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Moire materials exhibit diverse quantum properties such as superconductivity and correlated topo logical phases, making them ideal for studying strongly correlated systems. While moire materials are typically formed by stacking two-dimensional materials with interlayer interaction dominated by weak van der Waals (vdW) forces, we explore the possibility for constructing moire covalent super lattices by fluorinating twisted bilayer graphene. With first principle calculations, we demonstrate that fluorination of twisted bilayer graphene (TBG) can induce covalent bonds between adjacent layers, transforming the vdW-dominated interactions. This results in enhanced modulation of the electronic structure, with abundant flat bands across the spectrum. Our findings suggest that cova lent moire superlattices offer new platforms for exploring correlated quantum phenomena and moire covalent chemistry.

Super-moire materials represent a novel playground to engineer states of matter beyond the possibilities of conventional moire materials. However, from the computational point of view, understanding correlated matter in these systems requires solving models with several millions of atoms, a formidable task for state-of-the-art methods. Conventional wavefunction methods for correlated matter scale with a cubic power with the number of sites, a major challenge for super-moire materials. Here, we introduce a methodology capable of solving correlated states in super-moire materials by combining a kernel polynomial method with a quantics tensor cross matrix product state algorithm. This strategy leverages a mapping of the super-moire structure to a many-body Hilbert space efficiently sampled with a tensor cross matrix product state method, where individual evaluations are performed with a Chebyshev kernel polynomial algorithm. We demonstrate this approach with interacting super-moire systems with up to several millions of atoms, showing its ability to capture correlated states in moire-of-moire systems and domain walls between different moire systems. Our manuscript puts forward a widely applicable methodology to study correlated matter in ultra-long length scales, enabling rationalizing correlated super-moire phenomena., Comment: 11 pages, 5 figures

Moire lattices attract intensive attention in the double graphene/TMD layers and photonic crystals due to the interesting exotic physics within these structures. However, precise measurement of the moir'e ground states, excited states and Bloch bands in the twisted photonic lattices is still illusive. In this work we report the strong coupling between the excitons of CsPbBr3 microplates and the photonic modes of the moire lattice at room temperature. Depending on the coupling strength between the nearest potential sites, we observe staggered moire polariton ground states, excited states trapped in the potential sites and moire polariton bands across the twisted photonic lattice. In addition, the phase locking of moire zero (stable in-phase) states and moire pi (metastable antiphase) states with different spatial distributions are measured. Moir'e polariton distribution can be tuned in the shape of parallelogram by controlling the depth and width of the potential in one photonic lattice with another one fixed. Our work lays the foundation to study moir'e exciton polariton Wigner crystals and Luttinger liquid in twisted photonic lattices at room temperature.

We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of 1/3, 1/2, and 2/3 to model the dynamics of generalized Wigner crystals in moire heterostructures. At low temperatures where thermal fluctuations are irrelevant, for commensurate fillings we find a strongly pinned state that depins into a sliding crystal, while at incommensurate fillings, the depinning threshold is strongly reduced. For fillings below 1/2, the depinning occurs in a two-step process. Above the first depinning threshold, there is an extended range of drives where the conduction occurs via the sliding of anti-kinks along the charge stripes, followed by a second threshold where all of the charges begin to slide. At finite temperatures, the external driving reduces the effective melting temperature at commensurate fillings and enhances creep at incommensurate fillings. We show that depinning into different sliding states, such as moving fluids or moving crystals, produces nonlinear features in the transport curves. We also show that transport is asymmetric on either side of a commensurate filling due to the different dynamics for interstitials versus holes in the commensurate structure. A variety of sliding states should be accessible for generalized Wigner crystals at finite temperatures even for low drives. If experiments can realize sliding dynamics in moire systems, it would open a new class of commensurate and incommensurate phases for study. Additionally, the sliding dynamics and anti-kink flow could provide new functionalities for charge transport in moire heterostructures., Comment: 14 pages, 22 figures

Deepfake detection is critical in mitigating the societal threats posed by manipulated videos. While various algorithms have been developed for this purpose, challenges arise when detectors operate externally, such as on smartphones, when users take a photo of deepfake images and upload on the Internet. One significant challenge in such scenarios is the presence of Moir\'e patterns, which degrade image quality and confound conventional classification algorithms, including deep neural networks (DNNs). The impact of Moir\'e patterns remains largely unexplored for deepfake detectors. In this study, we investigate how camera-captured deepfake videos from digital screens affect detector performance. We conducted experiments using two prominent datasets, CelebDF and FF++, comparing the performance of four state-of-the-art detectors on camera-captured deepfake videos with introduced Moir\'e patterns. Our findings reveal a significant decline in detector accuracy, with none achieving above 68% on average. This underscores the critical need to address Moir\'e pattern challenges in real-world deepfake detection scenarios., Comment: 7 page, 4 figures, 1 table, Accepted for publication in IEEE International Conference on Image Processing (ICIP 2024)

Displacement fields are one of the main tuning knobs employed to engineer flat electronic band dispersions in twisted van der Waals multilayers. Here, we show that electric fields can also be used to tune the phonon dispersion of moir\'e superlattices formed by non-centrosymmetric materials, focusing on twisted transition metal dichalcogenide homobilayers. This effect arises from the intertwining between the local stacking configuration and the formation of polar domains within the moir\'e supercell. For small twist angles, increasing the electric field leads to a universal moir\'e phonon spectrum characterized by a substantially softened longitudinal acoustic phason mode and a flat optical phonon mode, both of which cause a significant enhancement in the vibrational density of states. The phasons also acquire a prominent chiral character, displaying a nonzero angular momentum spread across the Brillouin zone. We discuss how the tunability of the moir\'e phonon spectra may affect electronic properties, focusing on the recently discovered phenomenon of van der Waals ferroelectricity., Comment: 6 pages + SM; comments are welcome

Fractional quantum anomalous hall effect (FQAHE), a transport effect with fractionally quantized Hall plateau emerging under zero magnetic field, provides a radically new opportunity to engineer topological quantum electronics. By construction of topological flat band with moire engineering, intrinsic FQAHE has been observed in twisted MoTe2 system and rhombohedral pentalayer graphene/hBN moire superlattices with anomalous Hall resistivity quantization number C <= 2/3 including the gapless composite Fermi-liquid state with C = 1/2. Here we experimentally demonstrate a new system of rhombohedral hexalayer graphene (RHG)/hBN moire superlattices showing both fractional and integer quantum anomalous Hall effects when the lowest flat Chern band is fractionally and fully filled at zero magnetic field. The zero-field Hall resistance Rho_xy = h/Ce2 is quantized to values corresponding to C = 3/5, 2/3, 5/7, 3/4, 7/9 and 1 at moire filling factors v = 3/5, 2/3, 5/7, 3/4, 7/9 and 1, respectively. Particularly, the C = 3/4 FQAHE state at v = 3/4 moire filling featuring a minimum of longitudinal resistance Rho_xx and fractionally quantized Hall resistance Rho_xy = 4h/3e2, is observed for the first time under zero magnetic field. Such a state may be similar to the C = 3/4 fractional quantum hall (FQHE) state recently observed at high magnetic fields9,10 and possibly host fractional charge excitations obeying non-Abelian statistics. By tuning the electrical and magnetic fields at 0 < v < 1, we have observed a sign reversal of the Hall resistivity for v = 2/3 state, indicating a transition from quasi-electron-like excitations to quasi-hole ones. Our experiment has established RHG/hBN moire superlattices a promising platform to explore quasi-particles with fractional charge excitations and non-Abelian anyons at zero magnetic field.

The stacking order and twist angle provide abundant opportunities for engineering band structures of two-dimensional materials, including the formation of moire bands, flat bands, and topologically nontrivial bands. The inversion symmetry breaking in rhombohedral-stacked transitional metal dichalcogenides (TMDCs) endows them with an interfacial ferroelectricity associated with an out-of-plane electric polarization. By utilizing twist angle as a knob to construct rhombohedral-stacked TMDCs, antiferroelectric domain networks with alternating out-of-plane polarization can be generated. Here, we demonstrate that such spatially periodic ferroelectric polarizations in parallel-stacked twisted WSe2 can imprint their moire potential onto a remote bilayer graphene. This remote moire potential gives rise to pronounced satellite resistance peaks besides the charge-neutrality point in graphene, which are tunable by the twist angle of WSe2. Our observations of ferroelectric hysteresis at finite displacement fields suggest the moire is delivered by a long-range electrostatic potential. The constructed superlattices by moire ferroelectricity represent a highly flexible approach, as they involve the separation of the moire construction layer from the electronic transport layer. This remote moire is identified as a weak potential and can coexist with conventional moire. Our results offer a comprehensive strategy for engineering band structures and properties of two-dimensional materials by utilizing moire ferroelectricity.

Interfacial ferroelectricity emerges in heterostructures consisting of nonpolar van der Waals (vdW) layers, greatly expanding the scope of two dimensional ferroelectrics. In particular, the unconventional moire ferroelectricity observed in bilayer graphene/boron nitride (BN) heterostructures, exhibits promising functionalities with topological current, superconductivity and synaptic responses. However, the debate about its mechanism - correlation driven charge transfer between two graphene layers - limits device reproducibility and hence large-scale production. Here by designing a single-layer graphene encapsulated by lattice-mismatched WSe2, we identify the ferroelectricity as stemming from - instead of graphene moire bands - the particular BN, where interfacial sliding ferroelectricity must play a role. With similar structures, multilayer twisted MoS2 is found to reproduce the ferroelectricity. The key is a conductive moire ferroelectric, where the screened gate and the pinned domain wall together result in unchanged electronic states, i.e. anomalous screening. The intimate connection to interfacial sliding ferroelectricity thus provides advantages of diverse choices of constituent materials and robust polarization switching while preserving the unique anomalous screening, paving the way to reproducible and reliable memory-based devices in artificial intelligence.

At near-parallel orientation, twisted bilayer of transition metal dichalcogenides exhibit inter-layer charge transfer-driven out-of-plane ferroelectricity that may lead to unique electronic device architectures. Here we report detailed electrical transport in a dual-gated graphene field-effect transistor placed on 3R stacked twisted bilayer of WSe2 at a twist angle of 2.1 degree. We observe hysteretic transfer characteristics and an emergent charge inhomogeneity with multiple local Dirac points as the electric displacement field (D) is increased. Concomitantly, we also observe a strong non-local voltage signal at D = 0 V/nm that decreases rapidly with increasing D. A linear scaling of the non-local signal with longitudinal resistance suggests edge mode transport, which we attribute to the breaking of valley symmetry of the graphene channel due to the spatially fluctuating electric field from the moire domains of the underlying twisted WSe2. A quantitative analysis connecting the non-locality and channel inhomogeneity suggests emergence of finite-size domains in the graphene channel that modulate the charge and the valley currents simultaneously. This work underlines efficient control and impact of interfacial ferroelectricity that can trigger a new genre of devices for twistronic applications., Comment: 16 pages, 15 figures

Twist-controlled moire superlattices (MS) have emerged as a versatile platform in which to realize artificial systems with complex electronic spectra. Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) form an interesting example of the MS that has recently featured a set of unexpected behaviors, such as unconventional ferroelectricity and electronic ratchet effect. Yet, the understanding of the BLG/hBN MS electronic properties has, at present, remained fairly limited. Here we develop a multi-messenger approach that combines standard magnetotransport techniques with low-energy sub-THz excitation to get insights into the properties of this MS. We show that BLG/hBN lattice alignment results in the emergence of compensated semimetals at some integer fillings of the moire bands separated by van Hove singularities where Lifshitz transition occurs. A particularly pronounced semimetal develops when 8 electrons reside in the moire unit cell, where coexisting high-mobility electron and hole systems feature a strong magnetoresistance reaching 2350 % already at B=0.25 T. Next, by measuring the THz-driven Nernst effect in remote bands, we observe valley splitting, pointing to an orbital magnetization characterized by a strongly enhanced effective g-factor of 340. Last, using THz photoresistance measurements, we show that the high-temperature conductivity of the BLG/hBN MS is limited by electron-electron umklapp processes. Our multi-facet analysis introduces THz-driven magnetotransport as a convenient tool to probe the band structure and interaction effects in vdW materials and provides a comprehension of the BLG/hBN MS., Comment: 9 pages, 4 figures

Moire materials like twisted bilayer graphene have emerged as a rich playground of strongly correlated physics, where the effect of interactions can be drastically enhanced by tuning the non-interacting density of states via twist angle. A key feature of bilayer graphene at small twist angles is that the two valleys of graphene are effectively decoupled at the non-interacting level, leading to an emergent U(1) symmetry corresponding to the conservation of valley-charge. Theoretical studies invariably find that short-ranged interactions tend to break this symmetry, leading to inter-valley coherence (IVC). However, there is no direct experimental probe of this ubiquitous ordering tendency. Here, I propose an experimental signature of IVC order by coupling with a closely related system where valley-mixing is guaranteed - the pentagonal disclinations of graphene. Such disclinations are naturally found in fullerenes. The tunneling current between twisted bilayer graphene and an appropriately oriented large buckyball has a sharp signature of the onset of IVC order. Successfully integrating these fullerenes in a scanning tunneling microscope would allow spatial resolution of the IVC order parameter on a sub-moire scale. Experimentally constraining the broken symmetries and order parameters in the multitude of emerging correlated insulators is a crucial first step to understanding the superconductivity that develops on doping these exotic `normal' states., Comment: 3 pages, 1 figure, comments are welcome

In magnetic insulators, the sense of rotation of the magnetization is associated with novel phases of matter and exotic transport phenomena. Aimed to find new sources of chiral magnetism rooted in intrinsic fields and geometry, twisted square bilayers of magnetic dipoles with easy plane anisotropy are studied. For no twist, each lattice settles in the zig-zag magnetic state and orders antiferromagnetically to the other layer. The moire patterns that result from the mutual rotation of the two square lattices influence such zig-zag order, giving rise to several phases that depict non-collinear magnetic textures with chiral motifs that break both time and inversion symmetry. For certain moire angles, helical and toroidal magnetic orders arise. Changing the vertical distance between layers can further manipulate these novel phases. It is shown that the dipolar interlayer interaction induces an emergent twist-dependent chiral magnetic field orthogonal to the direction of the zig-zag chains, which is responsible for the internal torques conjugated to the toroidal orders., Comment: 15 pages, 3 figures

Reservoir computing has been considered as a promising intelligent computing paradigm for effectively processing complex temporal information. Exploiting tunable and reproducible dynamics in the single electronic device have been desired to implement the reservoir and the readout layer of reservoir computing system. Two-dimensional moire material, with an artificial lattice constant many times larger than the atomic length scale, is one type of most studied artificial quantum materials in community of material science and condensed-matter physics over the past years. These materials are featured with gate-tunable periodic potential and electronic correlation, thus varying the electric field allows the electrons in the moire potential per unit cell to exhibit distinct and reproducible dynamics, showing great promise in robust reservoir computing. Here, we report that a moire synaptic transistor can be used to implement the reservoir computing system with a homogeneous reservoir-readout architecture. The synaptic transistor is fabricated based on a h-BN/bilayer graphene/h-BN moire heterostructure, exhibiting ferroelectricity-like hysteretic gate voltage dependence of resistance. Varying the magnitude of the gate voltage enables the moire transistor to be switched between long-term memory and short-term memory with nonlinear dynamics. By employing the short- and long-term memory as the reservoir nodes and weights of the readout layer, respectively, we construct a full-moire physical neural network and demonstrate that the classification accuracy of 90.8% can be achieved for the MNIST handwritten digit database. Our work would pave the way towards the development of neuromorphic computing based on the moire materials.

The topological electronic structure of crystalline materials often gives rise to intriguing surface states, such as Dirac surface states in topological insulators, Fermi arc surface states in Dirac semimetals, and topological superconductivity in iron-based superconductors. Recently, rhombohedral multilayer graphene has emerged as a promising platform for exploring exotic surface states due to its hosting of topologically protected surface flat bands at low energy, with the layer-dependent energy dispersion. These flat bands can promote electron correlations, leading to a plethora of quantum phenomena, including spontaneous symmetry breaking, superconductivity, ferromagnetism, and topological Chern insulators. Nevertheless, the intricate connection between the surface flat bands in rhombohedral multilayer graphene and the highly dispersive high-energy bands hinders the exploration of correlated surface states. Here, we present a method to isolate the surface flat bands of rhombohedral heptalayer (7L) graphene by introducing moire superlattices. The pronounced screening effects observed in the moire potential-modulated rhombohedral 7L graphene indicate its essential three-dimensional (3D) nature. The isolated surface flat bands favor correlated states on the surface in the regions away from charge-neutrality points. Most notably, we observe tunable surface ferromagnetism, manifested as an anomalous Hall effect with hysteresis loops, which is achieved by polarizing surface states using finite displacement fields. Our work establishes rhombohedral multilayer graphene moire superlattice as a unique 3D system for exploring correlated surface states.

The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The demonstration of FQAHE could lead to non-Abelian anyons which form the basis of topological quantum computation. So far, FQAHE has been observed only in twisted MoTe2 (t-MoTe2) at moire filling factor v > 1/2. Graphene-based moire superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene/hBN moire superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance Rxy = h/(ve^2) at filling factors v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moire superlattice respectively. These features are accompanied by clear dips in the longitudinal resistance Rxx. In addition, at zero magnetic field, Rxy equals 2h/e^2 at v = 1/2 and varies linearly with the filling factor-similar to the composite Fermi liquid (CFL) in the half-filled lowest Landau level at high magnetic fields. By tuning the gate displacement field D and v, we observed phase transitions from CFL and FQAH states to other correlated electron states. Our graphene system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field, especially considering a lateral junction between FQAHE and superconducting regions in the same device., Comment: Nature, in press

Twisted van der Waals materials have risen as highly tunable platform for realizing unconventional superconductivity. Here we demonstrate how a topological superconducting state can be driven in a twisted graphene multilayer at a twist angle of approximately 1.6 degrees proximitized to other 2D materials. We show that an encapsulated twisted bilayer subject to induced Rashba spin-orbit coupling, s-wave superconductivity and exchange field generates a topological superconducting state enabled by the moire pattern. We demonstrate a variety of topological states with different Chern numbers highly tunable through doping, strain and bias voltage. Our proposal does not depend on a fine tuning of the twist angle, but solely on the emergence of moire minibands and is applicable for twist angles between 1.3 and 3 degrees. Our results establish the potential of twisted graphene bilayers to create artificial topological superconductivity without requiring ultraflat dispersions., Comment: 6 pages, 3 figures

We show that any two-dimensional system with a non-zero \textit{symmetric} off-diagonal component of the resistance matrix, $R_{xy}=R_{yx} \neq 0$, must have the in-plane rotational symmetry broken down to $C_2$. Such a resistance response is Ohmic, and is different from the Hall response which is the \textit{anti-symmetric} part of the resistance tensor, $R_{xy}=-R_{yx}$, is rotationally symmetric in the 2D plane, and requires broken time-reversal symmetry. We show how a minute amount of strain due to lattice mismatch - less than $1 \%$ - can produce a vastly exaggerated symmetric off-diagonal response - $\frac{R_{xy}}{R_{xx}} \sim 20\%$ - because of the momentum matching constraints in a Moire system. Our results help explain an important new transport experiment on graphene-WSe$_2$ heterostructures, as well as are relevant for other experimental systems with rotational symmetry breaking, such as nematic systems and Kagome charge density waves. Additionally, our work predicts an example of a `magic' angle, $\theta\sim 27^0$, in a Moire system which is a significant fraction of $\pi$. Our prediction that the anomalous resistance anisotropy occurs at a large value of magic angle, in contrast to known examples of magic angle transport anomalies that are small fractions of $\pi$, can be experimentally tested in graphene-WSe$_2$ heterostructures., Comment: 5 pages, 2 figures

Extracting Hamiltonian parameters from available experimental data is a challenge in quantum materials. In particular, real-space spectroscopy methods such as scanning tunneling spectroscopy allow probing electronic states with atomic resolution, yet even in those instances extracting effective Hamiltonian is an open challenge. Here we show that impurity states in modulated systems provide a promising approach to extracting non-trivial Hamiltonian parameters of a quantum material. We show that by combining the real-space spectroscopy of different impurity locations in a moire topological superconductor, modulations of exchange and superconducting parameters can be inferred via machine learning. We demonstrate our strategy with a physically-inspired harmonic expansion combined with a fully-connected neural network that we benchmark against a conventional convolutional architecture. We show that while both approaches allow extracting exchange modulations, only the former approach allows inferring the features of the superconducting order. Our results demonstrate the potential of machine learning methods to extract Hamiltonian parameters by real-space impurity spectroscopy as local probes of a topological state., Comment: 11 pages, 8 figures

We show that optical moire lattices enable the existence of vortex solitons of different types in self-focusing Kerr media. We address the properties of such states both in lattices having commensurate and incommensurate geometries (i.e., constructed with Pythagorean and non-Pythagorean twist angles, respectively), in the different regimes that occur below and above the localization-delocalization transition. We find that the threshold power required for the formation of vortex solitons strongly depends on the twist angle and, also, that the families of solitons exhibit intervals where their power is a nearly linear function of the propagation constant and they exhibit strong stability. Also, in the incommensurate phase above the localization-delocalization transition, we found stable embedded vortex solitons whose propagation constants belong to the linear spectral domain of the system.

Most non-ferroelectric two-dimensional materials can be endowed with so-called sliding ferroelectricity via non-equivalent homo-bilayer stacking, which is not applicable to mono-element systems like pure graphene bilayer with inversion symmetry at any sliding vector. Herein we show first-principles evidence that multilayer graphene with N>3 can all be ferroelectric, where the polarizations of polar states stem from the symmetry breaking in stacking configurations of across-layer instead of adjacent-layer, which are electrically switchable via interlayer sliding. The non-polar states can also be electrically driven to polar states via sliding, all nearly degenerate in energy, and more diverse states with distinct polarizations will emerge in more layers. In contrast to the ferroelectric Moire domains with opposite polarization directions in twisted bilayers reported previously, the Moire pattern in some multilayer graphene systems (e.g., twisted monolayer-trilayer graphene) possess nonzero net polarizations with domains of the same direction separated by non-polar regions, which can be electrically reversed upon interlayer sliding. The distinct Moire bands of two polar states should facilitate electrical detection of such sliding Moire ferroelectricity during switching.

We propose a polariton-moir\'e coupled system to realize an exact solvable model of strongly correlated superconductors. The polariton condensate induces intervalley attraction between moir\'e electrons in quasi-flat topological bands, leading to emergent SU(2) symmetry and exactly solutions of the many-body ground state. This system expands the condensate-induced superconductivity to the strong-correlation regime, enabling superconductivity at elevated temperatures and allowing the study of non-Fermi liquid states with a solvable, predictive model. It is promising as a versatile platform for emulating unconventional superconductivity and other strongly correlated phenomena in complex, correlated materials.

We show that rhombohedral four-layer graphene (4LG) nearly aligned with a hexagonal boron nitride (hBN) substrate often develops nearly flat isolated low energy bands with non-zero valley Chern numbers. The bandwidths of the isolated flatbands are controllable through an electric field and twist angle, becoming as narrow as $\sim10~$meV for interlayer potential differences between top and bottom layers of $|\Delta|\approx 10\sim15~$meV and $\theta \sim 0.5^{\circ}$ at the graphene and boron nitride interface. The local density of states (LDOS) analysis shows that the nearly flat band states are associated to the non-dimer low energy sublattice sites at the top or bottom graphene layers and their degree of localization in the moire superlattice is strongly gate tunable, exhibiting at times large delocalization despite of the narrow bandwidth. We verified that the first valence bands' valley Chern numbers are $C^{\nu=\pm1}_{V1} = \pm n$, proportional to layer number for $n$LG/BN systems up to $n = 8$ rhombohedral multilayers.

This work put forward a comprehensive study of moire pattern in commensurate twisted bilayer graphene (TBG) to determine the connection of moire period with corresponding twist angle. Using the understanding of moire pattern, computational codes are developed to simulate the planar positions of carbon atoms lying in a large specimen of commensurate twisted bilayer graphene (CTBG) with any commensurate twist angle. With the help of simulated moire patterns of CTBG it is demonstrated that for many commensurate twist angles the apparent moire period may be quite different from the actual moire period, and the same moire pattern may have multiple slightly different values of the apparent moire period. These multiple slightly different values of the apparent moire period show that strain and broken rotational symmetry in moire pattern of CTBG are intrinsic. From various values of apparent moire period, the apparent strain in moire pattern of CTBG is calculated for many commensurate twist angles; the calculated values of apparent strain are in good agreement with experimentally reported values. Taking some insight from available experimental data related to twisted bilayer graphene systems and conventional bilayer graphene systems, corrugation in CTBG is modelled and incorporated with the simulated positions of carbon atoms., Comment: 25 PAGES, 25 FIGURES

The moire potential, induced by stacking two monolayer semiconductors with slightly different lattice mismatches, acts as periodic quantum confinement for optically generated excitons, resulting in spatially ordered zero-dimensional quantum systems. However, there are limitations to exploring intrinsic optical properties of moire excitons due to ensemble averaged and broadened emissions from many peaks caused by the inhomogeneity of the moire potential. In this study, we proposed a microfabrication technique based on focused Ga+ ion beams, which enables us to control the number of peaks originating from the moire potential and thus explore unknown moire optical characteristics of WSe2/MoSe2 heterobilayers. By taking advantage of this approach, we reveal emissions from a single moire exciton and charged moire exciton (trion) under electrostatic doping conditions. We show the momentum dark moire trion state above the bright trion state with a splitting energy of approximately 4 meV and clarify that the dynamics are determined by the initial trion population in the bright state. Furthermore, the degree of negative circularly polarized emissions and their valley dynamics of moire trions are dominated by a very long valley relaxation process lasting ~700 ns. Our findings on microfabricated heterobilayers could be viewed as an extension of our groundbreaking efforts in the field of quantum optics application using moire superlattices., Comment: 41 pages, 4 figures

We study the commensuration torques and layer sliding energetics of alternating twist trilayer graphene (t3G) and twisted bilayer graphene on hexagonal boron nitride (t2G/BN) that have two superposed moire interfaces. Lattice relaxations for typical graphene twist angles of $\sim 1^{\circ}$ in t3G or t2G/BN are found to break the out-of-plane layer mirror symmetry, give rise to layer rotation energy local minima dips of the order of $\sim 10^{-1}$ meV/atom at double moire alignment angles, and have sliding energy landscape minima between top-bottom layers of comparable magnitude. Moire superlubricity is restored for twist angles as small as $\sim 0.03^\circ$ away from alignment resulting in suppression of sliding energies by several orders of magnitude of typically $\sim 10^{-4}$ meV/atom, hence indicating the precedence of rotation over sliding in the double moire commensuration process., Comment: 9 pages, 4 figures

In recent years, twisted bilayer graphene has become a hot topic and inspired the research upsurge of photonic moir\'e lattice. Here, we designed a photonic moir\'e superlattice with two synthetic twist angles and constructed a synthetic moir\'e sphere based on these two angles. Thus, we have more degrees of freedom to design the band structure flexibly. A type of transition photonic bands (TPBs) is obtained in such a moir\'e superlattice. We investigate the influence of two twist angles on TPBs and find a series of magic angle pairs with optimal band compression of TPB. The interesting optical properties of TPBs are experimentally demonstrated, including pulse delay, nonlinear optical enhancement, and pulse width compression. Our work introduces a new path to explore multi-twist angles moir\'e superlattices and reveals that the designed photonic moir\'e superlattice based on moir\'e spheres has broad application prospects including optical signal processing, nonlinear optics processes ,and other light-matter interactions.

To improve the light extraction efficiency of organic light emitting diodes (OLEDs), we developed a novel substrate, i.e., a metamaterial based flat Moire micro-lens array formed using double nanoimprint, termed Mlens-array, consisting of a hexagonal moir\'e pattern pillar array. By choosing a low refractive index dielectric material for the pillar array and a high refractive index dielectric material for the layer capped on top of the pillar array, we fabricated the Mlens-array behaving as a conventional convex optical micro-lens array. The Mlens-array was fabricated on a 4-inch wafer-size glass substrate by double-cycle compositional nanoimprint lithography (NIL) which is easy for achieving high throughput fabrication in large-scale. Applying the Mlens-array substrate in a typical green-emitting OLED, the light extraction efficiency was enhanced by over 100% (2.08-fold) compared to a control device fabricated on the conventional planar glass substrate., Comment: 20 pages, 12 figures