Observation of Kekulé vortices around hydrogen adatoms in graphene.

Fractional charges are one of the wonders of the fractional quantum Hall effect. Such objects are also anticipated in two-dimensional hexagonal lattices under time reversal symmetry-emerging as bound states of a rotating bond texture called a Kekulé vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realization. Here, we report the observation of Kekulé vortices in the local density of states of graphene under time reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms. We uncover that their 2π winding is reminiscent of the Berry phase π of the massless Dirac electrons. We can also induce a Kekulé pattern without vortices by creating point scatterers such as divacancies, which break different point symmetries. Our local-probe study thus confirms point defects as versatile building blocks for Kekulé engineering of graphene's electronic structure.

Anomalous electrons in a metallic kagome ferromagnet.

Ordinary metals contain electron liquids within well-defined 'Fermi' surfaces at which the electrons behave as if they were non-interacting. In the absence of transitions to entirely new phases such as insulators or superconductors, interactions between electrons induce scattering that is quadratic in the deviation of the binding energy from the Fermi level. A long-standing puzzle is that certain materials do not fit this 'Fermi liquid' description. A common feature is strong interactions between electrons relative to their kinetic energies. One route to this regime is special lattices to reduce the electron kinetic energies. Twisted bilayer graphene1-4 is an example, and trihexagonal tiling lattices (triangular 'kagome'), with all corner sites removed on a 2 × 2 superlattice, can also host narrow electron bands5 for which interaction effects would be enhanced. Here we describe spectroscopy revealing non-Fermi-liquid behaviour for the ferromagnetic kagome metal Fe3Sn2 (ref. 6). We discover three C3-symmetric electron pockets at the Brillouin zone centre, two of which are expected from density functional theory. The third and most sharply defined band emerges at low temperatures and binding energies by means of fractionalization of one of the other two, most likely on the account of enhanced electron-electron interactions owing to a flat band predicted to lie just above the Fermi level. Our discovery opens the topic of how such many-body physics involving flat bands7,8 could differ depending on whether they arise from lattice geometry or from strongly localized atomic orbitals9,10.

Five-Membered Rings Create Off-Zero Modes in Nanographene.

The low-energy electronic structure of nanographenes can be tuned through zero-energy π-electron states, typically referred to as zero-modes. Customizable electronic and magnetic structures have been engineered by coupling zero-modes through exchange and hybridization interactions. Manipulation of the energy of such states, however, has not yet received significant attention. We find that attaching a five-membered ring to a zigzag edge hosting a zero-mode perturbs the energy of that mode and turns it into an off-zero mode: a localized state with a distinctive electron-accepting character. Whereas the end states of typical 7-atom-wide armchair graphene nanoribbons (7-AGNRs) lose their electrons when physisorbed on Au(111) (due to its high work function), converting them into off-zero modes by introducing cyclopentadienyl five-membered rings allows them to retain their single-electron occupation. This approach enables the magnetic properties of 7-AGNR end states to be explored using scanning tunneling microscopy (STM) on a gold substrate. We find a gradual decrease of the magnetic coupling between off-zero mode end states as a function of GNR length, and evolution from a more closed-shell to a more open-shell ground state.

Selective Photonic Gasification of Strained Oxygen Clusters on Graphene for Tuning Pore Size in the Å Regime.

Controlling the size of single-digit pores, such as those in graphene, with an Å resolution has been challenging due to the limited understanding of pore evolution at the atomic scale. The controlled oxidation of graphene has led to Å-scale pores; however, obtaining a fine control over pore evolution from the pore precursor (i.e., the oxygen cluster) is very attractive. Herein, we introduce a novel "control knob" for gasifying clusters to form pores. We show that the cluster evolves into a core/shell structure composed of an epoxy group surrounding an ether core in a bid to reduce the lattice strain at the cluster core. We then selectively gasified the strained core by exposing it to 3.2 eV of light at room temperature. This allowed for pore formation with improved control compared to thermal gasification. This is because, for the latter, cluster-cluster coalescence via thermally promoted epoxy diffusion cannot be ruled out. Using the oxidation temperature as a control knob, we were able to systematically increase the pore density while maintaining a narrow size distribution. This allowed us to increase H2 permeance as well as H2 selectivity. We further show that these pores could differentiate CH4 from N2, which is considered to be a challenging separation. Dedicated molecular dynamics simulations and potential of mean force calculations revealed that the free energy barrier for CH4 translocation through the pores was lower than that for N2. Overall, this study will inspire research on the controlled manipulation of clusters for improved precision in incorporating Å-scale pores in graphene.

Electrical detection of the flat-band dispersion in van der Waals field-effect structures.

Two-dimensional flat-band systems have recently attracted considerable interest due to the rich physics unveiled by emergent phenomena and correlated electronic states at van Hove singularities. However, the difficulties in electrically detecting the flat-band position in field-effect structures are slowing down the investigation of their properties. In this work, we use indium selenide (InSe) as a flat-band system due to a van Hove singularity at the valence-band edge in a few-layer form of the material without the requirement of a twist angle. We investigate tunnelling photocurrents in gated few-layer InSe structures and relate them to ambipolar transport and photoluminescence measurements. We observe an appearance of a sharp change in tunnelling mechanisms due to the presence of the van Hove singularity at the flat band. We further corroborate our findings by studying tunnelling currents as a reliable probe for the flat-band position up to room temperature. Our results create an alternative approach to studying flat-band systems in heterostructures of two-dimensional materials.

Engineering SYK Interactions in Disordered Graphene Flakes under Realistic Experimental Conditions.

We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100 nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices.

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking.

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moiré superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.

Electrical spectroscopy of defect states and their hybridization in monolayer MoS2.

Defects in solids are unavoidable and can create complex electronic states that can significantly influence the electrical and optical properties of semiconductors. With the rapid progress in the integration of 2D semiconductors in practical devices, it is imperative to understand and characterize the influence of defects in this class of materials. Here, we examine the electrical response of defect filling and emission using deep level transient spectroscopy (DLTS) and reveal defect states and their hybridization in a monolayer MOCVD-grown material deposited on CMOS-compatible substrates. Supported by aberration-corrected STEM imaging and theoretical calculations, we find that neighboring sulfur vacancy pairs introduce additional shallow trap states via hybridization of individual vacancy levels. Even though such vacancy pairs only represent ~10% of the total defect concentration, they can have a substantial influence on the off currents and switching slopes of field-effect transistors based on 2D semiconductors. Our technique, which can quantify the energy states of different defects and their interactions, allows rapid and nondestructive electrical characterization of defect states important for the defect engineering of 2D semiconductors.

Flat-Band-Induced Many-Body Interactions and Exciton Complexes in a Layered Semiconductor.

Interactions among a collection of particles generate many-body effects in solids that result in striking modifications of material properties. The heavy carrier mass that yields strong interactions and gate control of carrier density over a wide range makes two-dimensional semiconductors an exciting playground to explore many-body physics. The family of III-VI metal monochalcogenides emerges as a new platform for this purpose because of its excellent optical properties and the flat valence band dispersion. In this work, we present a complete study of charge-tunable excitons in few-layer InSe by photoluminescence spectroscopy. From the optical spectra, we establish that free excitons in InSe are more likely to be captured by ionized donors leading to the formation of bound exciton complexes. Surprisingly, a pronounced red shift of the exciton energy accompanied by a decrease of the exciton binding energy upon hole-doping reveals a significant band gap renormalization induced by the presence of the Fermi reservoir.

Mott versus Hybridization Gap in the Low-Temperature Phase of 1T-TaS_{2}.

We address the long-standing problem of the ground state of 1T-TaS_{2} by computing the correlated electronic structure of stacked bilayers using the GW+EDMFT method. Depending on the surface termination, the semi-infinite uncorrelated system is either band insulating or exhibits a metallic surface state. For realistic values of the on-site and inter-site interactions, a Mott gap opens in the surface state, but it is smaller than the gap originating from the bilayer structure. Our results are consistent with recent scanning tunneling spectroscopy measurements for different terminating layers, and with our own photoemission measurements, which indicate the coexistence of spatial regions with different gaps in the electronic spectrum. By comparison to exact diagonalization data, we clarify the interplay between Mott insulating and band insulating behavior in this archetypal layered system.

Multiple mobile excitons manifested as sidebands in quasi-one-dimensional metallic TaSe3.

Charge neutrality and their expected itinerant nature makes excitons potential transmitters of information. However, exciton mobility remains inaccessible to traditional optical experiments that only create and detect excitons with negligible momentum. Here, using angle-resolved photoemission spectroscopy, we detect dispersing excitons in the quasi-one-dimensional metallic trichalcogenide, TaSe3. The low density of conduction electrons and the low dimensionality in TaSe3 combined with a polaronic renormalization of the conduction band and the poorly screened interaction between these polarons and photo-induced valence holes leads to various excitonic bound states that we interpret as intrachain and interchain excitons, and possibly trions. The thresholds for the formation of a photo-hole together with an exciton appear as side valence bands with dispersions nearly parallel to the main valence band, but shifted to lower excitation energies. The energy separation between side and main valence bands can be controlled by surface doping, enabling the tuning of certain exciton properties.

Temperature dependence of quantum oscillations from non-parabolic dispersions.

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically nontrivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where π-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a T2-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd3As2 and the multiband Dirac metal LaRhIn5. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi2O2Se, no frequency shift associated to linear bands is observed as expected. However, the π-phase shift in Bi2O2Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.

Magnetization Signature of Topological Surface States in a Non-Symmorphic Superconductor.

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting the main characteristics of 2D topological superconductors. Yet, bulk materials known to combine inherent superconductivity with nontrivial topology remain scarce, largely because distinguishing their central characteristic-the topological surface states-has proved challenging due to a dominant contribution from the superconducting bulk. In this work, a highly anomalous behavior of surface superconductivity in topologically nontrivial 3D superconductor In2 Bi, where the surface states result from its nontrivial band structure, itself a consequence of the non-symmorphic crystal symmetry and strong spin-orbit coupling, is reported. In contrast to smoothly decreasing diamagnetic susceptibility above the bulk critical field, Hc2 , as seen in conventional superconductors, a near-perfect, Meissner-like screening of low-frequency magnetic fields well above Hc2 is observed. The enhanced diamagnetism disappears at a new phase transition close to the critical field of surface superconductivity, Hc3 . Using theoretical modeling, the anomalous screening is shown to be consistent with modification of surface superconductivity by the topological surface states. The possibility of detecting signatures of the surface states using macroscopic magnetization provides a new tool for the discovery and identification of topological superconductors.

Crystal Field Effect and Electric Field Screening in Multilayer Graphene with and without Twist.

We address the intrinsic polarization and screening of an external electric field in a broad range of ordered and twisted configurations of multilayer graphene, using an ab initio approach combining density functional theory and the Wannier function formalism. We show that multilayer graphene is intrinsically polarized due to the crystal field effect, an effect that is often neglected in tight-binding models of twisted bilayer graphene and similar systems. This intrinsic polarization of the order of up to a few tens of millielectronvolts has different out-of-plane alignments in ordered and twisted graphene multilayers, while the in-plane potential modulation is found to be much stronger in twisted systems. We further investigate the dielectric permittivity ε in same multilayer graphene configurations at different electric field strengths. Our findings establish a deep insight into intrinsic and extrinsic polarization in graphene multilayers and provide parameters necessary for building accurate models of these systems.

Edge Disorder in Bottom-Up Zigzag Graphene Nanoribbons: Implications for Magnetism and Quantum Electronic Transport.

We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite" defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conductance across graphene nanoribbons is more sensitive to "bite" defects forming at the zigzag edges than at the armchair ones. Our work establishes a comprehensive understanding of the low-energy electronic properties of disordered bottom-up graphene nanoribbons.

Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices.

We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moiré superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational C_{2} and time-reversal T symmetries. Our results can be readily extended to other twisted graphene multilayers and h-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the nontrivial valley band topology.

Probing magnetism in atomically thin semiconducting PtSe2.

Atomic-scale disorder in two-dimensional transition metal dichalcogenides is often accompanied by local magnetic moments, which can conceivably induce long-range magnetic ordering into intrinsically non-magnetic materials. Here, we demonstrate the signature of long-range magnetic orderings in defective mono- and bi-layer semiconducting PtSe2 by performing magnetoresistance measurements under both lateral and vertical measurement configurations. As the material is thinned down from bi- to mono-layer thickness, we observe a ferromagnetic-to-antiferromagnetic crossover, a behavior which is opposite to the one observed in the prototypical 2D magnet CrI3. Our first-principles calculations, supported by aberration-corrected transmission electron microscopy imaging of point defects, associate this transition to the interplay between the defect-induced magnetism and the interlayer interactions in PtSe2. Furthermore, we show that graphene can be effectively used to probe the magnetization of adjacent semiconducting PtSe2. Our findings in an ultimately scaled monolayer system lay the foundation for atom-by-atom engineering of magnetism in otherwise non-magnetic 2D materials.

Controlling the Quantum Spin Hall Edge States in Two-Dimensional Transition Metal Dichalcogenides.

Two-dimensional transition metal dichalcogenides (TMDs) of Mo and W in their 1T' crystalline phase host the quantum spin Hall (QSH) insulator phase. We address the electronic properties of the QSH edge states by means of first-principles calculations performed on realistic models of edge terminations of different stoichiometries. The QSH edge states show a tendency to have complex band dispersions and coexist with topologically trivial edge states. We nevertheless identify two stable edge terminations that allow isolation of a pair of helical edge states within the band gap of TMDs, with monolayer 1T'-WSe2 being the most promising material. We also characterize the finite-size effects in the electronic structure of 1T'-WSe2 nanoribbons. Our results provide guidance to the experimental studies and possible practical applications of QSH edge states in monolayer 1T'-TMDs.