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 $\sqrt{3}$ 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 $\textit{et al.}$, Phys. Rev. B $\textbf{106}$, 115418 (2022)] and may provide ideal platforms for the realization of strongly correlated topological phases.
A kagome lattice is composed of corner-sharing triangles arranged on a honeycomb lattice such that each honeycomb bond hosts a kagome site while each kagome triangle encloses a honeycomb site. Such close relation implies that the two lattices share common features. We predict here that a kagome crystal, similar to the honeycomb lattice graphene, reacts to elastic strain in a unique way that the bulk electronic states in the vicinity of Dirac points are reorganized by the strain-induced pseudomagnetic field into flat Landau levels, while the degenerate edge states in the undeformed crystal beco…
We theoretically study the effect of magnetic moiré superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moiré potentials generically gap out the moiré surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $Δ_1$ moiré potential s…
Emergent Kagome lattice and non-Abelian lattice gauge field of biexcitons in t-MoTe$_2$
New Cornerstone Science Laboratory, Department of Physics, University of Hong Kong（香港大学物理系新Cornerstone科学实验室）；HK Institute of Quantum Science and Technology, University of Hong Kong（香港大学香港量子科学技术研究院）
We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmet…
Stack of correlated insulating states in bilayer graphene kagome superlattice
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室）；ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University（上海科技大学拓扑物理实验室）；Department of Physics and Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）；Department of Physics, University of Oxford（牛津大学物理系）；School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）
The possibility of dissipationless chiral edge states without the need of an external magnetic field in the quantum anomalous Hall effect (QAHE) offers a great potential in electronic/spintronic applications. The biggest hurdle for the realization of a room-temperature magnetic Chern insulator is to find a structurally stable material with a sufficiently large energy gap and Curie temperature that can be easily implemented in electronic devices. This work based on first-principle methods shows that a single atomic layer of V2O3 with honeycomb-kagome (HK) lattice is structurally stable with a s…
Sliding and twisting van der Waals layers with respect to each other gives rise to moiré structures with emergent electronic properties. Electrons in these moiré structures feel weak potentials that are typically in the tens of millielectronvolt range when the moiré structures are smooth at the atomic scale. Here we report a facile technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial strain drives a commensurate-incommensurate lattice transition in a multilaye…
In 2015 experiments were performed with superconducting microwave photonic crystals emulating artificial graphene B. Dietz, T. Klaus, M. Miski-Oglu, and A. Richter, Phys. Rev. B 91, 035411 (2015)]. The associated density of states comprises two Dirac points with adjacent bands including van Hove singularities, thus exhibiting the characteristic features originating from the extraordinary electronic band structure of graphene. They are separated by a narrow region of particularly high resonance density corresponding to a nearly flatband in the band structure, which is reminiscent of that of a h…
The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $Γ$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moirè minibands that are formed in the valence bands of $Γ$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $Γ$-valley moirè holes differ qualitatively from their K-valley counterparts addressed previ…
We predict that twisted bilayers of 1T-ZrS$_2$ realize a novel and tunable platform to engineer two-dimensional topological quantum phases dominated by strong spin-orbit interactions. At small twist angles, ZrS$_2$ heterostructures give rise to an emergent and twist-controlled moiré Kagomé lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We devise a generic pseudo-spin theory for group-IV transition metal dichalcogenides that relies on the two-component character…
We present a low-energy model describing the reconstruction of the electronic spectrum in twisted bilayers of honeycomb crystals with broken sublattice symmetry. The resulting moiré patterns are classified into two families with different symmetry. In both cases, flat bands appear at relatively large angles, without any magic angle condition. Transitions between them give rise to sharp resonances in the optical absorption spectrum at frequencies well below the gap of the monolayer. Owing to their chiral symmetry, twisted bilayers display circular dichroism, i.e., different absorption of left a…
We introduce a general framework to study moiré structures of two-dimensional Van der Waals magnets using continuum field theory. The formalism eliminates quasiperiodicity and allows a full understanding of magnetic structures and their excitations. In particular, we analyze in detail twisted bilayers of Néel antiferromagnets on the honeycomb lattice. A rich phase diagram with non-collinear twisted phases is obtained, and spin waves are further calculated. Direct extensions to zig-zag antiferromagnets and ferromagnets are also presented. We anticipate the results and formalism presented to lea…
The growing skill in the synthesis processes of new materials has intensified the interest in exploring the properties of systems modeled by more complex lattices. Two-dimensional super-honeycomb lattices, have been investigated in metallic organic frameworks. They turned out as a significant route to the emergence of localized electronic responses, manifested as flat bands in their structure with topological isolating behavior. A natural inquiry is a complete analysis of their topological phases in the presence of electronic correlation effects. Here we analyse of the electron-electron correl…
We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekulé-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized $\mathbb{Z}_Q$ Berry phase. Highlights include phases with high Chern numbers, a novel $\mathbb{Z}_6$ topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phas…
Twisted graphene multi-layers have been recently demonstrated to share several correlation-driven behaviours with twisted bilayer graphene. In general, the van Hove singularities (VHSs) can be used as a proxy of the tendency for correlated behaviours. In this paper, we adopt an atomistic method by combining tight-binding method with the semi-classical molecular dynamics to investigate the electronic structures of twisted trilayer graphene (TTG) with two independent twist angles. The two independent twist angles can lead to the interference of the moiré patterns forming a variety of commensurat…
We theoretically study a generalized Hubbard model on moiré superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the moiré-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc, providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In…
The moiré pattern observed in stacked non-commensurate crystal lattices, such as hetero-bilayers of transition metal dichalcogenides, produces a periodic modulation of their bandgap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasi-particle dubbed moiré exciton. In the case of MoS$_2$/WSe$_2$ hetero-bilayers, the moiré trapping potential has honeycomb symmetry and, consequently, the moiré exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we…
Two-dimensional heterostructures with layers of slightly different lattice vectors exhibit a new periodic structure known as moire lattices. Moire lattice formation provides a powerful new way to engineer the electronic structure of two-dimensional materials for realizing novel correlated and topological phenomena. In addition, superstructures of moire lattices can emerge from multiple misaligned lattice vectors or inhomogeneous strain distribution, which offers an extra degree of freedom in the electronic band structure design. High-resolution imaging of the moire lattices and superstructures…
Epitaxial graphene grown on transition metal surfaces typically exhibits a moiré pattern due to the lattice mismatch between graphene and the underlying metal surface. We use both scanning tunneling microscopy (STM) and atomic force microscopy (AFM) experiments to probe the electronic and topographic contrast of the graphene moiré on the Ir(111) surface. While STM topography is influenced by the local density of states close to the Fermi energy and the local tunneling barrier height, AFM is capable of yielding the 'true' surface topography once the background force arising from the van der Waa…
Twisted moiré superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moiré twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topo…
Topological flat bands at the Fermi level offer a promising platform to study a variety of intriguing correlated phase of matter. Here we present band engineering in the twisted orbital-active bilayers with spin-orbit coupling. The symmetry constraints on the interlayer coupling that determines the effective potential for low-energy physics of moiré electrons are exhaustively derived for two-dimensional point groups. We find the line graph or biparticle sublattice of moiré pattern emerge with a minimal $C_3$ symmetry, which exhibit isolated electronic flat bands with nontrivial topology. The b…
We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping, and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the $\mathbb{Z}_2$ topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization…
We establish experimentally a photonic super-honeycomb lattice (sHCL) by use of a cw-laser writing technique, and thereby demonstrate two distinct flatband line states that manifest as noncontractible-loop-states in an infinite flatband lattice. These localized states (straight and zigzag lines) observed in the sHCL with tailored boundaries cannot be obtained by superposition of conventional compact localized states because they represent a new topological entity in flatband systems. In fact, the zigzag-line states, unique to the sHCL, are in contradistinction with those previously observed in…
According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1 degree and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1 degree, and tunneling densitie…
Imaging moiré flat bands and Wigner molecular crystals in twisted bilayer MoTe2
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学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 and Astronomy, University of Tennessee（田纳西大学物理与天文系）；Department of Physics, Tsinghua University（清华大学物理系）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（日本国立材料研究所电子光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（日本国立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）；Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee（田纳西大学明海华电气与计算机工程系）
Landau quantization of $C_3$ high-fold fermions in honeycomb lattices
International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）；Department of Physics and I3N, University of Aveiro（阿威罗大学物理系及I3N）；Departamento de Física, Universidad de Alicante（阿利坎特大学物理系）
The interplay of charge, spin, lattice, and orbital degrees of freedom leads to a wide range of emergent phenomena in strongly correlated systems. In heterobilayer transition metal dichalcogenide moiré systems, recent observations of Mott insulators and generalized Wigner crystals are well described by triangular lattice single-orbital Hubbard models based on K-valley derived moiré bands. Richer phase diagrams, mapped onto multi-orbital Hubbard models, are possible with hexagonal lattices in $Γ$-valley derived moiré bands and additional layer degrees of freedom. Here we report the tunable inte…
