the recent progress of the folding method from the perspective of principles, techniques, and applications, as well as to discuss the existing challenges and future prospectives.

Interface-Governed Deformation of Nanobubbles and Nanotents Formed by Two-Dimensional Materials

Nanoblisters such as nanobubbles and nanotents formed by two-dimensional (2D) materials have been extensively exploited for strain engineering purposes as they can produce self-sustained, nonuniform in-plane strains through out-of-plane deformation. However, deterministic measure and control of strain fields in these systems are challenging because of the atomic thinness and unconventional interface behaviors of 2D materials. Here, we experimentally characterize a simple and unified power law for the profiles of a variety of nanobubbles and nanotents formed by 2D materials such as graphene and MoS_{2} layers. Using membrane theory, we analytically unveil what sets the in-plane strains of these blisters regarding their shape and interface characteristics. Our analytical solutions are validated by Raman spectroscopy measured strain distributions in bulged graphene bubbles supported by strong and weak shear interfaces. We advocate that both the strain magnitudes and distributions can be tuned by 2D material-substrate interface adhesion and friction properties.

Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20-30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

Strain Modulation of Graphene by Nanoscale Substrate Curvatures: A Molecular View

Spatially nonuniform strain is important for engineering the pseudomagnetic field and band structure of graphene. Despite the wide interest in strain engineering, there is still a lack of control on device-compatible strain patterns due to the limited understanding of the structure-strain relationship. Here, we study the effect of substrate corrugation and curvature on the strain profiles of graphene via combined experimental and theoretical studies of a model system: graphene on closely packed SiO₂ nanospheres with different diameters (20-200 nm). Experimentally, via quantitative Raman analysis, we observe partial adhesion and wrinkle features and find that smaller nanospheres induce larger tensile strain in graphene; theoretically, molecular dynamics simulations confirm the same microscopic structure and size dependence of strain and reveal that a larger strain is caused by a stronger, inhomogeneous interaction force between smaller nanospheres and graphene. This molecular-level understanding of the strain mechanism is important for strain engineering of graphene and other two-dimensional materials.

Universal deformation pathways and flexural hardening of nanoscale 2D-material standing folds

In the present work, we use atomic force microscopy nanomanipulation of 2D-material standing folds to investigate their mechanical deformation. Using graphene, h-BN and talc nanoscale wrinkles as testbeds, universal force-strain pathways are clearly uncovered and well-accounted for by an analytical model. Such universality further enables the investigation of each fold bending stiffness κ as a function of its characteristic height h ₀. We observe a more than tenfold increase of κ as h ₀ increases in the 10-100 nm range, with power-law behaviors of κ versus h ₀ with exponents larger than unity for the three materials. This implies anomalous scaling of the mechanical responses of nano-objects made from these materials.

Low-force spectroscopy on graphene membranes by scanning tunneling microscopy

Two-dimensional atomically flat sheets with a high mechanical flexibility are very attractive as ultrathin membranes but are also inherently challenging for microscopic investigations. We report on a method using Scanning Tunneling Microscopy (STM) under ultra-high vacuum conditions for non-indenting low-force spectroscopy on micrometer-sized freestanding graphene membranes. The method is based on applying quasi-static voltage ramps with active feedback at low tunneling currents and ultimately relies on the attractive electrostatic force between the tip and the membrane. As a result a bulge-test scenario can be established. The convenience and simplicity of the method relies on the fact that the loading force and the membrane deflection detection are both provided simultaneously by the STM. This permits the continuous measurement of the stress-strain relation. Electrostatic forces applied are typically below 1 nN and the membrane deflection is detected at sub-nanometer resolution. Experiments on single-layer graphene membranes with a strain of 0.1% reveal a two-dimensional elastic modulus E_2D = 220 N m^-1.

Quantum Wires and Waveguides Formed in Graphene by Strain

Confinement of electrons in graphene to make devices has proven to be a challenging task. Electrostatic methods fail because of Klein tunneling, while etching into nanoribbons requires extreme control of edge terminations, and bottom-up approaches are limited in size to a few nanometers. Fortunately, its mechanical flexibility raises the possibility of using strain to alter graphene's properties and create novel straintronic devices. Here, we report transport studies of nanowires created by linearly-shaped strained regions resulting from individual folds formed by layer transfer onto hexagonal boron nitride. Conductance measurements across the folds reveal Coulomb blockade signatures, indicating confined charges within these structures, which act as quantum dots. Along folds, we observe sharp features in traverse resistivity measurements, attributed to an amplification of the dot conductance modulations by a resistance bridge incorporating the device. Our data indicates ballistic transport up to ∼1 μm along the folds. Calculations using the Dirac model including strain are consistent with measured bound state energies and predict the existence of valley-polarized currents. Our results show that graphene folds can act as straintronic quantum wires.

The role of the strain induced population imbalance in Valley polarization of graphene: Berry curvature perspective

Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points (K and K') of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points. In other words each of these gauges alone could not induce any topological valley-polarized current in the system at zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as a result of the external strain even at zero magnetic field. In the context of Berry curvature within the linear response regime the valley polarization (both magnetic free polarization, Π0, and field dependent response function, χ α ) in different values of gauge fields of lattice deformation has been obtained.

Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: perspectives for a strain sensor

We consider the scattering of Dirac particles in graphene due to the superposition of an external magnetic field and mechanical strain. As a model for a graphene nanobubble, we find exact analytical solutions for single-particle states inside and outside a circular region submitted to the fields. Finally, we obtain analytical expressions for the scattering cross-section, as well as for the Landauer current through the circular region. Our results provide a fully-analytical treatment for electronic transport through a graphene nanobubble, showing that a combination of a physical magnetic field and strain leads to valley polarization and filtering of the electronic current. Moreover, our analytical model provides an explicit metrology principle to measure strain by performing conductance experiments under a controlled magnetic field imposed over the sample.

Quantized Transport, Strain-Induced Perfectly Conducting Modes, and Valley Filtering on Shape-Optimized Graphene Corbino Devices

The extreme mechanical resilience of graphene and the peculiar coupling it hosts between lattice and electronic degrees of freedom have spawned a strong impetus toward strain-engineered graphene where, on the one hand, strain augments the richness of its phenomenology and makes possible new concepts for electronic devices, and on the other hand, new and extreme physics might take place. Here, we demonstrate that the shape of substrates supporting graphene sheets can be optimized for approachable experiments where strain-induced pseudomagnetic fields (PMF) can be tailored by pressure for directionally selective electronic transmission and pinching-off of current flow down to the quantum channel limit. The Corbino-type layout explored here furthermore allows filtering of charge carriers according to valley and current direction, which can be used to inject or collect valley-polarized currents, thus realizing one of the basic elements required for valleytronics. Our results are based on a framework developed to realistically determine the combination of strain, external parameters, and geometry optimally compatible with the target spatial profile of a desired physical property-the PMF in this case. Characteristic conductance profiles are analyzed through quantum transport calculations on large graphene devices having the optimal shape.

Electronic and optical properties of strained graphene and other strained 2D materials: a review

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Strain Engineering a 4a×√3a Charge Density Wave Phase in Transition Metal Dichalcogenide 1T-VSe2

We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a×√3a periodicity, as opposed to the previously reported hexagonal 4a×4a structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a×√3a CDW periodicity and an energy gap of 2ΔCDW = (9.1 ± 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a×4a and 4a×√3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.