When single layers of 2D materials are stacked on top of one another with a small twist in orientation, the resulting structure often involves incommensurate moiré patterns. In these patterns, the ...loss of angstrom-scale periodicity poses a significant theoretical challenge, and the new moiré length scale leads to emergent physical phenomena. The range of physics arising from twisted bilayers has led to significant advances that are shaping into a new field, twistronics. At the moiré scale, the large number of atoms in these systems can make their accurate simulation daunting, necessitating the development of efficient multiscale methods. In this Review, we summarize and compare such modelling methods — focusing in particular on density functional theory, tight-binding Hamiltonians and continuum models — and provide examples spanning a broad range of materials and geometries.When single layers of 2D materials are stacked on top of one another with a small twist, the resulting moiré pattern introduces new electronic properties. This Review surveys and compares the modelling techniques used in this emerging field of twistronics.
Electronic flat bands in momentum space, arising from strong localization of electrons in real space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat bands can ...naturally arise in certain geometrically frustrated lattices, often with nontrivial topology if combined with spin-orbit coupling. Here, we report the observation of topological flat bands in frustrated kagome metal CoSn, using angle-resolved photoemission spectroscopy and band structure calculations. Throughout the entire Brillouin zone, the bandwidth of the flat band is suppressed by an order of magnitude compared to the Dirac bands originating from the same orbitals. The frustration-driven nature of the flat band is directly confirmed by the chiral d-orbital texture of the corresponding real-space Wannier functions. Spin-orbit coupling opens a large gap of 80 meV at the quadratic touching point between the Dirac and flat bands, endowing a nonzero Z
invariant to the flat band. These findings demonstrate that kagome-derived flat bands are a promising platform for novel emergent phases of matter at the confluence of strong correlation and topology.
Control of the interlayer twist angle in two-dimensional van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale
. In twisted bilayer ...graphene, the simple moiré superlattice band description suggests that the electronic bandwidth can be tuned to be comparable to the vdW interlayer interaction at a 'magic angle'
, exhibiting strongly correlated behaviour. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favouring interlayer commensurability, which competes with the intralayer lattice distortion
. Here we report atomic-scale reconstruction in twisted bilayer graphene and its effect on the electronic structure. We find a gradual transition from an incommensurate moiré structure to an array of commensurate domains with soliton boundaries as we decrease the twist angle across the characteristic crossover angle, θ
≈ 1°. In the solitonic regime (θ < θ
) where the atomic and electronic reconstruction become significant, a simple moiré band description breaks down and the secondary Dirac bands appear. On applying a transverse electric field, we observe electronic transport along the network of one-dimensional topological channels that surround the alternating triangular gapped domains. Atomic and electronic reconstruction at the vdW interface provide a new pathway to engineer the system with continuous tunability.
We introduce a complete physical model for the single-particle electronic structure of twisted bilayer graphene (TBLG), which incorporates the crucial role of lattice relaxation. Our model, based on ...k·p perturbation theory and openly available, combines the accuracy of density functional theory calculations through effective tight-binding Hamiltonians with the computational efficiency and complete control of the twist angle offered by continuum models. The inclusion of relaxation significantly changes the band structure at the first magic-angle twist corresponding to flat bands near the Fermi level (the “low-energy” states), and eliminates the appearance of a second magic-angle twist. We show that minimal models for the low-energy states of TBLG can be easily modified to capture the changes in electronic states as a function of twist angle.
A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the ...paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.
Abstract
The kagome lattice has long been regarded as a theoretical framework that connects lattice geometry to unusual singularities in electronic structure. Transition metal kagome compounds have ...been recently identified as a promising material platform to investigate the long-sought electronic flat band. Here we report the signature of a two-dimensional flat band at the surface of antiferromagnetic kagome metal FeSn by means of planar tunneling spectroscopy. Employing a Schottky heterointerface of FeSn and an n-type semiconductor Nb-doped SrTiO
3
, we observe an anomalous enhancement in tunneling conductance within a finite energy range of FeSn. Our first-principles calculations show this is consistent with a spin-polarized flat band localized at the ferromagnetic kagome layer at the Schottky interface. The spectroscopic capability to characterize the electronic structure of a kagome compound at a thin film heterointerface will provide a unique opportunity to probe flat band induced phenomena in an energy-resolved fashion with simultaneous electrical tuning of its properties. Furthermore, the exotic surface state discussed herein is expected to manifest as peculiar spin-orbit torque signals in heterostructure-based spintronic devices.
The layered vanadium antimonides AV3Sb5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals that exhibit a range of strongly correlated electronic phases including charge ...order and superconductivity. However, it is not yet understood how the distinctive electronic structure of the kagome lattice is linked to the observed many-body phenomena. Here we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHS) coexisting near the Fermi level of CsV3Sb5 and analyse their contribution to electronic symmetry breaking. The vHS are characterized by two distinct sublattice flavours (p-type and m-type), which originate, respectively, from their pure and mixed sublattice characters. These twofold vHS flavours of the kagome lattice critically determine the pairing symmetry and unconventional ground states emerging in the AV3Sb5 series. We establish that, among the multiple vHS in CsV3Sb5, the m-type vHS of the dxz/dyz kagome band and the p-type vHS of the dxy/dx2–y2 kagome band are located very close to the Fermi level, setting the stage for electronic symmetry breaking. The former band is characterized by pronounced Fermi surface nesting, while the latter exhibits a higher-order vHS. Our work reveals the essential role of kagome-derived vHS for the collective phenomena realized in the AV3Sb5 family.Spectroscopic measurements show how the features of the band structure related to the kagome lattice in CsV3Sb5 contribute to the observed strongly correlated phases.
Defects in materials give rise to fluctuations in electrostatic fields that reflect the local charge density, but imaging this with single atom sensitivity is challenging. However, if possible, this ...provides information about the energetics of adatom binding, localized conduction channels, molecular functionality and their relationship to individual bonds. Here, ultrastable electron-optics are combined with a high-speed 2D electron detector to map electrostatic fields around individual atoms in 2D monolayers using 4D scanning transmission electron microscopy. Simultaneous imaging of the electric field, phase, annular dark field and the total charge in 2D MoS
and WS
is demonstrated for pristine areas and regions with 1D wires. The in-gap states in sulphur line vacancies cause 1D electron-rich channels that are mapped experimentally and confirmed using density functional theory calculations. We show how electrostatic fields are sensitive in defective areas to changes of atomic bonding and structural determination beyond conventional imaging.
Following the recent isolation of monolayer CrI3 (ref. 1), many more two-dimensional van der Waals magnetic materials have been isolated2–12. Their incorporation in van der Waals heterostructures ...offers a new platform for spintronics5–9, proximity magnetism13 and quantum spin liquids14. A primary question in this field is how exfoliating crystals to the few-layer limit influences their magnetism. Studies of CrI3 have shown a different magnetic ground state for ultrathin exfoliated films1,5,6 compared with the bulk, but the origin is not yet understood. Here, we use electron tunnelling through few-layer crystals of the layered antiferromagnetic insulator CrCl3 to probe its magnetic order and find a tenfold enhancement of the interlayer exchange compared with bulk crystals. Moreover, temperature- and polarization-dependent Raman spectroscopy reveals that the crystallographic phase transition of bulk crystals does not occur in exfoliated films. This results in a different low-temperature stacking order and, we hypothesize, increased interlayer exchange. Our study provides insight into the connection between stacking order and interlayer interactions in two-dimensional magnets, which may be relevant for correlating stacking faults and mechanical deformations with the magnetic ground states of other more exotic layered magnets such as RuCl3 (ref. 14).
PDF
