Critical Twist Angle Research Articles

Nonlinear Optical Response Modulated by Lattice Reconstruction in Small‐Angle Twisted Bilayer MoS2

AbstractSubtle perturbations in interlayer twist angles offer a novel investigational avenue for revealing intriguing optical characteristics within the domain of 2D materials. In this study, a homogeneous bilayer structure featuring precisely defined interlayer twist angles is meticulously engineered by stacking monolayer single‐crystal MoS2 in a controlled, layer‐by‐layer manner. Scanning tunneling microscopy (STM) reveals an unexpected lattice reconstruction, particularly at twist angles of ≤ 2°, which induces the emergence of expansive rhombohedral‐stacked large triangular domains. Furthermore, a second‐harmonic generation (SHG) is utilized as a sensitive modality to demonstrate profound transformations in the local electron band structures. By combining the linear spectra with SHG, the change in the C‐exciton optical response in the band‐nesting region of the small‐angle twisted bilayer MoS2 before and after crossing a critical twist angle of 2° is discussed. The study shows that SHG can be used as a nondestructive method to characterize the lattice structure of small‐angle twisted bilayer samples. Furthermore, determining the potential relationship between the lattice reconstruction and the linear and nonlinear spectra further demonstrates the regulatory effect of the interlayer twist angle on the nonlinear optical effects of 2D materials.

Extraordinary Phonon Displacement and Giant Resonance Raman Enhancement in WSe2/WS2 Moiré Heterostructures.

Twisted van der Waals heterostructures are known to induce surprisingly diverse and intriguing phenomena, such as correlated electronic phase and unconventional optical properties. This can be realized by controlled rotation of adjacent atomic planes, which provides an uncommon way to manipulate inelastic light-matter interactions. Here, we discover an extraordinary blue shift of 5-6 wavenumbers for high-frequency phonon modes in WS2/WSe2 twisted heterobilayers, captured meticulously using Raman spectroscopy. Phonon spectra displace rapidly over a subtle change in interlayer twist angle owing to heterostrain and atomic reconstruction from the Moiré pattern. First-order linear coefficients of the phonon modes in twisted heterostructures are further found to increase largely compared to their monolayer counterpart and vary immensely with the twist angle. Exceptional and extravagant enhancement of up to 50-fold is observed in the Raman vibrational intensity at a specific twist angle; this is largely influenced by the resonance process derived from a simple critical twist angle model. In addition, we depict how the resonance can be modulated by changing the thermal conditions and also the stacking angle. Therefore, our work further highlights the twist-driven phonon dynamics in pristine two-dimensional heterostructures, adding vital insight into Moiré physics and promoting comprehensive understanding of structural and optical properties in Moiré superlattices.

Finite-Frequency Topological Maxwell Modes in Mechanical Self-Dual Kagome Lattices.

In this Letter, an elastic twisted kagome lattice at a critical twist angle, called self-dual kagome lattice, is shown to exhibit peculiar finite-frequency topological modes which emerge when certain conditions are satisfied. These states are topologically reminiscent of the zero energy (floppy) modes of Maxwell lattices, but they occur at a finite frequency in the band gap of the self-dual kagome lattice. Thus, we present a completely new class of topological modes that share similarities with both the zero frequency floppy modes in Maxwell lattices and the finite energy in-gap modes in topological insulators. We envision the presented mathematical and numerical framework to be invaluable for many technological advances pertaining to wave phenomena, such as reconfigurable waveguide designs.

On the Kink Instability of Twisted Coronal Loops: Nonneutralized Electric Current

Based on linear magnetohydrodynamic equations and an energy principle we analyze the ideal kink instability of a twisted force-free coronal loop (flux rope) surrounded by an outer potential magnetic field by using the sharp-boundary approximation at the surface. Unlike Tsap et al., a magnetic flux rope with nonneutralized (uncompensated) electric current is considered. We have shown that the twist angle of magnetic field lines is closely related to coronal mass ejections and solar flares. The kink instability condition does not depend on the radial profile of the magnetic field inside a flux rope in the long-wavelength limit but depends strongly on the reverse electric currents at the surface. The total critical twist angle of magnetic field lines, which determines the kink instability threshold, can be much greater than π radians due to reverse azimuthal surface current. This agrees with observations and illustrates the importance of the role of reverse currents for stabilization of a flux rope. Additional arguments in favor of the energy release models based on the uncompensated electric currents are presented.

Existence of corner modes in elastic twisted kagome lattices

This Letter investigates the emergence of corner modes in elastic twisted Kagome lattices at a critical twist angle, known as self-dual point. We show that a special type of corner modes exist and they are localized at a very specific type of corners independent of the overall shape of the finite lattice. Moreover, these modes appear even in the perturbed lattice at the corners with mirror planes. By exploring its counterpart in electronic system, we attribute such corner modes to charge accumulation at the boundary, which is confirmed by the plot of charge distribution in a finite lattice.

Coexisting ferromagnetic-antiferromagnetic state in twisted bilayer CrI3.

Moiré engineering1-3 of van der Waals magnetic materials4-9 can yield new magnetic ground states via competing interactions in moiré superlattices10-13. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states10, non-collinear magnetic states10-13, moiré magnon bands and magnon networks14 in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally. Here, by utilizing the stacking-dependent interlayer exchange interactions in two-dimensional magnetic materials15-18, we demonstrate a coexisting ferromagnetic (FM) and antiferromagnetic (AF) ground state in small-twist-angle CrI3 bilayers. The FM-AF state transitions to a collinear FM ground state above a critical twist angle of about 3°. The coexisting FM and AF domains result from a competition between the interlayer AF coupling, which emerges in the monoclinic stacking regions of the moiré superlattice, and the energy cost for forming FM-AF domain walls. Our observations are consistent with the emergence of a non-collinear magnetic ground state with FM and AF domains on the moiré length scale10-13. We further employ the doping dependence of the interlayer AF interaction to control the FM-AF state by electrically gating a bilayer sample. These experiments highlight the potential to create complex magnetic ground states in twisted bilayer magnetic crystals, and may find application in future gate-voltage-controllable high-density magnetic memory storage.

Stability Analysis of Arteries Under Torsion.

Vascular tortuosity may impede blood flow, occlude the lumen, and ultimately lead to ischemia or even infarction. Mechanical loads like blood pressure, axial force, and also torsion are key factors participating in this complex mechanobiological process. The available studies on arterial torsion instability followed computational or experimental approaches, yet single available theoretical study had modeled the artery as isotropic linear elastic. This paper aim is to validate a theoretical model of arterial torsion instability against experimental data. The artery is modeled as a single-layered, nonlinear, hyperelastic, anisotropic solid, with parameters calibrated from experiment. Linear bifurcation analysis is then performed to predict experimentally measured stability margins. Uncertainties in geometrical parameters and in measured mechanical response were considered. Also, the type of rate (incremental) boundary conditions (RBCs) impact on the results was examined (e.g., dead load, fluid pressure). The predicted critical torque and twist angle followed the experimentally measured trends. The closest prediction errors in the critical torque and twist rate were 22% and 67%, respectively. Using the different RBCs incurred differences of up to 50% difference within the model predictions. The present results suggest that the model may require further improvements. However, it offers an approach that can be used to predict allowable twist levels in surgical procedures (like anastomosis and grafting) and in the design of stents for arteries subjected to high torsion levels (like the femoropopliteal arteries). It may also be instructive in understanding biomechanical processes like arterial tortuosity, kinking, and coiling.

Twist buckling of veins under torsional loading

Veins are often subjected to torsion and twisted veins can hinder and disrupt normal blood flow but their mechanical behavior under torsion is poorly understood. The objective of this study was to investigate the twist deformation and buckling behavior of veins under torsion. Twist buckling tests were performed on porcine internal jugular veins (IJVs) and human great saphenous veins (GSVs) at various axial stretch ratio and lumen pressure conditions to determine their critical buckling torques and critical buckling twist angles. The mechanical behavior under torsion was characterized using a two-fiber strain energy density function and the buckling behavior was then simulated using finite element analysis. Our results demonstrated that twist buckling occurred in all veins under excessive torque characterized by a sudden kink formation. The critical buckling torque increased significantly with increasing lumen pressure for both porcine IJV and human GSV. But lumen pressure and axial stretch had little effect on the critical twist angle. The human GSVs are stiffer than the porcine IJVs. Finite element simulations captured the buckling behavior for individual veins under simultaneous extension, inflation, and torsion with strong correlation between predicted critical buckling torques and experimental data (R2=0.96). We conclude that veins can buckle under torsion loading and the lumen pressure significantly affects the critical buckling torque. These results improve our understanding of vein twist behavior and help identify key factors associated in the formation of twisted veins.

Influence of twist angle on crack propagation of nanoscale bicrystal nickel film based on molecular dynamics simulation

Tensile deformation of nanoscale bicrystal nickel film with twist grain boundary, which includes various twist angles, is investigated via molecular dynamics simulation to obtain the influence of twist angle on crack propagation. The twist angle has a significant influence on crack propagation. At the tensile strain of 0.667, as for the twist angles of 0°, 3.54° and 7.05°, the bicrystal nickel films are subjected to complete fracture, while as for the twist angles of 16.1° and 33.96°, no complete fracture occurs in the bicrystal nickel films. When the twist angles are 16.1° and 33.96°, the dislocations emitted from the crack tip are almost unable to go across the grain boundary and enter into the other grain along the slip planes {111}. There should appear a critical twist angle above which the crack propagation is suppressed at the grain boundary. The higher energy in the grain boundary with larger twist angle contributes to facilitating the movement of the glissile dislocation along the grain boundary rather than across the grain boundary, which leads to the propagation of the crack along the grain boundary.

Acute mechano-electronic responses in twisted phosphorene nanoribbons.

Many different forms of mechanical and structural deformations have been employed to alter the electronic structure of various modern two-dimensional (2D) nanomaterials. Given the recent interest in the new class of 2D nanomaterials - phosphorene, here we investigate how the rotational strain-dependent electronic properties of low-dimensional phosphorene may be exploited for technological gain. Here, using first-principles density-functional theory, we investigate the mechanical stability of twisted one-dimensional phosphorene nanoribbons (TPNR) by measuring their critical twist angle (θc) and shear modulus as a function of the applied mechanical torque. We find a strong anisotropic, chirality-dependent mechano-electronic response in the hydrogen-passivated TPNRs upon vortical deformation, resulting in a striking difference in the change in the carrier effective mass as a function of torque angle (and thus, the corresponding change in carrier mobility) between the zigzag and armchair directions in these TPNRs. The accompanied tunable band-gap energies for the hydrogen-passivated zigzag TPNRs may then be exploited for various key opto-electronic nanodevices.

Stability of a helicoidal surface inside a cylinder with pinned diameters

A mathematical analysis is presented of the stability of a soap film with uniform surface tension when stretched between two diameters on the inside of a circular cylinder. The stability boundary is found as a critical twist angle θ between the two diameters, as a function of the aspect ratio ℓ of the cylinder. Numerical and asymptotic results agree well with previous numerical simulations and experiments by Cox and Jones ( J. Engr. Math ., 86 (2014), 1–7). Their hypothesis that the stability boundary for the multiple-vane case is identical to the single film case is confirmed. It is also shown that two distinct instability mechanisms operate. For moderate and small θ/ℓ , the instability is driven by the decrease in area caused by the film moving to an off-diameter position. But for larger θ/ℓ (more twisted films), the decrease in area is dominated by an internal rearrangement of the surface. The latter mechanism is more relevant to Plateau borders in foams, and our results indicate that straight Plateau borders should be stable at any length provided the total twist is less than π/2 .

Atomic corrugation and electron localization due to Moiré patterns in twisted bilayer graphenes

We report on unprecedentedly large-scale density-functional calculations that clarify atomic and electronic structures of twisted bilayer graphene (BLG). We find the existence of the critical twist angle from either the AB or the AA stacking BLG, above which the two graphene layers are essentially decoupled and below which the atomic planes are corrugated and the Dirac electrons are localized. We also find a magic angle at which the Fermi velocity of the Dirac electron vanishes. We clarify that the Moir\'e pattern in tBLG with a tiny twist angle generates inhomogeneity for the electron systems and thus causes the drastic modification of the electronic properties, leading to flat bands at the Fermi level. Sensitivity to the Moir\'e of the valence-electron density and the electron state near the Fermi level is discussed.

Probing interlayer coupling in twisted single‐crystal bilayer graphene by Raman spectroscopy

Twisted bilayer graphene, in which interlayer interaction plays a critical role in this coupled system, is characterized for its angle‐dependent electronic and optical properties. Here, we present a systematic Raman study of single‐crystal twisted bilayer graphene grains, with the spectra of each bilayer graphene precisely correlated to its twist angle using combined transmission electron microscopic technique. Van Hove singularities develop as a result of band rehybridization at the crossing Dirac cones of the two layers, giving rise to a critical twist angle that determines the energy separation between the saddle points in the band structure and the resonance Raman spectra accordingly. The 2D mode becomes sensitive to the twist angle, showing the angle‐dependent position, peak width, and intensity. Our results interpreted in the framework of angle‐dependent double resonance scattering provide an important experimental perspective in understanding the coupled bilayer graphene system. Copyright © 2014 John Wiley & Sons, Ltd.

TWISTED MAGNETIC FLUX TUBES IN THE SOLAR WIND

Magnetic flux tubes in the solar wind can be twisted as they are transported from the solar surface, where the tubes are twisted owing to photospheric motions. It is suggested that the twisted magnetic tubes can be detected as the variation of total (thermal+magnetic) pressure during their passage through observing satellite. We show that the total pressure of several observed twisted tubes resembles the theoretically expected profile. The twist of isolated magnetic tube may explain the observed abrupt changes of magnetic field direction at tube walls. We have also found some evidence that the flux tube walls can be associated with local heating of the plasma and elevated proton and electron temperatures. For the tubes aligned with the Parker spiral, the twist angle can be estimated from the change of magnetic field direction. Stability analysis of twisted tubes shows that the critical twist angle of the tube with a homogeneous twist is 70$^0$, but the angle can further decrease owing to the motion of the tube with regards to the solar wind stream. The tubes with a stronger twist are unstable to the kink instability, therefore they probably can not reach 1 AU.

CONTINUUM SHELL MODEL FOR BUCKLING OF ARMCHAIR CARBON NANOTUBES UNDER COMPRESSION OR TORSION

Molecular dynamics (MD) simulations are performed using adaptive intermolecular reactive bond order potential to analyze single-walled and double-walled carbon nanotubes. These carbon nanotubes were analyzed for buckling under compression and under torsion. The MD simulations create a comprehensive database for the critical buckling loads/strains and critical buckling torques/twist angles for armchair SWCNTs and DWCNTs of varying diameters and lengths. Using MD results as a computational benchmark, an equivalent thick shell model of CNT is proposed, which is amenable for analysis using a commercially available software ABAQUS. Based on our MD results, an empirical equation that describes the size-dependent Young's modulus for a single-walled carbon nanotube is established. Buckling analysis of CNT under compression and under torsion are performed with the equivalent shell model using size-dependent Young's modulus, Poisson's ratio = 0.19 and shell thickness h = 0.066 nm. We show that the equivalent shell model gives good estimate of critical buckling load/strain and critical buckling torque with respect to the MD results. Variation of critical twist angle with length of CNT, predicted by the shell model is in good qualitative agreement with MD simulation. However, the equivalent shell model underestimates the critical twist angle by 30% because the continuum shell model overestimates torsional stiffness of CNT compared to an atomistic model of CNT. The equivalent shell model is less computational intensive to implement as compared with MD. Its accuracy for predicting the buckling states for long carbon nanotubes allows it to be used for moderately long CNTs under compression/torsion, in-lieu of MD simulations.

Graphene in Color

Materials Science![Figure][1] CREDIT: J. T. ROBINSON The properties of bilayer graphene films depend on the relative orientation or twist of the two layers. Robinson et al. grew single-layer graphene on copper surfaces and then performed two transfers of these films onto silica-coated silicon substrates to create bilayer regions. Because these films are polycrystalline, a variety of twist angles between the layers were created across the surface and resulted in a patchwork of colored regions that appeared red, yellow, or blue. Raman spectroscopy was used to characterize the twist angles; the enhancement of the G peak at ∼1600 cm−1 occurred at optical excitation wavelengths that differed for the red and yellow regions, and the extent of enhancement corresponded to the deviation of the orientation of the layers from a distinctive critical twist angle. The twist angles were also confirmed by low-energy electron diffraction studies. The coupling could be minimized by chemical functionalization: fluorination of the top graphene layers with XeF2 quenched the colors, which could be recovered by thermally desorbing the fluorine atoms. ACS Nano 10.1021/nn304834p (2012). [1]: pending:yes

Twist buckling behavior of arteries

Arteries are often subjected to torsion due to body movement and surgical procedures. While it is essential that arteries remain stable and patent under twisting loads, the stability of arteries under torsion is poorly understood. The goal of this work was to experimentally investigate the buckling behavior of arteries under torsion and to determine the critical buckling torque, the critical buckling twist angle, and the buckling shape. Porcine common carotid arteries were slowly twisted in vitro until buckling occurred while subjected to a constant axial stretch ratio (1.1, 1.3, 1.5 (in vivo level) and 1.7) and lumen pressure (20, 40, 70 and 100mmHg). Upon buckling, the arteries snapped to form a kink. For a group of six arteries, the axial stretch ratio significantly affected the critical buckling torque ([Formula: see text]) and the critical buckling twist angle ([Formula: see text]). Lumen pressure also significantly affected the critical buckling torque ([Formula: see text]) but had no significant effect on the critical twist angle ([Formula: see text]). Convex material constants for a Fung strain energy function were determined and fit well with the axial force, lumen pressure, and torque data measured pre-buckling. The material constants are valid for axial stretch ratios, lumen pressures, and rotation angles of 1.3-1.5, 20-100mmHg, and 0-270[Formula: see text], respectively. The current study elucidates the buckling behavior of arteries under torsion and provides new insight into mechanical instability of blood vessels.

Effects of die shape modifications on the geometrical and dimensional accuracies of cold forged AUV propeller blade

Geometrical and dimensional accuracies are two major concerns in precision forging and they become more critical with increasing part complexity. In this study, the geometrical error of an autonomous underwater vehicle (AUV) propeller blade is quantified by comparing the blade and punch profiles. The nominal geometry of the blade is compared to the blade profile measured using the optical technique Infinite Focus Alicona system to determine profile deviation. The current study aims to investigate the contributions of die shape modifications on the error formation of the two most critical geometries, namely, blade thickness and twist angle. The results show that die modification has a significant effect on geometrical and dimensional errors.

AN INVESTIGATION INTO THE TORSIONAL BUCKLING OF CARBON NANOTUBES USING MOLECULAR AND STRUCTURAL MECHANICS

In this work, the critical twist angles of two types of CNTs, zigzag and armchair of different lengths are determined using molecular and structural mechanics. The results show that the torsional buckling modes predicted by the two methods are the same. It is also shown that critical twist angle decreases as CNTs length increases. Structural mechanics underpredicts the critical angle for both armchair and zigzag nonotubes. It is also shown that the critical angle for armchair nanotubes is higher than that for zigzag nanotubes.

Microwave Generation on Geometrically Constrained Magnetic Wall: Effect of Twist Angle

We studied the current-induced magnetization dynamics of geometrically constrained magnetic walls (GCMWs) with twist angles of 90–180°, in order to examine their possibility as microwave generators using the effects of the twist angles. We numerically solved the Landau–Lifshitz–Gilbert equation with a spin-transfer torque term and found that the magnetic structures of GCMWs with certain twist angles oscillate between the Bloch and Néel walls (OBN) with microwave frequency, even though the twist angle is not 180°. We also found the critical twist angle below which the oscillation of the magnetic structure is inhibited. We showed that the oscillation frequency shows a hysteresis when we vary the twist angle of a GCMW or the corresponding applied magnetic field. Then, we also discussed the microwave generation induced by the periodic-deformation dynamics of GCMWs in the OBN.