Статті в журналах: "Graphene moiré superlattice"

1

Peña, Tara, Aditya Dey, Shoieb A. Chowdhury, Ahmad Azizimanesh, Wenhui Hou, Arfan Sewaket, Carla Watson, Hesam Askari, and Stephen M. Wu. "Moiré engineering in 2D heterostructures with process-induced strain." Applied Physics Letters 122, no. 14 (April 3, 2023): 143101. http://dx.doi.org/10.1063/5.0142406.

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We report deterministic control over a moiré superlattice interference pattern in twisted bilayer graphene by implementing designable device-level heterostrain with process-induced strain engineering, a widely used technique in industrial silicon nanofabrication processes. By depositing stressed thin films onto our twisted bilayer graphene samples, heterostrain magnitude and strain directionality can be controlled by stressor film force (film stress × film thickness) and patterned stressor geometry, respectively. We examine strain and moiré interference with Raman spectroscopy through in-plane and moiré-activated phonon mode shifts. Results support systematic C3 rotational symmetry breaking and tunable periodicity in moiré superlattices under the application of uniaxial or biaxial heterostrain. Experimental results are validated by molecular statics simulations and density functional theory based first principles calculations. This provides a method not only to tune moiré interference without additional twisting but also to allow for a systematic pathway to explore different van der Waals based moiré superlattice symmetries by deterministic design.

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2

Jadaun, Priyamvada, and Bart Soreé. "Review of Orbital Magnetism in Graphene-Based Moiré Materials." Magnetism 3, no. 3 (August 28, 2023): 245–58. http://dx.doi.org/10.3390/magnetism3030019.

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Recent years have seen the emergence of moiré materials as an attractive platform for observing a host of novel correlated and topological phenomena. Moiré heterostructures are generated when layers of van der Waals materials are stacked such that consecutive layers are slightly mismatched in their lattice orientation or unit cell size. This slight lattice mismatch gives rise to a long-wavelength moiré pattern that modulates the electronic structure and leads to novel physics. The moiré superlattice results in flat superlattice bands, electron–electron interactions and non-trivial topology that have led to the observation of superconductivity, the quantum anomalous Hall effect and orbital magnetization, among other interesting properties. This review focuses on the experimental observation and theoretical analysis of orbital magnetism in moiré materials. These systems are novel in their ability to host magnetism that is dominated by the orbital magnetic moment of Bloch electrons. This orbital magnetic moment is easily tunable using external electric fields and carrier concentration since it originates in the quantum anomalous Hall effect. As a result, the orbital magnetism found in moiré superlattices can be highly attractive for a wide array of applications including spintronics, ultra-low-power magnetic memories, spin-based neuromorphic computing and quantum information technology.

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3

Lin, Miao-Ling, Min Feng, Jiang-Bin Wu, Fei-Rong Ran, Tao Chen, Wei-Xia Luo, Heng Wu, et al. "Intralayer Phonons in Multilayer Graphene Moiré Superlattices." Research 2022 (May 30, 2022): 1–11. http://dx.doi.org/10.34133/2022/9819373.

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Moiré pattern in twisted multilayers (tMLs) induces many emergent phenomena by subtle variation of atomic registry to modulate quasiparticles and their interactions, such as superconductivity, moiré excitons, and moiré phonons. The periodic superlattice potential introduced by moiré pattern also underlies patterned interlayer coupling at the interface of tMLs. Although this arising patterned interfacial coupling is much weaker than in-plane atomic interactions, it is crucial in moiré systems, as captured by the renormalized interlayer phonons in twisted bilayer transitional metal dichalcogenides. Here, we determine the quantitative relationship between the lattice dynamics of intralayer out-of-plane optical (ZO) phonons and patterned interfacial coupling in multilayer graphene moiré superlattices (MLG-MS) by the proposed perturbation model, which is previously challenging for MLGs due to their out-of-phase displacements of adjacent atoms in one atomic plane. We unveil that patterned interfacial coupling introduces profound modulations on Davydov components of nonfolded ZO phonon that are localized within the AB-stacked constituents, while the coupling results in layer-extended vibrations with symmetry of moiré pattern for moiré ZO phonons. Our work brings further degrees of freedom to engineer moiré physics according to the modulations imprinted on the phonon frequency and wavefunction.

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4

Miao, Wenjing, Hao Sheng, and Jingang Wang. "Vertical Stress Induced Anomalous Spectral Shift of 13.17° Moiré Superlattice in Twist Bilayer Graphene." Molecules 28, no. 7 (March 28, 2023): 3015. http://dx.doi.org/10.3390/molecules28073015.

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The electronic states of the twist bilayer graphene (TBG) moiré superlattice are usually regulated by the rotation angle, applied electric field, applied magnetic field, carrier concentration and applied stress, and thus exhibit novel physical properties. Squeezing, that is, applying vertical compressive stress to the graphene layers, has profound significance in regulating the photoelectric properties of the moiré superlattice and constructing optical nanodevices. This paper presents the photoelectric properties of a TBG moiré superlattice with a twist angle of 13.17° and tunability under vertical stress. Interlayer distance decreases nonlinearly with compressive stress from 0 to 10 GPa, giving rise to weakened interlayer coupling compared to a Bernal-stacked graphene bilayer and an enhanced repulsive effect between the layers. The calculated Bloch wave functions show a strong dependence on stress. With the increase in stress, the band gaps of the system present a nonlinear increase, which induces and enhances the interlayer charge transfer and leads to the redshift of the absorption spectrum of the moiré superlattice system. By analyzing the differences in the Bloch wave function and charge density differences, we explain the nature of the physical mechanism of photoelectric property change in a stress-regulated twist superlattice system. This study provides a theoretical basis for the identification of piezoelectric properties and the stress regulation of photoelectric devices based on TBG, and also provides a feasible method for regulating the performance of TBG.

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5

Dai, Guoqiang, Xiangtao Chen, Ying Jing, and Jingang Wang. "Anti-Symmetric Electromagnetic Interactions’ Response in Electron Circular Dichroism and Chiral Origin of Periodic, Complementary Twisted Angle in Twisted Bilayer Graphene." Molecules 27, no. 19 (October 2, 2022): 6525. http://dx.doi.org/10.3390/molecules27196525.

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Many novel physical properties of twisted bilayer graphene have been discovered and studied successively, but the physical mechanism of the chiral modulation of BLG by a twisted angle lacks theoretical research. In this work, the density functional theory, the wavefunction analysis of the excited state, and the quantum theory of atoms in molecules are used to calculate and analyze the anti-symmetric chiral characteristics of zigzag-edge twisted bilayer graphene quantum dots based on periodic complementary twisted angles. The analysis of the partial density of states shows that Moiré superlattices can effectively adjust the contribution of the atomic basis function of the fragment to the transition dipole moment. The topological analysis of electron density indicates that the Moiré superlattices structure can enhance the localization of the system, increasing the electron density of the Moiré central ring, reducing the electron surge capacity in general and inducing the reversed helical properties of the top and underlying graphene, which can be used as the origin of the chiral discrimination; it also reveals the mole in the superlattice chiral physical mechanism. On this basis, we will also study the nonlinear optical properties of twisted bilayer graphene based on a twisted angle.

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6

Gao, Lei, Xinchun Chen, Yuan Ma, Yu Yan, Tianbao Ma, Yanjing Su, and Lijie Qiao. "Origin of the moiré superlattice scale lateral force modulation of graphene on a transition metal substrate." Nanoscale 10, no. 22 (2018): 10576–83. http://dx.doi.org/10.1039/c8nr01558a.

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The moiré superlattice scale lateral force modulation of graphene on a transition metal substrate originates from the joint effects of the graphene–substrate interfacial interaction and the tip–graphene interaction.

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7

Li, Hu, Raffaello Papadakis, Tanveer Hussain, Amir Karton, and Jiangwei Liu. "Moiré patterns arising from bilayer graphone/graphene superlattice." Nano Research 13, no. 4 (April 2020): 1060–64. http://dx.doi.org/10.1007/s12274-020-2744-6.

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8

Li, Zhenyao, Jia-Min Lai, and Jun Zhang. "Review of phonons in moiré superlattices." Journal of Semiconductors 44, no. 1 (January 1, 2023): 011902. http://dx.doi.org/10.1088/1674-4926/44/1/011902.

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Abstract Moiré patterns in physics are interference fringes produced when a periodic template is stacked on another similar one with different displacement and twist angles. The phonon in two-dimensional (2D) material affected by moiré patterns in the lattice shows various novel physical phenomena, such as frequency shift, different linewidth, and mediation to the superconductivity. This review gives a brief overview of phonons in 2D moiré superlattice. First, we introduce the theory of the moiré phonon modes based on a continuum approach using the elastic theory and discuss the effect of the moiré pattern on phonons in 2D materials such as graphene and MoS2. Then, we discuss the electron–phonon coupling (EPC) modulated by moiré patterns, which can be detected by the spectroscopy methods. Furthermore, the phonon-mediated unconventional superconductivity in 2D moiré superlattice is introduced. The theory of phonon-mediated superconductivity in moiré superlattice sets up a general framework, which promises to predict the response of superconductivity to various perturbations, such as disorder, magnetic field, and electric displacement field.

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9

Moutinho, Marcus V. O., Pedro Venezuela, and Marcos A. Pimenta. "Raman Spectroscopy of Twisted Bilayer Graphene." C 7, no. 1 (January 26, 2021): 10. http://dx.doi.org/10.3390/c7010010.

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When two periodic two-dimensional structures are superposed, any mismatch rotation angle between the layers generates a Moiré pattern superlattice, whose size depends on the twisting angle θ. If the layers are composed by different materials, this effect is also dependent on the lattice parameters of each layer. Moiré superlattices are commonly observed in bilayer graphene, where the mismatch angle between layers can be produced by growing twisted bilayer graphene (TBG) samples by CVD or folding the monolayer back upon itself. In TBG, it was shown that the coupling between the Dirac cones of the two layers gives rise to van Hove singularities (vHs) in the density of electronic states, whose energies vary with θ. The understanding of the behavior of electrons and their interactions with phonons in atomically thin heterostructures is crucial for the engineering of novel 2D devices. Raman spectroscopy has been often used to characterize twisted bilayer graphene and graphene heterostructures. Here, we review the main important effects in the Raman spectra of TBG discussing firstly the appearance of new peaks in the spectra associated with phonons with wavevectors within the interior of the Brillouin zone of graphene corresponding to the reciprocal unit vectors of the Moiré superlattice, and that are folded to the center of the reduced Brillouin Zone (BZ) becoming Raman active. Another important effect is the giant enhancement of G band intensity of TBG that occurs only in a narrow range of laser excitation energies and for a given twisting angle. Results show that the vHs in the density of states is not only related to the folding of the commensurate BZ, but mainly associated with the Moiré pattern that does not necessarily have a translational symmetry. Finally, we show that there are two different resonance mechanisms that activate the appearance of the extra peaks: the intralayer and interlayer electron–phonon processes, involving electrons of the same layer or from different layers, respectively. Both effects are observed for twisted bilayer graphene, but Raman spectroscopy can also be used to probe the intralayer process in any kind of graphene-based heterostructure, like in the graphene/h-BN junctions.

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10

Thomas, Loji K., and Michael Reichling. "Capillary force-induced superlattice variation atop a nanometer-wide graphene flake and its moiré origin studied by STM." Beilstein Journal of Nanotechnology 10 (April 1, 2019): 804–10. http://dx.doi.org/10.3762/bjnano.10.80.

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We present strong experimental evidence for the moiré origin of superlattices on graphite by imaging a live transition from one superlattice to another with concurrent and direct measurement of the orientation angle before and after rotation using scanning tunneling microscopy (STM). This has been possible due to a fortuitous observation of a superlattice on a nanometer-sized graphene flake wherein we have induced a further rotation of the flake utilizing the capillary forces at play at a solid–liquid interface using STM tip motion. We propose a more “realistic” tip–surface meniscus relevant to STM at solid–liquid interfaces and show that the capillary force is sufficient to account for the total expenditure of energy involved in the process.

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11

Fernandes, Rafael M., and Jörn W. F. Venderbos. "Nematicity with a twist: Rotational symmetry breaking in a moiré superlattice." Science Advances 6, no. 32 (August 2020): eaba8834. http://dx.doi.org/10.1126/sciadv.aba8834.

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Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moiré superlattice degrees of freedom on nematicity. In TBG, the nematic order parameter is not Ising like, as in tetragonal crystals, but has a three-state Potts character related to the threefold rotational symmetry (C3z) of the moiré superlattice. We find that, even in the presence of static strain that explicitly breaks the C3z symmetry, the system can still undergo a nematic-flop phase transition that spontaneously breaks in-plane twofold rotations. Moreover, elastic fluctuations, manifested as acoustic phonons, mediate a nemato-orbital coupling that ties the nematic director orientation to certain soft directions in momentum space, rendering the Potts-nematic transition mean field and first order. In contrast to the case of rigid crystals, the Fermi surface hot spots associated with these soft directions are maximally coupled to low-energy nematic fluctuations in the moiré superlattice case.

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12

Wang, Jingang, Fengcai Ma, Wenjie Liang, Rongming Wang, and Mengtao Sun. "Optical, photonic and optoelectronic properties of graphene, h-BN and their hybrid materials." Nanophotonics 6, no. 5 (June 22, 2017): 943–76. http://dx.doi.org/10.1515/nanoph-2017-0015.

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AbstractBecause of the linear dispersion relation and the unique structure of graphene’s Dirac electrons, which can be tuned the ultra-wide band, this enables more applications in photonics, electronics and plasma optics. As a substrate, hexagonal boron nitride (h-BN) has an atomic level flat surface without dangling bonds, a weak doping effect and a response in the far ultraviolet area. So the graphene/h-BN heterostructure is very attractive due to its unique optical electronics characteristics. Graphene and h-BN which are stacked in different ways could open the band gap of graphene, and form a moiré pattern for graphene on h-BN and the superlattice in the Brillouin zone, which makes it possible to build photoelectric devices.

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13

Rakib, Tawfiqur, Pascal Pochet, Elif Ertekin, and Harley T. Johnson. "Moiré engineering in van der Waals heterostructures." Journal of Applied Physics 132, no. 12 (September 28, 2022): 120901. http://dx.doi.org/10.1063/5.0105405.

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Isolated atomic planes can be assembled into a multilayer van der Waals (vdW) heterostructure in a precisely chosen sequence. These heterostructures feature moiré patterns if the constituent 2D material layers are stacked in an incommensurable way, due to a lattice mismatch or twist. This design-by-stacking has opened up the promising area of moiré engineering, a term that can be understood in two different perspectives, namely, (i) structural—engineering a moiré pattern by introducing twist, relative strain, or defects that affect the commensurability of the layers and (ii) functional—exploiting a moiré pattern to find and tune resulting physical properties of a vdW heterostructure. The latter meaning, referring to the application of a moiré pattern, is seen in the literature in the specific context of the observation of correlated electronic states and unconventional superconductivity in twisted bilayer graphene. The former meaning, referring to the design of the moiré pattern itself, is present in the literature but less commonly discussed or less understood. The underlying link between these two perspectives lies in the deformation field of the moiré superlattice. In this Perspective, we describe a path from designing a moiré pattern to employing the moiré pattern to tune physical properties of a vdW heterostructure. We also discuss the concept of moiré engineering in the context of twistronics, strain engineering, and defect engineering in vdW heterostructures. Although twistronics is always associated with moiré superlattices, strain and defect engineering are often not. Here, we demonstrate how strain and defect engineering can be understood within the context of moiré engineering. Adopting this perspective, we note that moiré engineering creates a compelling opportunity to design and develop multiscale electronic devices.

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14

Wu, Sanfeng, Lei Wang, You Lai, Wen-Yu Shan, Grant Aivazian, Xian Zhang, Takashi Taniguchi, et al. "Multiple hot-carrier collection in photo-excited graphene Moiré superlattices." Science Advances 2, no. 5 (May 2016): e1600002. http://dx.doi.org/10.1126/sciadv.1600002.

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In conventional light-harvesting devices, the absorption of a single photon only excites one electron, which sets the standard limit of power-conversion efficiency, such as the Shockley-Queisser limit. In principle, generating and harnessing multiple carriers per absorbed photon can improve efficiency and possibly overcome this limit. We report the observation of multiple hot-carrier collection in graphene/boron-nitride Moiré superlattice structures. A record-high zero-bias photoresponsivity of 0.3 A/W (equivalently, an external quantum efficiency exceeding 50%) is achieved using graphene’s photo-Nernst effect, which demonstrates a collection of at least five carriers per absorbed photon. We reveal that this effect arises from the enhanced Nernst coefficient through Lifshtiz transition at low-energy Van Hove singularities, which is an emergent phenomenon due to the formation of Moiré minibands. Our observation points to a new means for extremely efficient and flexible optoelectronics based on van der Waals heterostructures.

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15

Sunku, S. S., G. X. Ni, B. Y. Jiang, H. Yoo, A. Sternbach, A. S. McLeod, T. Stauber, et al. "Photonic crystals for nano-light in moiré graphene superlattices." Science 362, no. 6419 (December 6, 2018): 1153–56. http://dx.doi.org/10.1126/science.aau5144.

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Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moiré superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus-obtained twisted bilayer graphene (TBG). We studied the propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG into a natural plasmon photonic crystal for propagating nano-light. This discovery points to a pathway for controlling nano-light by exploiting quantum properties of graphene and other atomically layered van der Waals materials, eliminating the need for arduous top-down nanofabrication.

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16

Lv, Xinyu, Lu Wen, Zhenbing Dai, Guoyu Luo, and Zhiqiang Li. "Tuning polaritons in van der Waals moiré superlattices with interlayer spacing." Applied Physics Letters 121, no. 5 (August 1, 2022): 053101. http://dx.doi.org/10.1063/5.0091952.

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We theoretically study the interference and propagation of phonon polaritons in hexagonal boron nitride (hBN) in van der Waals heterostructures composed of hBN and twisted bilayer graphene (TBG) with different interlayer spacing in TBG. We show that varying the interlayer spacing and, hence, the interlayer coupling strength results in dramatic modifications of the local optical conductivity at the domain walls (DWs) in TBG, which leads to significant changes in the polariton interference profile near DWs. Moreover, our simulation reveals that the two-dimensional near-field interference pattern generated by polariton propagation in hBN/TBG heterostructures can be dramatically changed by interlayer spacing and the superlattice period. Our study demonstrates that combining interlayer spacing modification with moiré superlattices is a valuable route to control light at the nanoscale and design nanophotonic devices with tunable functionalities.

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17

Handschin, Clevin, Péter Makk, Peter Rickhaus, Ming-Hao Liu, K. Watanabe, T. Taniguchi, Klaus Richter, and Christian Schönenberger. "Fabry-Pérot Resonances in a Graphene/hBN Moiré Superlattice." Nano Letters 17, no. 1 (December 16, 2016): 328–33. http://dx.doi.org/10.1021/acs.nanolett.6b04137.

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18

Xin, Kaiyao, Xingang Wang, Kasper Grove-Rasmussen, and Zhongming Wei. "Twist-angle two-dimensional superlattices and their application in (opto)electronics." Journal of Semiconductors 43, no. 1 (January 1, 2022): 011001. http://dx.doi.org/10.1088/1674-4926/43/1/011001.

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Abstract Twist-angle two-dimensional systems, such as twisted bilayer graphene, twisted bilayer transition metal dichalcogenides, twisted bilayer phosphorene and their multilayer van der Waals heterostructures, exhibit novel and tunable properties due to the formation of Moiré superlattice and modulated Moiré bands. The review presents a brief venation on the development of “twistronics” and subsequent applications based on band engineering by twisting. Theoretical predictions followed by experimental realization of magic-angle bilayer graphene ignited the flame of investigation on the new freedom degree, twist-angle, to adjust (opto)electrical behaviors. Then, the merging of Dirac cones and the presence of flat bands gave rise to enhanced light-matter interaction and gate-dependent electrical phases, respectively, leading to applications in photodetectors and superconductor electronic devices. At the same time, the increasing amount of theoretical simulation on extended twisted 2D materials like TMDs and BPs called for further experimental verification. Finally, recently discovered properties in twisted bilayer h-BN evidenced h-BN could be an ideal candidate for dielectric and ferroelectric devices. Hence, both the predictions and confirmed properties imply twist-angle two-dimensional superlattice is a group of promising candidates for next-generation (opto)electronics.

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19

Yang, Jixiang, Guorui Chen, Tianyi Han, Qihang Zhang, Ya-Hui Zhang, Lili Jiang, Bosai Lyu, et al. "Spectroscopy signatures of electron correlations in a trilayer graphene/hBN moiré superlattice." Science 375, no. 6586 (March 18, 2022): 1295–99. http://dx.doi.org/10.1126/science.abg3036.

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ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice (TLG/hBN) has emerged as a playground for correlated electron physics. We report spectroscopy measurements of dual-gated TLG/hBN using Fourier transform infrared photocurrent spectroscopy. We observed a strong optical transition between moiré minibands that narrows continuously as a bandgap is opened by gating, indicating a reduction of the single-particle bandwidth. At half-filling of the valence flat band, a broad absorption peak emerges at ~18 milli–electron volts, indicating direct optical excitation across an emerging Mott gap. Similar photocurrent spectra are observed in two other correlated insulating states at quarter- and half-filling of the first conduction band. Our findings provide key parameters of the Hubbard model for the understanding of electron correlation in TLG/hBN.

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Chu, Yanbang, Le Liu, Yalong Yuan, Cheng Shen, Rong Yang, Dongxia Shi, Wei Yang, and Guangyu Zhang. "A review of experimental advances in twisted graphene moiré superlattice." Chinese Physics B 29, no. 12 (December 2020): 128104. http://dx.doi.org/10.1088/1674-1056/abb221.

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Chen, Guorui, Aaron L. Sharpe, Patrick Gallagher, Ilan T. Rosen, Eli J. Fox, Lili Jiang, Bosai Lyu, et al. "Signatures of tunable superconductivity in a trilayer graphene moiré superlattice." Nature 572, no. 7768 (July 17, 2019): 215–19. http://dx.doi.org/10.1038/s41586-019-1393-y.

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Li, Xiao-Feng, Ruo-Xuan Sun, Su-Yun Wang, Xiao Li, Zhi-Bo Liu, and Jian-Guo Tian. "Recent Advances in Moiré Superlattice Structures of Twisted Bilayer and Multilayer Graphene." Chinese Physics Letters 39, no. 3 (March 1, 2022): 037301. http://dx.doi.org/10.1088/0256-307x/39/3/037301.

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Twisted bilayer graphene (TBG), which has drawn much attention in recent years, arises from van der Waals materials gathering each component together via van der Waals force. It is composed of two sheets of graphene rotated relatively to each other. Moiré potential, resulting from misorientation between layers, plays an essential role in determining the band structure of TBG, which directly relies on the twist angle. Once the twist angle approaches a certain critical value, flat bands will show up, indicating the suppression of kinetic energy, which significantly enhances the importance of Coulomb interaction between electrons. As a result, correlated states like correlated insulators emerge from TBG. Surprisingly, superconductivity in TBG is also reported in many experiments, which drags researchers into thinking about the underlying mechanism. Recently, the interest in the atomic reconstruction of TBG at small twist angles comes up and reinforces further understandings of properties of TBG. In addition, twisted multilayer graphene receives more and more attention, as they could likely outperform TBG although they are more difficult to handle experimentally. In this review, we mainly introduce theoretical and experimental progress on TBG. Besides the basic knowledge of TBG, we emphasize the essential role of atomic reconstruction in both experimental and theoretical investigations. The consideration of atomic reconstruction in small-twist situations can provide us with another aspect to have an insight into physical mechanism in TBG. In addition, we cover the recent hot topic, twisted multilayer graphene. While the bilayer situation can be relatively easy to resolve, multilayer situations can be really complicated, which could foster more unique and novel properties. Therefore, in the end of the review, we look forward to future development of twisted multilayer graphene.

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23

Yao, Wei, Eryin Wang, Changhua Bao, Yiou Zhang, Kenan Zhang, Kejie Bao, Chun Kai Chan, et al. "Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling." Proceedings of the National Academy of Sciences 115, no. 27 (June 18, 2018): 6928–33. http://dx.doi.org/10.1073/pnas.1720865115.

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The interlayer coupling can be used to engineer the electronic structure of van der Waals heterostructures (superlattices) to obtain properties that are not possible in a single material. So far research in heterostructures has been focused on commensurate superlattices with a long-ranged Moiré period. Incommensurate heterostructures with rotational symmetry but not translational symmetry (in analogy to quasicrystals) are not only rare in nature, but also the interlayer interaction has often been assumed to be negligible due to the lack of phase coherence. Here we report the successful growth of quasicrystalline 30° twisted bilayer graphene (30°-tBLG), which is stabilized by the Pt(111) substrate, and reveal its electronic structure. The 30°-tBLG is confirmed by low energy electron diffraction and the intervalley double-resonance Raman mode at 1383 cm−1. Moreover, the emergence of mirrored Dirac cones inside the Brillouin zone of each graphene layer and a gap opening at the zone boundary suggest that these two graphene layers are coupled via a generalized Umklapp scattering mechanism—that is, scattering of a Dirac cone in one graphene layer by the reciprocal lattice vector of the other graphene layer. Our work highlights the important role of interlayer coupling in incommensurate quasicrystalline superlattices, thereby extending band structure engineering to incommensurate superstructures.

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Yi-Ru, Ji, Chu Yan-Bang, Xian Le-De, Yang Wei, and Zhang Guang-Yu. "From magic angle twisted bilayer graphene to moiré superlattice auantum simulator." Acta Physica Sinica 70, no. 11 (2021): 118101. http://dx.doi.org/10.7498/aps.70.20210476.

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25

Lyu, Xin-Yu, and Zhi-Qiang Li. "Topological properties of graphene moiré superlattice systems and recent optical studies." Acta Physica Sinica 68, no. 22 (2019): 220303. http://dx.doi.org/10.7498/aps.68.20191317.

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Avvisati, Giulia, Pierluigi Gargiani, Pierluigi Mondelli, Francesco Presel, Luca Bignardi, Alessandro Baraldi, and Maria Grazia Betti. "Metal phthalocyanines interaction with Co mediated by a moiré graphene superlattice." Journal of Chemical Physics 150, no. 5 (February 7, 2019): 054704. http://dx.doi.org/10.1063/1.5080533.

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27

Wallbank, John R., Marcin Mucha-Kruczyński, Xi Chen, and Vladimir I. Fal'ko. "Moiré superlattice effects in graphene/boron-nitride van der Waals heterostructures." Annalen der Physik 527, no. 5-6 (April 28, 2015): 359–76. http://dx.doi.org/10.1002/andp.201400204.

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28

Fortin-Deschenes, Matthieu, Rui Pu, Chao Ma, Yanfeng Zhou, Fan Zhang, Xu Du, and Fengnian Xia. "Unravelling the Topological Edge States of Twisted Bilayer Graphene." ECS Meeting Abstracts MA2022-01, no. 12 (July 7, 2022): 875. http://dx.doi.org/10.1149/ma2022-0112875mtgabs.

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Stacking two slightly lattice-mismatched or relatively twisted two-dimensional (2D) materials gives rise to an unexpected richness of physical phenomena due to the emerging moiré pattern. In particular, twisted-bilayer graphene (t-BLG) has recently been shown to host strongly correlated phases as well as unconventional superconductivity [1, 2]. While recent studies have hinted at the non-trivial topology of the moiré bands [3, 4], direct experimental observations of the topological edge states are still conspicuously missing. Herein, using superconducting quantum interference, we reconstruct the real-space current distribution in t-BLG Josephson junctions (JJs) and reveal the presence of conductive edge states when the Fermi level is placed in the superlattice induced band gaps. These results suggest the non-trivial topology of t-BLG and lay the groundwork to understand and exploit the edge states in moiré materials. [1] Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Jarillo-Herrero, P. Nature 2018, 556, (7699), 43. [2] Cao, Y., Fatemi, V., Demir, A., Fang, S., Tomarken, S. L., Luo, J. Y., ... & Jarillo-Herrero, P. (2018). Nature, 556(7699), 80-84. [3] Park, M. J., Kim, Y., Cho, G. Y., & Lee, S. (2019). Physical review letters, 123(21), 216803. [4] Ma, C.; Wang, Q.; Mills, S.; Chen, X.; Deng, B.; Yuan, S.; Li, C.; Watanabe, K.; Taniguchi, T.; Du, X.; Zhang, F.; Xia, F. Nano Letters 2020, 20, (8), 6076-6083.

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29

Sboychakov, Artem O., Kliment I. Kugel, and Antonio Bianconi. "Moiré-like Superlattice Generated van Hove Singularities in a Strained CuO2 Double Layer." Condensed Matter 7, no. 3 (August 23, 2022): 50. http://dx.doi.org/10.3390/condmat7030050.

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While it is known that the double-layer Bi2Sr2CaCu2O8+y (BSCCO) cuprate superconductor exhibits a one-dimensional (1D) incommensurate superlattice (IS), the effect of IS on the electronic structure remains elusive. Following the recent shift of interest from an underdoped phase to optimum and overdoped phases in BSCCO by increasing the hole doping x, controlled by the oxygen interstitials concentration y, here we focus on the multiple splitting of the density of states (DOS) peaks and emergence of higher order van Hove singularities (VHS) due to the 1D incommensurate superlattice. It is known that the 1D incommensurate wave vector q=ϵb (where b is the reciprocal lattice vector of the orthorhombic lattice) is controlled by the misfit strain between different atomic layers in the range 0.209–0.215 in BSCCO and in the range 0.209–0.25 in Bi2Sr2Ca1−xYxCu2O8+y (BSCYCO). This work reports the theoretical calculation of a complex pattern of VHS due to the 1D incommensurate superlattice with large 1D quasi-commensurate supercells with the wave vector ϵ=9/η in the range 36>η>43. The similarity of the complex VHS splitting and appearing of higher order VHS in a mismatched CuO2 bilayer with VHS due to the moiré lattice in strained twisted bilayer graphene is discussed. This makes a mismatched CuO2 bilayer quite promising for constructing quantum devices with tuned physical characteristics.

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30

Wong, Dillon, Kevin P. Nuckolls, Myungchul Oh, Ryan L. Lee, Kenji Watanabe, Takashi Taniguchi, and Ali Yazdani. "Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride." Low Temperature Physics 49, no. 6 (June 1, 2023): 655–61. http://dx.doi.org/10.1063/10.0019422.

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At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θGr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.

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31

Chen, Guorui, Lili Jiang, Shuang Wu, Bosai Lyu, Hongyuan Li, Bheema Lingam Chittari, Kenji Watanabe, et al. "Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice." Nature Physics 15, no. 3 (January 21, 2019): 237–41. http://dx.doi.org/10.1038/s41567-018-0387-2.

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32

Liu, Jun, Shuai Zhang, Qunyang Li, Xi-Qiao Feng, Zengfeng Di, Chang Ye, and Yalin Dong. "Lateral force modulation by moiré superlattice structure: Surfing on periodically undulated graphene sheets." Carbon 125 (December 2017): 76–83. http://dx.doi.org/10.1016/j.carbon.2017.09.028.

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33

Wu, Di, Yi Pan, and Tai Min. "Twistronics in Graphene, from Transfer Assembly to Epitaxy." Applied Sciences 10, no. 14 (July 8, 2020): 4690. http://dx.doi.org/10.3390/app10144690.

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The twistronics, which is arising from the moiré superlattice of the small angle between twisted bilayers of 2D materials like graphene, has attracted much attention in the field of 2D materials and condensed matter physics. The novel physical properties in such systems, like unconventional superconductivity, come from the dispersionless flat band that appears when the twist reaches some magic angles. By tuning the filling of the fourfold degeneracy flat bands, the desired effects are induced due to the strong correlation of the degenerated Bloch electrons. In this article, we review the twistronics in twisted bi- and multi-layer graphene (TBG and TMG), which is formed both by transfer assembly of exfoliated monolayer graphene and epitaxial growth of multilayer graphene on SiC substrates. Starting from a brief history, we then introduce the theory of flat band in TBG. In the following, we focus on the major achievements in this field: (a) van Hove singularities and charge order; (b) superconductivity and Mott insulator in TBG and (c) transport properties in TBG. In the end, we give the perspective of the rising materials system of twistronics, epitaxial multilayer graphene on the SiC.

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34

Talantsev, Evgueni. "Quantifying the Charge Carrier Interaction in Metallic Twisted Bilayer Graphene Superlattices." Nanomaterials 11, no. 5 (May 15, 2021): 1306. http://dx.doi.org/10.3390/nano11051306.

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The mechanism of charge carrier interaction in twisted bilayer graphene (TBG) remains an unresolved problem, where some researchers proposed the dominance of the electron–phonon interaction, while the others showed evidence for electron–electron or electron–magnon interactions. Here we propose to resolve this problem by generalizing the Bloch–Grüneisen equation and using it for the analysis of the temperature dependent resistivity in TBG. It is a well-established theoretical result that the Bloch–Grüneisen equation power-law exponent, p, exhibits exact integer values for certain mechanisms. For instance, p = 5 implies the electron–phonon interaction, p = 3 is associated with the electron–magnon interaction and p = 2 applies to the electron–electron interaction. Here we interpret the linear temperature-dependent resistance, widely observed in TBG, as p→1, which implies the quasielastic charge interaction with acoustic phonons. Thus, we fitted TBG resistance curves to the Bloch–Grüneisen equation, where we propose that p is a free-fitting parameter. We found that TBGs have a smoothly varied p-value (ranging from 1.4 to 4.4) depending on the Moiré superlattice constant, λ, or the charge carrier concentration, n. This implies that different mechanisms of the charge carrier interaction in TBG superlattices smoothly transition from one mechanism to another depending on, at least, λ and n. The proposed generalized Bloch–Grüneisen equation is applicable to a wide range of disciplines, including superconductivity and geology.

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35

Kerelsky, Alexander, Carmen Rubio-Verdú, Lede Xian, Dante M. Kennes, Dorri Halbertal, Nathan Finney, Larry Song, et al. "Moiréless correlations in ABCA graphene." Proceedings of the National Academy of Sciences 118, no. 4 (January 19, 2021): e2017366118. http://dx.doi.org/10.1073/pnas.2017366118.

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Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

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36

Hamer, Matthew J., Alessio Giampietri, Viktor Kandyba, Francesca Genuzio, Tevfik O. Menteş, Andrea Locatelli, Roman V. Gorbachev, Alexei Barinov, and Marcin Mucha-Kruczyński. "Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Bilayer Graphene." ACS Nano 16, no. 2 (January 24, 2022): 1954–62. http://dx.doi.org/10.1021/acsnano.1c06439.

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37

Politano, Antonio, Guus J. Slotman, Rafael Roldán, Gennaro Chiarello, Davide Campi, Mikhail I. Katsnelson, and Shengjun Yuan. "Effect of moiré superlattice reconstruction in the electronic excitation spectrum of graphene-metal heterostructures." 2D Materials 4, no. 2 (January 11, 2017): 021001. http://dx.doi.org/10.1088/2053-1583/aa53ba.

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38

Zou, Q., B. D. Belle, L. Z. Zhang, W. D. Xiao, K. Yang, L. W. Liu, G. Q. Wang, et al. "Modulation of Fermi velocities of Dirac electrons in single layer graphene by moiré superlattice." Applied Physics Letters 103, no. 11 (September 9, 2013): 113106. http://dx.doi.org/10.1063/1.4821178.

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39

Ribeiro-Palau, Rebeca, Changjian Zhang, Kenji Watanabe, Takashi Taniguchi, James Hone, and Cory R. Dean. "Twistable electronics with dynamically rotatable heterostructures." Science 361, no. 6403 (August 16, 2018): 690–93. http://dx.doi.org/10.1126/science.aat6981.

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In heterostructures of two-dimensional materials, electronic properties can vary dramatically with relative interlayer angle. This effect makes it theoretically possible to realize a new class of twistable electronics in which properties can be manipulated on demand by means of rotation. We demonstrate a device architecture in which a layered heterostructure can be dynamically twisted in situ. We study graphene encapsulated by boron nitride, where, at small rotation angles, the device characteristics are dominated by coupling to a long-wavelength moiré superlattice. The ability to investigate arbitrary rotation angle in a single device reveals features of the optical, mechanical, and electronic response in this system not captured in static rotation studies. Our results establish the capability to fabricate twistable electronic devices with dynamically tunable properties.

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40

Kong, Xiangru, Linyang Li, and François M. Peeters. "Graphene-based heterostructures with moiré superlattice that preserve the Dirac cone: a first-principles study." Journal of Physics: Condensed Matter 31, no. 25 (April 10, 2019): 255302. http://dx.doi.org/10.1088/1361-648x/ab132f.

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41

Ren, Lingling, and Baojuan Dong. "Ferroelectric Polarization in an h-BN-Encapsulated 30°-Twisted Bilayer–Graphene Heterostructure." Magnetochemistry 9, no. 5 (April 26, 2023): 116. http://dx.doi.org/10.3390/magnetochemistry9050116.

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Recently, the emergent two-dimensional (2D) ferroelectric materials have provided new possibilities for the miniaturization of ferroelectric systems and the integration of novel 2D nano-electronic devices. In addition to the intrinsic ferroelectrics exfoliated from bulk, 2D heterostructures hybridized from electrically non-polarized van der Waals (vdW) materials have also been proven to be a promising platform for the construction of ferroelectricity. Here, we report 30° twisted bilayer–graphene (TBLG) incommensurate moiré superlattice encapsulated by hexagonal boron nitride (h-BN), in which robust hysteretic resistance was detected at the top interface between h-BN and the TBLG from room temperature down to 40 mK. The hysteretic phenomenon can be understood by the extra carrier induced by the interfacial 2D ferroelectric polarization, which is estimated to be around 0.7 pC/m. Our work of interfacial ferroelectric heterostructure achieved by a TBLG/h-BN hybrid system expands the 2D ferroelectric families and opens more possibilities for future coupling the ferroelectricity with rich electronic and optical properties in vdW twistronic devices.

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42

Cuxart, Marc G., Daniele Perilli, Sena Tömekce, Joel Deyerling, Felix Haag, Matthias Muntwiler, Francesco Allegretti, Cristiana Di Valentin, and Willi Auwärter. "Spatial segregation of substitutional B atoms in graphene patterned by the moiré superlattice on Ir(111)." Carbon 201 (January 2023): 881–90. http://dx.doi.org/10.1016/j.carbon.2022.09.087.

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43

Shi, Ruoyu, Lei Gao, Hongliang Lu, Qunyang Li, Tian-Bao Ma, Hui Guo, Shixuan Du, et al. "Moiré superlattice-level stick-slip instability originated from geometrically corrugated graphene on a strongly interacting substrate." 2D Materials 4, no. 2 (April 28, 2017): 025079. http://dx.doi.org/10.1088/2053-1583/aa6da2.

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44

Meng, Qinghao, Fan Yu, Gan Liu, Junyu Zong, Qichao Tian, Kaili Wang, Xiaodong Qiu, Can Wang, Xiaoxiang Xi та Yi Zhang. "Thickness-Dependent Evolutions of Surface Reconstruction and Band Structures in Epitaxial β–In2Se3 Thin Films". Nanomaterials 13, № 9 (3 травня 2023): 1533. http://dx.doi.org/10.3390/nano13091533.

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Ferroelectric materials have received great attention in the field of data storage, benefiting from their exotic transport properties. Among these materials, the two-dimensional (2D) In2Se3 has been of particular interest because of its ability to exhibit both in-plane and out-of-plane ferroelectricity. In this article, we realized the molecular beam epitaxial (MBE) growth of β–In2Se3 films on bilayer graphene (BLG) substrates with precisely controlled thickness. Combining in situ scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES) measurements, we found that the four-monolayer β–In2Se3 is a semiconductor with a (9 × 1) reconstructed superlattice. In contrast, the monolayer β–In2Se3/BLG heterostructure does not show any surface reconstruction due to the interfacial interaction and moiré superlattice, which instead results in a folding Dirac cone at the center of the Brillouin zone. In addition, we found that the band gap of In2Se3 film decreases after potassium doping on its surface, and the valence band maximum also shifts in momentum after surface potassium doping. The successful growth of high-quality β–In2Se3 thin films would be a new platform for studying the 2D ferroelectric heterostructures and devices. The experimental results on the surface reconstruction and band structures also provide important information on the quantum confinement and interfacial effects in the epitaxial β–In2Se3 films.

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45

Sun Qiaodong, 孙侨东, 黄鑫宇 Huang Xinyu, 林润峰 Lin Runfeng, 彭追日 Peng Zhuiri, 徐浪浪 Xu Langlang та 叶镭 Ye Lei. "石墨烯摩尔超晶格的近场纳米成像（特邀）". Infrared and Laser Engineering 51, № 7 (2022): 20211118. http://dx.doi.org/10.3788/irla20211118.

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46

Zhang, Shi-Hao, Bo Xie, Ran Peng, Xiao-Qian Liu, Xin Lu, and Jian-Peng Liu. "Novel electrical properties of moiré graphene systems." Acta Physica Sinica 72, no. 6 (2023): 1. http://dx.doi.org/10.7498/aps.72.20230120.

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In this review, we discuss the electronic structures, topological properties, correlated states, nonlinear optical responses, as well as phonon and electron-phonon coupling effects of moiré graphene superlattices. First, we illustrate that topologically non-trivial flat bands and moiré orbital magnetism are ubiquitous in various twisted graphene systems. In particular, the topological flat bands of magic-angle twisted bilayer graphene (TBG) can be explained from a zeroth pseudo-Landau-level picture, which can naturally explain the experimentally observed quantum anomalous Hall effect and some of the other correlated states. These topologically nontrivial flat bands may lead to nearly quantized piezoelectric response, which can be used to directly probe the valley Chern numbers in these moiré graphene systems. A simple and general chiral decomposition rule is reviewed and discussed, which can be used to predict the low-energy band dispersions of generic twisted mulilayer graphene system and alternating twisted multilayer graphene system. This review further discusses nontrivial interaction effects of magic-angle TBG such as the correlated insulator states, density wave states, cascade transitions, and nematic states, and proposes nonlinear optical measurement as an experimental probe to distinguish the different "featureless" correlated states.The phonon properties and electron-phonon coupling effects are also briefly reviewed. The novel physics emerging from band-aligned graphene-insulator heterostructres is also discussed in this review. In the end, we make a summary and an outlook about the novel physical properties of moiré superlattices, two-dimensional materials, moiré superlattices－ two dimensional materials.

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47

Zhang, Yiran, Robert Polski, Cyprian Lewandowski, Alex Thomson, Yang Peng, Youngjoon Choi, Hyunjin Kim, et al. "Promotion of superconductivity in magic-angle graphene multilayers." Science 377, no. 6614 (September 30, 2022): 1538–43. http://dx.doi.org/10.1126/science.abn8585.

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Graphene moiré superlattices show an abundance of correlated insulating, topological, and superconducting phases. Whereas the origins of strong correlations and nontrivial topology can be directly linked to flat bands, the nature of superconductivity remains enigmatic. We demonstrate that magic-angle devices made of twisted tri-, quadri-, and pentalayer graphene placed on monolayer tungsten diselenide exhibit flavor polarization and superconductivity. We also observe insulating states in the tril- and quadrilayer arising at finite electric displacement fields. As the number of layers increases, superconductivity emerges over an enhanced filling-factor range, and in the pentalayer it extends well beyond the filling of four electrons per moiré unit cell. Our results highlight the role of the interplay between flat and more dispersive bands in extending superconducting regions in graphene moiré superlattices.

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48

Chernozatonskii, L. A., V. A. Demin, and Ph Lambin. "Bilayered graphene as a platform of nanostructures with folded edge holes." Physical Chemistry Chemical Physics 18, no. 39 (2016): 27432–41. http://dx.doi.org/10.1039/c6cp05082d.

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49

Ni, G. X., H. Wang, J. S. Wu, Z. Fei, M. D. Goldflam, F. Keilmann, B. Özyilmaz, et al. "Plasmons in graphene moiré superlattices." Nature Materials 14, no. 12 (September 28, 2015): 1217–22. http://dx.doi.org/10.1038/nmat4425.

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50

Mukai, Fumiya, Kota Horii, Ryoya Ebisuoka, Kenji Watanabe, Takashi Taniguchi, and Ryuta Yagi. "Unconventional satellite resistance peaks in moiré superlattice of h-BN/ AB-stacked tetralayer-graphene heterostructures." Communications Physics 4, no. 1 (May 26, 2021). http://dx.doi.org/10.1038/s42005-021-00615-2.

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AbstractMost studies on moiré superlattices formed from a stack of h-BN (two-dimensional hexagonal boron nitride) and graphene have focused on single layer graphene; graphene with multiple layers is less understood. Here, we show that a moiré superlattice of multilayer graphene shows features arising from the anisotropic Fermi surface affected by the superlattice structure. The moiré superlattice of a h-BN/AB-stacked tetralayer graphene heterostructures exhibited resistivity peaks showing a complicated dependence on the perpendicular electric field. The peaks were not due to secondary Dirac cones forming, but rather opening of the energy gap due to folding of the anisotropic Fermi surface. In addition, superlattice peaks resulted from mixing of light- and heavy-mass bilayer-like bands via the superlattice potential. The gaps did not open on the boundary of the superlattice Brillouin zone, but rather opened inside it, which reflected the anisotropy of the Fermi surface of multilayer graphene.

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