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Here, a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations have revealed that picometre-scale lattice distortions reverse magnetic anisotropy and enhance magnetic frustration in atomically thin ruthenium trichloride — a key step towards realizing a quantum spin liquid in the two-dimensional limit.
π-Conjugated covalent organic frameworks provide a versatile molecular scaffold for the realization of designer quantum nanomaterials. Strong electron–electron correlation within these artificial lattices can give rise to exotic phases of matter. Their experimental realization, however, requires precise control over orbital symmetry, charge localization and band dispersion, all arising from the effective hybridization between molecular linkers and nodes. Here we present a modular strategy for constructing diatomic kagome lattices from aza-[3]triangulene nodes, in which a D 3h -symmetric ground state is stabilized through resonance contributions from a cumulenic linker. First-principles density functional theory and scanning tunnelling spectroscopy reveal that the hybridization of a sixfold-degenerate set of edge-localized Wannier functions in the unit cell gives rise to orbital-phase-frustration-induced non-trivial flat bands. These results establish a general design principle for engineering orbital interactions in organic lattices and open a pathway towards programmable covalent-organic-framework-based quantum materials with correlated electronic ground states.
Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. In this work, we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe 2 . We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe 2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe 2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid.
The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe 2 as a promising material for doing so in a highly tunable fashion. The ground state of this two-dimensional crystal can be electrostatically tuned from a quantum spin Hall insulator to a superconductor. However, much remains unknown about the gap-opening mechanism of the insulating state. In this work, we report evidence that the quantum spin Hall insulator is also an excitonic insulator, arising from the spontaneous formation of electron–hole bound states, namely excitons. We reveal the presence of an intrinsic insulating state at the charge neutrality point in clean samples and confirm the correlated nature of this charge-neutral insulator by tunnelling spectroscopy. We provide evidence against alternative scenarios of a band insulator or a localized insulator and support the existence of an excitonic insulator phase in the clean limit. These observations lay the foundation for understanding a new class of correlated insulators with nontrivial topology and identify monolayer WTe 2 as a promising candidate for exploring quantum phases of ground-state excitons.
Quantum spin liquids are highly entangled, disordered magnetic states that are expected to arise in frustrated Mott insulators and to exhibit exotic fractional excitations such as spinons and chargons. Despite being electrical insulators, some quantum spin liquids are predicted to exhibit gapless itinerant spinons that yield metallic behaviour in the charge-neutral spin channel. For this study, we deposited isolated magnetic atoms onto single-layer 1T-TaSe 2 , a candidate gapless spin liquid, to probe how itinerant spinons couple to impurity spin centres. Using scanning tunnelling spectroscopy, we observe the emergence of new, impurity-induced resonance peaks at the 1T-TaSe 2 Hubbard band edges when cobalt adatoms are positioned to have maximal spatial overlap with the local charge distribution. These resonance peaks disappear when the spatial overlap is reduced or when the magnetic impurities are replaced with nonmagnetic impurities. Theoretical simulations of a modified Anderson impurity model show that the observed peaks are consistent with a Kondo resonance induced by spinons combined with spin-charge binding effects that arise due to fluctuations of an emergent gauge field.
Tin adatoms on a Si(111) substrate with a one-third monolayer coverage form a two-dimensional triangular lattice with one unpaired electron per site. These electrons order into an antiferromagnetic Mott-insulating state, but doping the Sn layer with holes creates a two-dimensional conductor that becomes superconducting at low temperatures. Although the pairing symmetry of the superconducting state is currently unknown, the combination of repulsive interactions and frustration inherent in the triangular adatom lattice opens up the possibility of a chiral order parameter. Here we study the superconducting state of Sn/Si(111) using scanning tunneling microscopy, scanning tunneling spectroscopy and quasiparticle interference imaging. Here we find evidence for a doping-dependent superconducting critical temperature with a fully gapped order parameter, the presence of time-reversal symmetry breaking and a strong enhancement in zero-bias conductance near the edges of the superconducting domains. Although each individual piece of evidence could have a more mundane interpretation, our combined results suggest the possibility that Sn/Si(111) is an unconventional chiral d-wave superconductor.
Twisted homobilayers of transition-metal dichalcogenides have been established as an ideal platform for studying strong correlation phenomena, as exemplified by the recent discovery of fractional Chern insulator states in twisted MoTe 2 , as well as Chern insulators and unconventional superconductivity in twisted WSe 2 . In these systems, a non-trivial topology in the strongly layer-hybridized regime can arise from a spatial patterning of interlayer tunnelling amplitudes and layer-dependent potentials that yields a lattice of layer skyrmions. Here, in this work, we report experimental signatures of skyrmion textures in the layer degree of freedom of rhombohedral-stacked twisted WSe 2 homobilayers. Using scanning tunnelling spectroscopy that separately resolves the Γ-valley and K-valley moiré electronic states, we reveal opposite layer polarizations of the K valley at two different lattice sites with opposite stacking order within the moiré unit cell. These findings are consistent with the theoretically predicted layer-skyrmion texture. We also use our experimental results to parameterize a common continuum model of moiré bands in twisted bilayers, further establishing a direct correlation between the shape of the local density of states in real space and the topology of the topmost moiré band.
Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena that have sparked renewed interest in carbon-based spintronics. Zigzag graphene nanoribbons (ZGNRs)-quasi one-dimensional semiconducting strips of graphene bounded by parallel zigzag edges-host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width. Despite recent advances in the bottom-up synthesis of GNRs featuring symmetry protected topological phases and even metallic zero mode bands, the unique magnetic edge structure of ZGNRs has long been obscured from direct observation by a strong hybridization of the zigzag edge states with the surface states of the underlying support. Here, we present a general technique to thermodynamically stabilize and electronically decouple the highly reactive spin-polarized edge states by introducing a superlattice of substitutional N-atom dopants along the edges of a ZGNR. First-principles GW calculations and scanning tunnelling spectroscopy reveal a giant spin splitting of low-lying nitrogen lone-pair flat bands by an exchange field (~850 tesla) induced by the ferromagnetically ordered edge states of ZGNRs. Finally, our findings directly corroborate the nature of the predicted emergent magnetic order in ZGNRs and provide a robust platform for their exploration and functional integration into nanoscale sensing and logic devices.
Moiré superlattices based on van der Waals bilayers created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles ( θ t ), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θ t = 30° and the commensurate moiré crystals at θ t = 21.8° and 38.2°. Further, valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.
In this work, we have synthesized hydrogenated and deuterated amorphous carbon materials that have a density, 2.7 ± 0.1 g/cm 3 , consistent with almost entirely tetrahedral bonding. In hydrogen-free tetrahedral amorphous carbon, the presence of a minority of sp2 bonded atoms leads to localized states that could be passivated with hydrogen by analogy with hydrogenated amorphous silicon. Neutron diffraction analysis demonstrated that the local bonding environment is consistent with ab initio models of high density hydrogenated tetrahedral amorphous carbon and with the related tetrahedral molecular structure neopentane. The optical bandgap of our material, 4.5 eV, is close to the bandgap in the density of states determined by scanning tunneling spectroscopy (4.3 eV). This bandgap is considerably larger than that of hydrogen-free tetrahedral amorphous carbon, confirming that passivation of sp 2 associated tail-states has occurred. Both the structural and electronic measurements are consistent with a model in which the tetrahedrally bonded carbon regions are terminated by hydrogen, causing hopping conductivity to dominate.
Ultrathin (1–4 nm) films of wide-bandgap semiconductors are important to many applications in microelectronics, and the film properties can be sensitively affected by defects especially at the substrate/film interface. Motivated by this, an in vacuo atomic layer deposition (ALD) was developed for the synthesis of ultrathin films of Ga 2 O 3 /Al 2 O 3 atomic layer stacks (ALSs) on Al electrodes. It is found that the Ga 2 O 3 /Al 2 O 3 ALS can form an interface with the Al electrode with negligible interfacial defects under the optimal ALD condition whether the starting atomic layer is Ga 2 O 3 or Al 2 O 3 . Such an interface is the key to achieving an optimal and tunable electronic structure and dielectric properties in Ga 2 O 3 /Al 2 O 3 ALS ultrathin films. In situ scanning tunneling spectroscopy confirms that the electronic structure of Ga 2 O 3 /Al 2 O 3 ALS can have tunable bandgaps (E g ) between ~2.0 eV for 100% Ga 2 O 3 and ~3.4 eV for 100% Al 2 O 3 . With variable ratios of Ga:Al, the measured E g exhibits significant non-linearity, agreeing with the density functional theory simulation, and tunable carrier concentration. Furthermore, the dielectric constant of ultrathin Ga 2 O 3 /Al 2 O 3 ALS capacitors is tunable through the variation in the ratio of the constituent Ga 2 O 3 and Al 2 O 3 atomic layer numbers from 9.83 for 100% Ga 2 O 3 to 8.28 for 100% Al 2 O 3 . The high ε leads to excellent effective oxide thickness ~1.7–2.1 nm for the ultrathin Ga 2 O 3 /Al 2 O 3 ALS, which is comparable to that of high-K dielectric materials.
We present a systematic investigation of the edge states (ESs) of two-dimensional α-bismuthene (α-Bi) structures self-assembled on highly oriented pyrolytic graphite substrates, using scanning tunnelling microscopy and scanning tunnelling spectroscopy. The measurements are carried out for 3ML, 5ML and 7ML thick Bi structures. Our spectroscopy studies reveal clear features at the edges of the 5ML and 7ML thick structures, and the positions of the ESs coincide with the topographical step edges. In contrast, in 3ML structures the ESs appear to be absent and instead new states are sometimes observed, far from the topographical edge. These states are associated with a moiré pattern and result from strain-induced modulation of the topology. Our observations demonstrate the impact on the ESs of coupling to adjacent structures.
Cross-sectional scanning tunneling microscopy (X-STM) is used to experimentally study the influence of isovalent Bi atoms on the electronic structure of InP. In this work, we map the spatial pattern of the Bi impurity state, which originates from Bi atoms down to the sixth layer below the surface, in topographic, filled-state X-STM images on the natural {110} cleavage planes. The Bi impurity state has a highly anisotropic bowtielike structure and extends over several lattice sites. These Bi-induced charge redistributions extend along the $\langle$110$\rangle$ directions, which define the bowtielike structures we observe. Local tight-binding calculations reproduce the experimentally observed spatial structure of the Bi impurity state. In addition, the influence of the Bi atoms on the electronic structure is investigated in scanning tunneling spectroscopy measurements. These measurements show that Bi induces a resonant state in the valence band, which shifts the band edge toward higher energies. Furthermore, we show that the energetic position of the Bi-induced resonance and its influence on the onset of the valence band edge depend crucially on the position of the Bi atoms relative to the cleavage plane.
A detailed understanding of charged defects in two-dimensional semiconductors is needed for the development of ultrathin electronic devices. Here, we study negatively charged acceptor impurities in monolayer WS 2 using a combination of scanning tunnelling spectroscopy and large-scale atomistic electronic structure calculations. We observe several localized defect states of hydrogenic wave function character in the vicinity of the valence band edge. Some of these defect states are bound, while others are resonant. The resonant states result from the multi-valley valence band structure of WS$_2$, whereby localized states originating from the secondary valence band maximum at Γ hybridize with continuum states from the primary valence band maximum at K/K$^{\prime}$. Resonant states have important consequences for electron transport as they can trap mobile carriers for several tens of picoseconds.
Kagome superconductors with T C up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV 3 Sb 5 , with an ordering temperature of one order of magnitude higher than the T C . However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV 3 Sb 5 , and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV 3 Sb 5 via scanning tunneling microscopy (STM). We observe a 2 × 2 charge modulation and a 1 × 4 superlattice in both topographic data and tunneling spectroscopy. 2 × 2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1 × 4 superlattices form various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real-space modulations, and features 2 × 2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4 K reveals a superconducting energy gap with a gap size 2Δ = 0.85 meV, which estimates a moderate superconductivity coupling strength with 2Δ/k B T C = 3.9. Furthermore, when further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.
Kagome lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z 2 kagome metal AV 3 Sb 5 (A=K, Cs, Rb). This observation triggers wide interest in the interplay between frustrated crystal structure and Fermi surface instabilities. Here, we analyze the lattice effect and its impact on CDW in AV 3 Sb 5 . Based on published experimental data, we show that the 2×2×2 CDW breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagome layers and can explain the twofold symmetric CDW peak intensity observed by scanning tunneling spectroscopy. The coupling between the lattice and electronic degrees of freedom yields a weak first-order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV 3 Sb 5 .
One of the fundamental questions about high-temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single-particle spectral function for the Fermi-Hubbard model as a function of repulsion U and chemical potential μ, we find that the Fermi surface in the normal state undergoes a transition from a large Fermi surface matching the Luttinger volume as expected in a Fermi liquid, to a Fermi surface that encloses fewer electrons that we dub the “Luttinger breaking” phase, as the Mott insulator is approached. This transition into a non-Fermi-liquid phase that violates the Luttinger count occurs at a critical density in the absence of any other broken symmetry. We obtain the Fermi-surface contour from the spectral weight A k (ω = 0) and from an analysis of the singularities of the Green's function Re G k (E = 0), calculated using determinantal quantum Monte Carlo and analytic continuation methods. We discuss our numerical results in connection with experiments on Hall measurements, scanning tunneling spectroscopy, and angle-resolved photoemission spectroscopy.
A van der Waals coupled Weyl semimetal NbIrTe 4 is investigated by combining scanning tunneling microscopy/spectroscopy and first-principles calculations. Here we observe a sharp peak in the tunneling conductance near the Fermi energy (E F ). Comparison with calculations indicates that the peak originates from a van Hove singularity (vHs) associated with a Lifshitz transition of the surface Fermi-arc state. Interestingly, our tunneling spectroscopy also shows signatures of strong electron-boson coupling. This is potentially due to an anomalously enhanced charge susceptibility coming from the near-E F vHs formation.