A number of moiré graphene systems have nearly flat topological bands where electron motion is strongly correlated. Though microscopically these systems are only quasiperiodic, they can typically be treated as translation invariant to an excellent approximation. Here we reconsider this question for magic angle twisted bilayer graphene that is nearly aligned with a hexagonal boron nitride(h-BN) substrate. We carefully study the effect of the periodic potential induced by h-BN on the low energy physics. The combination of this potential and the moiré lattice produced by the twisted graphene generates a quasi-periodic term that depends on the alignment angle between h-BN and the moiré graphene. We find that the alignment angle has a significant impact on both the band gap near charge neutrality and the behavior of electrical transport. We also introduce and study toy models to illustrate how a quasi-periodic potential can give rise to localization and change in transport properties of topological bands.
Quasiperiodicity has long been known to be a potential platform to explore exotic phenomena, realizing an intricate middle point between ordered solids and disordered matter. In particular, quasiperiodic structures are promising playgrounds to engineer critical wavefunctions, a powerful starting point to engineer exotic correlated states. Here we show that systems hosting a quasiperiodic modulation of antiferromagnetism and spin-singlet superconductivity, as realized by atomic chains in twisted van der Waals materials, host a localization-delocalization transition as a function of the coupling…
Apparent corrugation variations in moiré patterns of dislocated graphene on Highly Oriented Pyrolytic Graphite and the origin of the van Hove singularities of the moiré system
We theoretically study in-plane acoustic phonons of graphene/hexagonal boron nitride moiré superlattice by using a continuum model. We demonstrate that the original phonon bands of individual layers are strongly hybridized and reconstructed into moiré phonon bands consisting of dispersive bands and flat bands. The phonon band structure can be effectively described by a spring-mass network model to simulate the motion of moiré domain walls, where the flat-band modes are interpreted as vibrations of independent, decoupled strings. We also show that the moiré phonon has angular momentum due to th…
Low-energy moiré flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moiré flat bands of tBG are based on the extended structures, i.e., the moiré patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moiré patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near th…
When using hexagonal boron-nitride (hBN) as a substrate for graphene, the resulting moiré pattern creates secondary Dirac points. By encapsulating a multilayer graphene within aligned hBN sheets the controlled moiré stacking may offer even richer benefits. Using advanced tight-binding simulations on atomistically-relaxed heterostructures, here we show that the gap at the secondary Dirac point can be opened in selected moiré-stacking configurations, and is independent of any additional vertical gating of the heterostructure. On the other hand, gating can broadly tune the gap at the principal Di…
Graphene moire superlattices are outstanding platforms to study correlated electron physics and superconductivity with exceptional tunability. However, robust superconductivity has been measured only in magic-angle twisted bilayer graphene (MA-TBG) and magic-angle twisted trilayer graphene (MA-TTG). The absence of a superconducting phase in certain moire flat bands raises a question on the superconducting mechanism. In this work, we investigate electronic structure and electron-phonon coupling in graphene moire superlattices based on atomistic calculations. We show that electron-phonon couplin…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
Stacking three monolayers of graphene with a twist generally produces two moiré patterns. A moiré of moiré structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moiré lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\bf Γ}_M$ point of the moiré Brillouin zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The velocities and small gaps exhibit a spatial dependence in the moiré-of-moiré unit cell, e…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be …
Graphene-based moiré superlattices are now established as an interesting platform for strongly-correlated many-electron physics, and have so far been characterized mainly by transport and scanning tunneling microscopy (STM) measurements. Motivated by recent experimental progress, we present a theoretical model study whose aim is to assess the potential of angle-resolved photoemission spectroscopy (ARPES) to resolve some of the many open issues in these systems. The theory is developed specifically for graphene on hexagonal boron nitride (G/hBN) and twisted bilayer graphene (TBG) moiré superlat…
Layers of two-dimensional materials stacked with a small twist-angle give rise to beating periodic patterns on a scale much larger than the original lattice, referred to as a moiré superlattice. When the stacking involves more than two layers with independent twist angles between adjacent layers, it generates moiré of moiré superlattices, with multiple length scales that control the system's behavior. Here we demonstrate these effects of a high-order moiré superlattice in twisted trilayer graphene with two consecutive small twist angles. We report correlated insulating states near the half fil…
In graphene moiré superlattices, electronic interactions between layers are mostly hidden as band structures get crowded because of folding, making their interpretation cumbersome. Here, the evolution of the electronic band structure as a function of the interlayer rotation angle is studied using Density Functional Theory followed by unfolding bands and then comparing them to their corresponding individual components. We observe interactions at regions not theoretically elucidated so far, where for small interlayer angles, gaps turn into discrete-like states that are evenly spaced in energy. W…
Moiré superlattices (MSL) formed in angle-aligned bilayers of van der Waals materials have become a promising platform to realize novel two-dimensional electronic states. Angle-aligned trilayer structures can form two sets of MSLs which could potentially interfere with each other. In this work, we directly image the moiré patterns in both monolayer graphene aligned on hBN and twisted bilayer graphene aligned on hBN, using combined scanning microwave impedance microscopy and conductive atomic force microscopy. Correlation of the two techniques reveals the contrast mechanism for the achieved ult…
We reexamine the electronic structure of graphene on SiC substrate by angle-resolved photoemission spectroscopy. We directly observed multiply cloning of Dirac cone, in addition to ones previously attributed to reconstruction. The locations, relative distances and anisotropy of Dirac cone replicas fully agree with the moiré pattern of graphene-SiC heterostructure. Our results provide a straightforward example of moiré potential modulation in engineering electronic structure with Dirac fermions.
Tunable high-Chern-number Chern insulators in rhombohedral tetralayer graphene/hBN moiré superlattices
State Key Laboratory of Micro-nano Engineering Science, Tsung-Dao Lee lnstitute & School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University（上海交通大学微纳电子工程科学国家重点实验室、李政道研究所及物理与天文学院人工结构与量子控制教育部重点实验室）；Department of Physics, City University of Hong Kong（香港城市大学物理系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国家材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国家材料研究所材料纳米结构研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）
We theoretically study the piezoelectric effects in moirè graphene systems. Since the strain couples to the electrons in the system as a pseudo vector potential, which has opposite signs for the $K$ and $K'$ valleys of graphene, its effects on the two valleys with opposite Chern numbers do not cancel out, but adds up. As a result, some components of the piezoelectric tensor in these systems, which typically have non-trivial topology in their flat bands, are nearly quantized in terms of the valley Chern numbers. Such a conclusion is verified by numerical calculations of the in-plane piezoelectr…
The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the $(θ_{\rm GG},θ_{\rm GBN})$ twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and show that the band Chern numbers are in this case sensitiv…
We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moiré patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moiré period give relatively minor effects on the …
In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at $M$ and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac …
Entangled Moire Chern Insulator in Rhombohedral Graphene
Peking University（北京大学）；National Institute of Material Sciences（国立材料研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Hefei National Laboratory（合肥国家实验室）
