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Interactions between electrons and the topology of their energy bands can create unusual quantum phases of matter. Most topological electronic phases appear in systems with weak electron-electron interactions. The instances in which topological phases emerge only as a result of strong interactions are rare and mostly limited to those realized in intense magnetic fields.sup.1. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for strongly correlated topological phases.sup.2-9. Here we introduce a local spectroscopic technique using a scanning tunnelling microscope to detect a sequence of topological insulators in MATBG with Chern numbers C = [plus or minus]1, [plus or minus]2 and [plus or minus]3, which form near filling factors of [plus or minus]3, [plus or minus]2 and [plus or minus]1 electrons per moiré unit cell, respectively, and are stabilized by modest magnetic fields. One of the phases detected here (C = +1) was previously observed when the sublattice symmetry of MATBG was intentionally broken by a hexagonal boron nitride substrate, with interactions having a secondary role.sup.9. We demonstrate that strong electron-electron interactions alone can produce not only the previously observed phase, but also other unexpected Chern insulating phases in MATBG. The full sequence of phases that we observe can be understood by postulating that strong correlations favour breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moiré systems beyond those anticipated from weakly interacting models. Strong electron-electron interactions in magic-angle twisted bilayer graphene can fundamentally change the topology of the system's flat bands, producing a hierarchy of strongly correlated topological insulators in modest magnetic fields., Author(s): Kevin P. Nuckolls [sup.1] , Myungchul Oh [sup.1] , Dillon Wong [sup.1] , Biao Lian [sup.2] , Kenji Watanabe [sup.3] , Takashi Taniguchi [sup.4] , B. Andrei Bernevig [sup.1] [...]

Magic-angle twisted bilayer graphene exhibits a variety of electronic states, including correlated insulators.sup.1-3, superconductors.sup.2-4 and topological phases.sup.3,5,6. Understanding the microscopic mechanisms responsible for these phases requires determination of the interplay between electron-electron interactions and quantum degeneracy (the latter is due to spin and valley degrees of freedom). Signatures of strong electron-electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements.sup.7-10, and transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moiré unit cell.sup.2-4. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Here we report a cascade of transitions in the spectroscopic properties of magic-angle twisted bilayer graphene as a function of electron filling, determined using high-resolution scanning tunnelling microscopy. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moiré flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions that we report here characterizes the correlated high-temperature parent phase.sup.11,12 from which various insulating and superconducting ground-state phases emerge at low temperatures in magic-angle twisted bilayer graphene. Electron-electron interactions in magic-angle twisted bilayer graphene can split usually degenerate electronic bands, giving rise to a cascade of electronic transitions revealed by spectroscopy., Author(s): Dillon Wong [sup.1] [sup.2] , Kevin P. Nuckolls [sup.1] [sup.2] , Myungchul Oh [sup.1] [sup.2] , Biao Lian [sup.3] , Yonglong Xie [sup.1] [sup.2] [sup.5] [sup.6] , Sangjun Jeon [...]

The discovery of superconducting and insulating states in magic-angle twisted bilayer graphene (MATBG).sup.1,2 has ignited considerable interest in understanding the nature of electronic interactions in this chemically pristine material. The transport properties of MATBG as a function of doping are similar to those of high-transition-temperature copper oxides and other unconventional superconductors.sup.1-3, which suggests that MATBG may be a highly interacting system. However, to our knowledge, there is no direct experimental evidence of strong many-body correlations in MATBG. Here we present high-resolution spectroscopic measurements, obtained using a scanning tunnelling microscope, that provide such evidence as a function of carrier density. MATBG displays unusual spectroscopic characteristics that can be attributed to electron-electron interactions over a wide range of doping levels, including those at which superconductivity emerges in this system. We show that our measurements cannot be explained with a mean-field approach for modelling electron-electron interactions in MATBG. The breakdown of a mean-field approach when applied to other correlated superconductors, such as copper oxides, has long inspired the study of the highly correlated Hubbard model.sup.3. We show that a phenomenological extended-Hubbard-model cluster calculation, which is motivated by the nearly localized nature of the relevant electronic states of MATBG, produces spectroscopic features that are similar to those that we observed experimentally. Our findings demonstrate the critical role of many-body correlations in understanding the properties of MATBG. Scanning tunnelling spectroscopy and extended-Hubbard-model cluster calculations reveal that magic-angle twisted bilayer graphene is a strongly correlated electron system, similar to other unconventional superconductors., Author(s): Yonglong Xie [sup.1] , Biao Lian [sup.2] , Berthold Jäck [sup.1] , Xiaomeng Liu [sup.1] , Cheng-Li Chiu [sup.1] , Kenji Watanabe [sup.3] , Takashi Taniguchi [sup.3] , B. [...]

Owing to the unusual geometry of kagome lattices--lattices made of corner-sharing triangles--their electrons are useful for studying the physics of frustrated, correlated and topological quantum electronic states.sup.1-9. In the presence of strong spin-orbit coupling, the magnetic and electronic structures of kagome lattices are further entangled, which can lead to hitherto unknown spin-orbit phenomena. Here we use a combination of vector-magnetic-field capability and scanning tunnelling microscopy to elucidate the spin-orbit nature of the kagome ferromagnet Fe.sub.3Sn.sub.2 and explore the associated exotic correlated phenomena. We discover that a many-body electronic state from the kagome lattice couples strongly to the vector field with three-dimensional anisotropy, exhibiting a magnetization-driven giant nematic (two-fold-symmetric) energy shift. Probing the fermionic quasi-particle interference reveals consistent spontaneous nematicity--a clear indication of electron correlation--and vector magnetization is capable of altering this state, thus controlling the many-body electronic symmetry. These spin-driven giant electronic responses go well beyond Zeeman physics and point to the realization of an underlying correlated magnetic topological phase. The tunability of this kagome magnet reveals a strong interplay between an externally applied field, electronic excitations and nematicity, providing new ways of controlling spin-orbit properties and exploring emergent phenomena in topological or quantum materials.sup.10-12.The topological magnet Fe.sub.3Sn.sub.2 exhibits a giant nematic energy shift of a many-body electronic state, demonstrating anisotropic spin-orbit tunability., Author(s): Jia-Xin Yin [sup.1] , Songtian S. Zhang [sup.1] , Hang Li [sup.2] , Kun Jiang [sup.3] , Guoqing Chang [sup.1] , Bingjing Zhang [sup.4] , Biao Lian [sup.5] , [...]

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter., (© 2022. Springer Nature Limited.)

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics 1-15 . Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry 14,15 . However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking 16-21 . Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn 6 Sn 6 , that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn 6 Sn 6 , and may enable the observation of topological quantum phenomena in the RMn 6 Sn 6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.