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Effective model of moiré mini lattice and flat bands. a) Moiré Brillouin zone of a nearly commensurate graphene heterostructure. b) Calculated band structure and density of states with α = 0.1, 0.586, and 2.221. The DOS plot in the middle panel includes an inset showing the tight‐binding DOS (the blue curve) from Figure 4f. c) Schematic of the two ways of assembling heterostructures with flat bands.
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Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two‐dimensional material, enhance electron correlations, and give rise to novel condensed‐matter phases such as superconductors, Mott insulators, Wigner crystals and quantum anomalous Hall insulators. Previous wo...
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... Due to their high mesoscale quality and compatibility of the SiC(0001) substrate with general semiconductor processing strategies, these epitaxial graphene-based systems attract significant attention [27][28][29][30][31] . In this case, the interface between the first epitaxial graphene layer (buffer layer; C buffer ) and SiC are primarily responsible for their unique electronic properties [32][33][34][35] . Controlling over this interface tunes the graphene electronic states, which leads to a rich variety of systems manifesting graphene-based physics of fundamental interest. ...
... Controlling over this interface tunes the graphene electronic states, which leads to a rich variety of systems manifesting graphene-based physics of fundamental interest. Particularly, they include ballistic transport in topological edge states of graphene nanoribbons 28,29,31,36 , graphene flat bands 34,35 , strain-induced pseudo-magnetic fields 30 , or superconductivity via intercalation of the interface [37][38][39][40] . On the other hand, epitaxial graphene is routinely used as a model material system, e.g., to study electric-field-dependent single-atom chemical bonding between metal and graphene 41 , or structural dislocations of graphene 42 and their dynamics 43 . ...
Precision of scanning tunneling microscopy (STM) enables control of matter at scales of single atoms. However, transition from atomic-scale manipulation strategies to practical devices encounters fundamental problems in protection of the designer structures formed atop the surface. In this context, STM manipulation of subsurface structures on technologically relevant materials is encouraging. Here, we propose a material platform and protocols for precise manipulation of a buried graphene interface. We show that an electric field from the STM tip reversibly controls breaking and restoring of covalent bonds between the graphene buffer layer and the SiC substrate. The process involves charge redistribution at the atomically sharp interface plane under the epitaxial graphene layer(s). This buried manipulation platform is laterally defined by unit cells from the corresponding (6×6)SiC moiré lattice of the epitaxial graphene. Local and reversible electric-field-induced patterning of graphene heterostructures from the bottom interface creates an alternative architecture concept for their applications.
... growing epitaxial graphene-SiC heterostructures [21][22][23][24][25][26] . Due to their unique electronic properties and compatibility of the SiC(0001) substrate with general semiconductor processing strategies, these epitaxial graphene-based systems attract signi cant attention [27][28][29][30][31][32][33][34][35] . Particularly, improved synthesis methods of a high-quality, long-range ordered interface between the rst epitaxial graphene layer (buffer layer; C buffer ) and SiC have realized a semiconducting graphene, a long-time challenge [36][37][38] . ...
Unprecedent precision of scanning tunneling microscopy (STM) enables control of matter at scales of single atoms. However, transition from atomic-scale manipulation strategies to practical devices encounters fundamental problems in protection of the designer structures formed atop the surface. In this context, STM manipulation of subsurface defects on technologically relevant materials is encouraging. Here, we propose a material platform and experimental protocols for ultimately precise manipulation of a buried interface. We show that an electric field from the STM-tip reversibly controls local coupling between the graphene buffer layer and the SiC substrate under epitaxial bilayer graphene (BLG). This process is vertically defined by the atomically sharp interface, located ~1 nm below the top graphene layer, and laterally by single sites from its (6×6)SiC moiré lattice. Local and reversible electric-field-induced patterning of BLG heterostructure on SiC from its bottom interface creates a novel architecture concept for epitaxial graphene applications.
... Since this potential varies on a scale comparable to graphene's lattice constant, it cannot be engineered by either twist or strain, but can be produced by electrostatic coupling to a substrate. Far from a theoretic abstraction, Ref. [40] presented a similar analysis motivated by their experimental data on a SiC/graphene heterostructure, noting the relation to the half-chiral model for large values of the graphenesubstrate coupling. ...
... Since the potential varies on a microscopic scale, it is unlikely to be realized by artificial patterning [54][55][56], which provides a valuable tuning knob for designer flat bands with a larger periodicity [18,[57][58][59][60][61]. Instead, inspired by recent experiments on SiC/graphene heterostructures [40], we propose to realize the model in a heterostructure where graphene sits on a substrate nearly lattice-matched to a √ 3 × √ 3 graphene supercell. In Sec. ...
... While preliminary data on a SiC/graphene heterostructure has already substantiated the relevance of our model [40], reaching the flat band limit will require a stronger coupling, a closer lattice match, and mitigating symmetry breaking effects. In Table II we propose several other material candidates. ...
We demonstrate that a single layer of graphene subject to a superlattice potential nearly commensurate to a $\sqrt{3} \times \sqrt{3}$ supercell exactly maps to the chiral model of twisted bilayer graphene, albeit with half as many degrees of freedom. We comprehensively review the properties of this ``half-chiral model,'' including the interacting phases stabilized at integer fillings and the effects of substrate-induced symmetry breaking. We list candidate substrates that could produce a superlattice potential on graphene with the correct periodicity to access the flat band limit. Experimental measurements on a half-chiral moire heterostructure, in which valley-skyrmions cannot form, could yield insights on the physics they mediate in twisted bilayer graphene.
... We note that commensurate bilayers with exactly √ 3 lattice constant ratio and perfect 30 • alignment have been studied using density functional theory [35,36]. Moiré materials near this configuration have also been considered [37][38][39]. However, these studies did not consider the case in which the moiré potentials are produced by a 2D spinless coirrep in the layer with a larger lattice constant, nor did they report kagome or honeycomb moiré flat bands. ...
... Realization.-A considerable number of 2D materials (e.g., germanene and CdS) are known to have lattice constant approximately √ 3 times that of graphene [37,39]. These materials can be considered candidate substrates for the coupled-valley graphene model in Eq. (3). ...
We propose a class of graphene-based moir\'e systems hosting flat bands on kagome and honeycomb moir\'e superlattices. These systems are formed by stacking a graphene layer on a 2D substrate with lattice constant approximately $\sqrt{3}$ times that of graphene. When the moir\'e potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift symmetry protected degeneracies and create spin Chern bands, and we observe spin Chern numbers up to $3$. We additionally propose a moir\'e system formed by stacking two graphene-like layers with similar lattice constants but opposite signs of the Dirac Fermi velocity. This system exhibits multiple kagome and honeycomb flat bands simultaneously. Both models we propose resemble the hypermagic model of [Phys. Rev. B 106, 115418] and may provide ideal platforms for the realization of strongly correlated topological phases.
... [7][8][9][10] Instead, their 2D nature makes each crystal very sensitive to the potential induced by an adjacent layer, so that the misorientation between stacked 2D crystals imposes a new periodicity at the interface. [11][12][13] Resultant Moiré potential with a long periodicity folds the electron band structure of each crystal into a much smaller Brillouin zone, resulting in heavily modified electronic structures and a variety of novel electronic phases, including unconventional superconductivity, [14] Mott insulating phase, [15] ferromagnetism, [16] and ferroelectricity. [17] Periodic adsorption of foreign atoms on a 2D material plays a similar role as the stacked 2D crystals. ...
The interface between two‐dimensional (2D) crystals often forms a Moiré superstructure that imposes a new periodicity, which is a key element in realizing complex electronic phases as evidenced in twisted bilayer graphene. Acombined angle‐resolved photoemission spectroscopy measurements and first‐principles calculations reveal the formation of a Moiré superstructure between a 2D Dirac semi‐metallic crystal, graphene, and a 2D insulating crystal of noble gas, xenon. Incommensurate diffraction pattern and folded Dirac cones around the Brillouin zone center imply the formation of hexagonal crystalline array of xenon atoms. The velocity of Dirac fermions increases upon the formation of the 2D xenon crystal on top of graphene due to the enhanced dielectric screening by the xenon over‐layer. These findings not only provide a novel method to produce a Moiré superstructure from the adsorption of noble gas on 2D materials, but also to control the physical properties of graphene by the formation of a graphene‐noble gas interface.
Moiré superlattices have become an emergent solid-state platform for simulating quantum lattice models. However, in a single moiré device, Hamiltonian parameters like the lattice constant, hopping, and interaction terms can hardly be manipulated, limiting the controllability and accessibility of a moiré quantum simulator. Here, by combining angle-resolved photoemission spectroscopy and theoretical analysis, we demonstrate that high-order moiré patterns in graphene-monolayered xenon/krypton heterostructures can simulate a honeycomb model in the mesoscale, with in situ tunable Hamiltonian parameters. The length scale of the simulated lattice constant can be tuned by annealing processes, which in situ adjusts intervalley interaction and hopping parameters in the simulated honeycomb lattice. The sign of the lattice constant can be switched by choosing a xenon or krypton monolayer deposited on graphene, which controls the sublattice degree of freedom and valley arrangement of Dirac fermions. In this letter, we establish a path for experimentally simulating the honeycomb model with tunable parameters by high-order moiré patterns.
We propose a class of graphene-based moiré systems hosting flat bands on kagome and honeycomb moiré superlattices. These systems are formed by stacking a graphene layer on a 2D substrate with lattice constant approximately 3 times that of graphene. When the moiré potentials are induced by a 2D irreducible corepresentation in the substrate, the model shows a rich phase diagram of low-energy bands including eigenvalue fragile phases as well as kagome and honeycomb flat bands. Spin-orbit coupling in the substrate can lift symmetry-protected degeneracies and create spin Chern bands, and we observe spin Chern numbers up to three. We additionally propose a moiré system formed by stacking two graphene-like layers with similar lattice constants and Fermi energies but with Dirac Fermi velocities of opposite sign. This system exhibits multiple kagome and honeycomb flat bands simultaneously. Both models we propose resemble the hypermagic model of [Scheer et al., Phys. Rev. B 106, 115418 (2022)] and may provide ideal platforms for the realization of strongly correlated topological phases.
The last decade has witnessed a flourish in two‐dimensional (2D) materials including graphene and transition metal dichalcogenides (TMDs) as atomic‐scale Legos. Artificial moiré superlattices via stacking 2D materials with a twist angle and/or a lattice mismatch have recently become a fertile playground exhibiting a plethora of emergent properties beyond their building blocks. These rich quantum phenomena stem from their nontrivial electronic structures that have been effectively tuned by the moiré periodicity. Modern angle‐resolved photoemission spectroscopy (ARPES) can directly visualize electronic structures with decent momentum, energy, and spatial resolution, thus could provide enlightening insights into fundamental physics in moiré superlattice systems and guides for designing novel devices. In this review, firstly a brief introduction is given on advanced ARPES techniques and basic ideas of band structures in a moiré superlattice system. Then ARPES research results of various moiré superlattice systems are highlighted, including graphene on substrates with small lattice mismatches, twisted graphene/TMD moiré systems, and high‐order moiré superlattice systems. Finally, we discuss on important questions that remain open, challenges in current experimental investigations and present an outlook on this field of research.
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We demonstrate that a single layer of graphene subject to a superlattice potential nearly commensurate to a 3×3 supercell exactly maps to the chiral model of twisted bilayer graphene, albeit with half as many degrees of freedom. We comprehensively review the properties of this “half-chiral model,” including the interacting phases stabilized at integer fillings and the effects of substrate-induced symmetry breaking. We list candidate substrates that could produce a superlattice potential on graphene with the correct periodicity to access the flat-band limit. Experimental measurements on a half-chiral moiré heterostructure, in which valley skyrmions cannot form, could yield insights on the physics they mediate in twisted bilayer graphene.
