Small Twist Angles Research Articles

Polar and quasicrystal vortex observed in twisted-bilayer molybdenum disulfide.

We report the observation of an electric field in twisted-bilayer molybdenum disulfide (MoS2) and elucidate its correlation with local polar domains using four-dimensional scanning transmission electron microscopy (4D-STEM) and first-principles calculations. We reveal the emergence of in-plane topological vortices within the periodic moiré patterns for both commensurate structures at small twist angles and the incommensurate quasicrystal structure that occurs at a 30° twist. The large-angle twist leads to mosaic chiral vortex patterns with tunable characteristics. A twisted quasicrystal bilayer, characterized by its 12-fold rotational symmetry, hosts complex vortex patterns and can be manipulated by picometer-scale interlayer displacement. Our findings highlight that twisting 2D bilayers is a versatile strategy for tailoring local electric polar vortices.

Designing Moiré Patterns by Shearing.

We analyze the elastic properties, structural effects, and low-energy physics of a sheared nanoribbon placed on top of graphene, which creates a gradually changing moiré pattern. By means of a classical elastic model we derive the strains in the ribbon and we obtain its electronic energy spectrum with a scaled tight-binding model. The size of the sheared region is determined by the balance between elastic and van der Waals energy, and different regimes are identified. Near the clamped edge, moderate strains and small twist angles lead to one-dimensional channels. Near the sheared edge, a long region behaves like magic angle twisted bilayer graphene (TBG), showing a sharp peak in the density of states, mostly isolated from the rest of the spectrum. We also calculate the band topology along the ribbon and we find that it is stable for large intervals of strains and twist angles. Together with the experimental observations, these results show that the sheared nanoribbon geometry is ideal for exploring superconductivity and correlated phases in TBG in the very sought-after regime of ultralow twist angle disorder.

Spinon Pairing Induced by Chiral In-Plane Exchange and the Stabilization of Odd-Spin Chern Number Spin Liquid in Twisted MoTe_{2}.

The unusual structure and symmetry of low-energy states in twisted transition metal dichalcogenides leads to large in-plane spin-exchange interactions between spin-valley locked holes. We demonstrate that this exchange interaction can stabilize a gapped spin-liquid phase with a quantized spin-Chern number of 3 when the twist angle is sufficiently small and the system lies in a Mott insulating phase. The gapped spin liquid may be understood as arising from spinon pairing in the DIII Altland-Zirnbauer symmetry class. Applying an out-of-plane electric field or increasing the twist angle is shown to drive a transition, respectively, to an anomalous Hall insulator or an in-plane antiferromagnet. Recent experiments indicate that a spin-Chern number 3 phase occurs in twisted MoTe_{2} at small twist angles with a transition to a quantum anomalous Hall phase as the twist angle is increased above a critical value of about 2.5° in the absence of an applied electric field.

Long-Lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: A Bosonic Kane-Mele Model Platform.

Moiré superlattices based on two-dimensional transition metal dichalcogenides (TMDs) have emerged as a highly versatile and fruitful platform for exploring correlated topological electronic phases. One of the most remarkable examples is the recently discovered fractional quantum anomalous Hall effect (FQAHE) under zero magnetic field. Here, we propose a minimal structure that hosts long-lived excitons-a ubiquitous bosonic excitation in TMD semiconductors-with narrow topological bosonic bands. The nontrivial exciton topology originates from hybridization of moiré interlayer excitons and is tunable by controlling twist angle and electric field. At small twist angle, the lowest exciton bands are isolated from higher energy bands and provide a solid-state realization of the bosonic Kane-Mele model with topological flatbands, which could potentially support the bosonic version of FQAHE.

Cathodoluminescence from interlayer excitons in a 2D semiconductor heterobilayer.

Photoluminescence has widely been used to study excitons in semiconducting transition metal dichalcogenide (MX$_2$) monolayers, demonstrating strong light matter interactions and locked spin and valley degrees of freedom. In heterobilayers composed of overlapping monolayers of two different MX$_2$, an interlayer exciton can form, with the hole localised in one layer and the electron in the other. These interlayer excitons are long-lived, field-tunable, and can be trapped by moir'e patterns formed at small twist angles between the layers. Here we demonstrate that emission from radiative recombination of interlayer excitons can be observed by cathodoluminescence from a WSe$_2$/MoSe$_2$ heterobilayer encapsulated in hexagonal boron nitride. The higher spatial resolution of cathodoluminescence, compared to photoluminescence, allows detailed analysis of sample heterogeneity at the 100s of nm lengthscales over which twist angles tend to vary in dry-transfer fabricated heterostructures.

Pressure-tuned superflat bands and electronic localization in twisted bilayer graphene-like materials

Electronic properties of twisted bilayer graphene-like materials can be modified substantially by manipulating twist angles, allowing for many exotic correlated phenomena. However, typical moiré flatbands holding these phenomena only appear with specific small twist angles. Here, we report a class of pressure-tuned superflat bands and localized electronic states over a wide range of twist angles, beyond the physics of twisted bilayer graphene near the Fermi energy. Under the slowly varying lattice distortion approximation, localized electronic states deterministically emerge in isolation at the edge of bulk spectra and are spatially centered around the AA stacked region, governed by macroscopic effective potential wells of moiré superlattices. Moreover, as macroscopic effects, pressure-tuned superflat bands and localized electronic states exhibit excellent stability against small perturbations. Our results suggest that applying pressure in generic twisted bilayer graphene-like materials may evoke widespread electronic correlations, providing opportunities for exploring electronic interactions and superconductivity.

Quantification of Two-Dimensional Interfaces: Quality of Heterostructures and What Is Inside a Nanobubble.

Trapped materials at the interfaces of two-dimensional heterostructures (HS) lead to reduced coupling between the layers, resulting in degraded optoelectronic performance and device variability. Further, nanobubbles can form at the interface during transfer or after annealing. The question of what is inside a nanobubble, i.e., the trapped material, remains unanswered, limiting the studies and applications of these nanobubble systems. In this work, we report two key advances. First, we quantify the interface quality using RAW format optical imaging (unprocessed image data) and distinguish between ideal and non-ideal interfaces. The HS/substrate ratio value is calculated using a transfer matrix model and is able to detect the presence of trapped layers. The second key advance is the identification of water as the trapped material inside a nanobubble. To the best of our knowledge, this is the first study to show that optical imaging alone can quantify interface quality and find the type of trapped material inside spontaneously formed nanobubbles. We also define a quality index parameter to quantify the interface quality of HS. Quantitative measurement of the interface will help answer the question whether annealing is necessary during HS preparation and will enable creation of complex HS with small twist angles. Identification of the trapped materials will pave the way toward using nanobubbles for optical and engineering applications.

Twist angle-dependent transport properties of twisted bilayer graphene

Twisted bilayer graphene (tBLG) with small twist angles has attracted significant attention because of its unique electronic properties arising from the formation of a moiré superlattice. In this study, we systematically characterized the twist-angle-dependent electronic and transport properties of tBLG grown via chemical vapor deposition. This characterization included parameters such as the charge-neutral point voltage, carrier concentration, resistance, and mobility, covering a wide range of twist angles from 0° to 30°. We experimentally demonstrated that these parameters exhibited twist-angle-dependent moiré period trends, with high twist angles exceeding 9°, revealing more practically useful features, including improved mobilities compared to those of single-layer graphene. In addition, we demonstrated that the doping states and work functions were weakly dependent on the twist angles, as confirmed by additional first-principles calculations. This study provides valuable insights into the transport properties of tBLG and its potential for practical applications in the emerging field of twistronics.

Theory of phonon sidebands in the absorption spectra of moiré exciton–polaritons

Excitons in twisted bilayers of transition metal dichalcogenides have strongly modified dispersion relations due to the formation of periodic moiré potentials. The strong coupling to a light field in an optical cavity leads to the appearance of moiré polaritons. In this paper, we derive a theoretical model for the linear absorption spectrum of the coupled moiré polariton–phonon system based on the time-convolutionless (TCL) approach. Results obtained by numerically solving the TCL equation are compared to those obtained in the Markovian limit and from a perturbative treatment of non-Markovian corrections. A key quantity for the interpretation of the findings is the generalized phonon spectral density. We discuss the phonon impact on the spectrum for realistic moiré exciton dispersions by varying twist angle and temperature. Key features introduced by the coupling to phonons are broadenings and energy shifts of the upper and lower polariton peak and the appearance of phonon sidebands between them. We analyze these features with respect to the role of Markovian and non-Markovian effects and find that they strongly depend on the twist angle. We can distinguish between the regimes of large, small, and intermediate twist angles. In the latter phonon effects are particularly pronounced due to dominating phonon transitions into regions which are characterized by van Hove singularities in the density of states.

Overcrowded 14,14'-Bidibenzo[a,j]anthracenes: Challenges in Syntheses and Atypical Property of Lacking Symmetry-Breaking Charge Transfer (SBCT).

14,14'-Bidibenzo[a,j]anthracenes (BDBAs) were prepared by iridium-catalyzed annulation of 5,5'-biterphenylene with alkynes. The molecular geometries of overcrowded BDBAs were verified by X-ray crystallography. The two dibenzo[a,j]anthryl moieties are connected through the sterically hindered 14 positions, resulting in highly distorted molecular halves. The conformation with a small twist angle between two molecular halves can minimize steric conflicts between the substituents at 1 and 13 positions and the carbon atoms of the central axis, as well as steric clashes between those substituents. One such example is octafluoro-substituted BDBA, where the interplanar angle between two anthryl moieties is approximately 31° (currently the lowest reported value, cf. 81° in 9,9'-bianthracene). The intramolecular interactions and electronic couplings between two molecular halves resulted in upfield 1H NMR signals, redshifted absorption and emission bands, and a reduced HOMO-LUMO gap. Photodynamic investigations on BDBAs indicated that the formation of the conventional symmetry-breaking charge transfer (SBCT) state was suspended by restricted rocking around the central C-C bond. Such a mechanism associated with this highly constrained conformation was examined for the first time.

Impact of out-of-plane deformation on atomic reconstruction in twisted van der Waals bilayers

The effects of out-of-plane deformation on atomic relaxation in twisted van der Waals bilayers are investigated by comprehensive multiscale modeling and simulations. The model integrates the DFT-informed generalized stacking-fault energy for interlayer interaction between layers and the Föppl–von Kármán plate theory for elastic energy in each layer with minimization of the total free energy for atomic relaxation governed by a gradient flow method. Our simulation results elucidate twist-angle dependent moiré pattern, strain field, tortional displacement field and stacking domain structures, in good agreement with recent experimental observations. In particular, we derive the strain soliton solution at a small twist angle and the soliton free elastic solution at a large twist angle for the reconstructed van der Waals bilayer with out-of-plane deformation. These results show that out-of-plane deformation not only modifies the strain soliton width but also induces substantial alterations in the strain field, local rotation, and stacking structures. Our findings reveal the non-neglectable role played by out-of-plane deformation in the atomic relaxation of twisted van der Waals bilayers, particularly at smaller twist angles. The intricate interplay between in-plane atomic relaxation and out-of-plane deformation provides opportunities for strain engineering in twisted van der Waals bilayers.

Ultra-flat bands at large twist angles in group-V twisted bilayer materials.

Flat bands in 2D twisted materials are key to the realization of correlation-related exotic phenomena. However, a flat band often was achieved in the large system with a very small twist angle, which enormously increases the computational and experimental complexity. In this work, we proposed group-V twisted bilayer materials, including P, As, and Sb in the β phase with large twist angles. The band structure of twisted bilayer materials up to 2524 atoms has been investigated by a deep learning method DeepH, which significantly reduces the computational time. Our results show that the bandgap and the flat bandwidth of twisted bilayer β-P, β-As, and β-Sb reduce gradually with the decreasing of twist angle, and the ultra-flat band with bandwidth approaching 0eV is achieved. Interestingly, we found that a twist angle of 9.43° is sufficient to achieve the band flatness for β-As comparable to that of twist bilayer graphene at the magic angle of 1.08°. Moreover, we also find that the bandgap reduces with decreasing interlayer distance while the flat band is still preserved, which suggests interlayer distance as an effective routine to tune the bandgap of flat band systems. Our research provides a feasible platform for exploring physical phenomena related to flat bands in twisted layered 2D materials.

Mapping twist-tuned multiband topology in bilayer WSe2.

Semiconductor moiré superlattices have been shown to host a wide array of interaction-driven ground states. However, twisted homobilayers have been difficult to study in the limit of large moiré wavelengths, where interactions are most dominant. In this study, we conducted local electronic compressibility measurements of twisted bilayer WSe2 (tWSe2) at small twist angles. We demonstrated multiple topological bands that host a series of Chern insulators at zero magnetic field near a "magic angle" around 1.23°. Using a locally applied electric field, we induced a topological quantum-phase transition at one hole per moiré unit cell. Our work establishes the topological phase diagram of a generalized Kane-Mele-Hubbard model in tWSe2, demonstrating a tunable platform for strongly correlated topological phases.

Optical Microcavity‐Induced Moiré Exciton Localization in Twisted WSe2 Homobilayer

Abstract2D moiré superlattices offer a versatile platform for manipulating quantum materials, exploiting their spatially varying atomic registry to modify electronic structures, resulting in the emergence of flat electronic minibands, enhanced electronic interactions, and the onset of novel quantum phenomena. Despite extensive investigations into moiré excitons within twisted bilayer moiré superlattices, the interplay between moiré superlattices and optical microcavities remains elusive. Here, a WSe2 homobilayer with a small twist angle positioned on optical microcavities atop a SiO2 (285 nm)/Si substrate is investigated. Utilizing low‐temperature photoluminescence (PL) spectroscopy, it is observed that the twisted homobilayer at the edge of the optical cavity (Edge‐THB) exhibits enhanced localization of moiré excitons and a deeper moiré potential. This behavior is attributed to the combined influence of strain induced by the optical microcavity structure on the moiré superlattice and the amplification of the electromagnetic field. Furthermore, the existence of moiré excitons through a comprehensive analysis, encompassing temperature‐dependent PL spectra, circularly polarized PL spectra, and Landé g‐factor measurements for Edge‐THB is validated. These findings provide valuable insights into the intricate interaction between moiré superlattices and optical microcavities, paving the way for future applications in quantum technologies.

Investigation of high-cycle fatigue property and fatigue crack propagation behavior of a die-forged 2014 aluminum alloy aircraft wheel

The high-cycle fatigue (HCF) property and fatigue crack propagation (FCP) behavior of aircraft wheels manufactured by die forging were investigated from two sampling directions (rims and discs). The results indicate that the HCF anisotropy of the rim and disc specimens increases with decreasing stress amplitude, and the fatigue strengths are 181 MPa and 157 MPa, respectively. Based on the quantitative analysis of the fatigue fractures, a fatigue life prediction model considering the Fe/Mn-containing particles quantity factor S has been established, and the predicted values are reasonably accurate to the test values. The crack path microstructure indicates that Fe/Mn-containing particles can cause crack deflection while acting as bridges for FCP; Crack closure induced by oxides and plastic zones significantly decelerated the FCP rate. Additionally, fatigue cracks tend to propagate toward grains with smaller twist angles and higher Schmid factors (SF).

Magic Angles and Fractional Chern Insulators in Twisted Homobilayer Transition Metal Dichalcogenides.

We explain the appearance of magic angles and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic approximation for the quantum mechanics of valence band holes in a layer-pseudospin field that is valid for sufficiently small twist angles and on a lowest Landau level approximation that is valid for sufficiently large twist angles. It provides a simple qualitative explanation for the nearly ideal quantum geometry of the lowest moiré miniband at particular twist angles, predicts that topological flat bands occur only when the valley-dependent moiré potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a convenient starting point for the study of interactions.

Tuning commensurability in twisted van der Waals bilayers.

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the Kvalley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Modification of interlayer interaction in bilayer MoS2 due to monolayer WSe2 in heterostructures

The low-frequency interlayer vibration modes in bilayer-MoS2/monolayer-WSe2 heterostructures were investigated to study the modification of interlayer interactions due to the moiré periodicity. The interplay of the interlayer interaction within bilayer MoS2 and the interfacial interaction between the two materials results in rich features in the phonon spectra. Several shear and breathing modes are observed for samples with small twist angles (<10°), whereas only one shear and two breathing modes are observed for larger twist angles. For larger twist angles, the interfacial interaction between the two materials amounts to ∼75% of the intrinsic interlayer interaction between the MoS2 layers. The phonon spectrum evolves non-monotonically as the twist angle increases, which is explained with the help of atomistic calculations.

A controllable interlayer shielding effect in twisted multilayer graphene quantum dots.

When multilayer graphene (MLG) is subjected to a vertical electric field, electrons traverse across the layers and its interlayer electrical conductance and shielding effect exhibit remarkable diversity, leading to exotic phenomena and diverse applications in photoelectric devices. The rearrangement of electrons induced by this external field is aptly described by polarizability, which quantifies the electronic response to the applied field. In this work, we have developed a polarizability decomposition scheme based on field-induced electron density variations computed using a first-principles approach. This scheme allows us to isolate the inter- and intra-layer contributions from the total polarizability of twisted multilayer graphene (TMG) quantum dots. The inter- and intra-layer counterparts reflect the charge transfer (CT) and field shielding effects among the layers, respectively. While the strongest shield effect is observed between the outermost two layers, the largest CT change is noted in the outermost layers, but small or nearly zero CT changes in the inner layers. Significant CT and shielding effects are observed not only in strongly coupled Bernal stacking, but also in the structures misaligned from full-(AA)N stacking by a small and size-dependent twist angle. The dielectric behaviors of the TMG quantum dots of a few layers are layer-dependent and different from those of typical dielectrics. Moreover, both the shielding and CT effects exhibit variation with thickness, twist angle and disc size, suggesting controllable conductive/dielectric conversion in the vertical direction. Considering the inter- and intralayer polarizability, our study addresses the precise modulation of interlayer conductance and shielding effect for TMG quantum dots, essential for microstructure design and performance manipulation of MLG-based photoelectric devices.

Bicrystallography-informed Frenkel–Kontorova model for interlayer dislocations in strained 2D heterostructures

In recent years, van der Waals (vdW) heterostructures and homostructures, which consist of stacks of two-dimensional (2D) materials, have risen to prominence due to their association with exotic quantum phenomena originating from correlated electronic states harbored by them. Atomistic scale relaxation effects play an extremely important role in the electronic scale quantum physics of these systems, providing means of manipulation of these materials and allowing them to be tailored for emergent technologies. We investigate such structural relaxation effects in this work using atomistic and mesoscale models, within the context of twisted bilayer graphene — a well-known heterostructure system that features moiré patterns arising from the lattices of the two graphene layers. For small twist angles, atomic relaxation effects in this system are associated with the natural emergence of interface dislocations or strain solitons, which result from the cyclic nature of the generalized stacking fault energy (GSFE), that measures the interface energy based on the relative movement of the two layers. In this work, we first demonstrate using atomistic simulations that atomic reconstruction in bilayer graphene under a large twist also results from interface dislocations, although the Burgers vectors of such dislocations are considerably smaller than those observed in small-twist systems. To reveal the translational invariance of the heterointerface responsible for the formation of such dislocations, we derive the translational symmetry of the GSFE of a 2D heterostructure using the notions of coincident site lattices (CSLs) and displacement shift complete lattices (DSCLs). The workhorse for this exercise is a recently developed Smith normal form bicrystallography framework. Next, we construct a bicrystallography-informed and frame-invariant Frenkel–Kontorova model, which can predict the formation of strain solitons in arbitrary 2D heterostructures, and apply it to study a heterostrained, large-twist bilayer graphene system. Our mesoscale model is found to produce results consistent with atomistic simulations. We anticipate that the model will be invaluable in predicting structural relaxation and for providing insights into various heterostructure systems, especially in cases where the fundamental unit cell is large and therefore, atomistic simulations are computationally expensive.