Tailoring Superconductivity in Large-Area Single-Layer NbSe2 via Self-Assembled Molecular Adlayers.

Two-dimensional transition metal dichalcogenides (TMDs) represent an ideal testbench for the search of materials by design, because their optoelectronic properties can be manipulated through surface engineering and molecular functionalization. However, the impact of molecules on intrinsic physical properties of TMDs, such as superconductivity, remains largely unexplored. In this work, the critical temperature (TC) of large-area NbSe2 monolayers is manipulated, employing ultrathin molecular adlayers. Spectroscopic evidence indicates that aligned molecular dipoles within the self-assembled layers act as a fixed gate terminal, collectively generating a macroscopic electrostatic field on NbSe2. This results in an ∼55% increase and a 70% decrease in TC depending on the electric field polarity, which is controlled via molecular selection. The reported functionalization, which improves the air stability of NbSe2, is efficient, practical, up-scalable, and suited to functionalize large-area TMDs. Our results indicate the potential of hybrid 2D materials as a novel platform for tunable superconductivity.

Visualization of Multifractal Superconductivity in a Two-Dimensional Transition Metal Dichalcogenide in the Weak-Disorder Regime.

Eigenstate multifractality is a distinctive feature of noninteracting disordered metals close to a metal-insulator transition, whose properties are expected to extend to superconductivity. While multifractality in three dimensions (3D) only develops near the critical point for specific strong-disorder strengths, multifractality in 2D systems is expected to be observable even for weak disorder. Here we provide evidence for multifractal features in the superconducting state of an intrinsic, weakly disordered single-layer NbSe2 by means of low-temperature scanning tunneling microscopy/spectroscopy. The superconducting gap, characterized by its width, depth, and coherence peaks' amplitude, shows a characteristic spatial modulation coincident with the periodicity of the quasiparticle interference pattern. The strong spatial inhomogeneity of the superconducting gap width, proportional to the local order parameter in the weak-disorder regime, follows a log-normal statistical distribution as well as a power-law decay of the two-point correlation function, in agreement with our theoretical model. Furthermore, the experimental singularity spectrum f(α) shows anomalous scaling behavior typical from 2D weakly disordered systems.

Coexistence of Elastic Modulations in the Charge Density Wave State of 2 H-NbSe2.

Bulk and single-layer 2 H-NbSe2 exhibit identical charge density wave order (CDW) with a quasi-commensurate 3 × 3 superlattice periodicity. Here we combine scanning tunnelling microscopy (STM) imaging at T = 1 K of 2 H-NbSe2 with first-principles density functional theory (DFT) calculations to investigate the structural atomic rearrangement of this CDW phase. Our calculations for single-layers reveal that six different atomic structures are compatible with the 3 × 3 CDW distortion, although all of them lie on a very narrow energy range of at most 3 meV per formula unit, suggesting the coexistence of such structures. Our atomically resolved STM images of bulk 2 H-NbSe2 unambiguously confirm this by identifying two of these structures. Remarkably, these structures differ from the X-ray crystal structure reported for the bulk 3 × 3 CDW which in fact is also one of the six DFT structures located for the single-layer. Our calculations also show that due to the minute energy difference between the different phases, the ground state of the 3 × 3 CDW could be extremely sensitive to doping, external strain or internal pressure within the crystal. The presence of multiphase CDW order in 2 H-NbSe2 may provide further understanding of its low temperature state and the competition between different instabilities.

Influence of Magnetic Ordering between Cr Adatoms on the Yu-Shiba-Rusinov States of the ß-Bi_{2}Pd Superconductor.

We show that the magnetic ordering of coupled atomic dimers on a superconductor is revealed by their intragap spectral features. Chromium atoms on the superconductor ß-Bi_{2}Pd surface display Yu-Shiba-Rusinov bound states, detected as pairs of intragap excitations in tunneling spectra. By means of atomic manipulation with a scanning tunneling microscope's tip, we form Cr dimers with different arrangements and find that their intragap features appear either shifted or split with respect to single atoms. These spectral variations are associated with the magnetic coupling, ferromagnetic or antiferromagnetic, of the dimer, as confirmed by density functional theory simulations. The striking qualitative differences between the observed tunneling spectra prove that intragap Shiba states are extremely sensitive to the magnetic ordering on the atomic scale.

Electronic Structure, Surface Doping, and Optical Response in Epitaxial WSe2 Thin Films.

High quality WSe2 films have been grown on bilayer graphene (BLG) with layer-by-layer control of thickness using molecular beam epitaxy. The combination of angle-resolved photoemission, scanning tunneling microscopy/spectroscopy, and optical absorption measurements reveal the atomic and electronic structures evolution and optical response of WSe2/BLG. We observe that a bilayer of WSe2 is a direct bandgap semiconductor, when integrated in a BLG-based heterostructure, thus shifting the direct-indirect band gap crossover to trilayer WSe2. In the monolayer limit, WSe2 shows a spin-splitting of 475 meV in the valence band at the K point, the largest value observed among all the MX2 (M = Mo, W; X = S, Se) materials. The exciton binding energy of monolayer-WSe2/BLG is found to be 0.21 eV, a value that is orders of magnitude larger than that of conventional three-dimensional semiconductors, yet small as compared to other two-dimensional transition metal dichalcogennides (TMDCs) semiconductors. Finally, our finding regarding the overall modification of the electronic structure by an alkali metal surface electron doping opens a route to further control the electronic properties of TMDCs.

Probing the role of interlayer coupling and coulomb interactions on electronic structure in few-layer MoSe2 nanostructures.

Despite the weak nature of interlayer forces in transition metal dichalcogenide (TMD) materials, their properties are highly dependent on the number of layers in the few-layer two-dimensional (2D) limit. Here, we present a combined scanning tunneling microscopy/spectroscopy and GW theoretical study of the electronic structure of high quality single- and few-layer MoSe2 grown on bilayer graphene. We find that the electronic (quasiparticle) bandgap, a fundamental parameter for transport and optical phenomena, decreases by nearly one electronvolt when going from one layer to three due to interlayer coupling and screening effects. Our results paint a clear picture of the evolution of the electronic wave function hybridization in the valleys of both the valence and conduction bands as the number of layers is changed. This demonstrates the importance of layer number and electron-electron interactions on van der Waals heterostructures and helps to clarify how their electronic properties might be tuned in future 2D nanodevices.

Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are emerging as a new platform for exploring 2D semiconductor physics. Reduced screening in two dimensions results in markedly enhanced electron-electron interactions, which have been predicted to generate giant bandgap renormalization and excitonic effects. Here we present a rigorous experimental observation of extraordinarily large exciton binding energy in a 2D semiconducting TMD. We determine the single-particle electronic bandgap of single-layer MoSe2 by means of scanning tunnelling spectroscopy (STS), as well as the two-particle exciton transition energy using photoluminescence (PL) spectroscopy. These yield an exciton binding energy of 0.55 eV for monolayer MoSe2 on graphene­orders of magnitude larger than what is seen in conventional 3D semiconductors and significantly higher than what we see for MoSe2 monolayers in more highly screening environments. This finding is corroborated by our ab initio GW and Bethe-Salpeter equation calculations which include electron correlation effects. The renormalized bandgap and large exciton binding observed here will have a profound impact on electronic and optoelectronic device technologies based on single-layer semiconducting TMDs.

Local electronic and chemical structure of oligo-acetylene derivatives formed through radical cyclizations at a surface.

Semiconducting π-conjugated polymers have attracted significant interest for applications in light-emitting diodes, field-effect transistors, photovoltaics, and nonlinear optoelectronic devices. Central to the success of these functional organic materials is the facile tunability of their electrical, optical, and magnetic properties along with easy processability and the outstanding mechanical properties associated with polymeric structures. In this work we characterize the chemical and electronic structure of individual chains of oligo-(E)-1,1'-bi(indenylidene), a polyacetylene derivative that we have obtained through cooperative C1-C5 thermal enediyne cyclizations on Au(111) surfaces followed by a step-growth polymerization of the (E)-1,1'-bi(indenylidene) diradical intermediates. We have determined the combined structural and electronic properties of this class of oligomers by characterizing the atomically precise chemical structure of individual monomer building blocks and oligomer chains (via noncontact atomic force microscopy (nc-AFM)), as well as by imaging their localized and extended molecular orbitals (via scanning tunneling microscopy and spectroscopy (STM/STS)). Our combined structural and electronic measurements reveal that the energy associated with extended π-conjugated states in these oligomers is significantly lower than the energy of the corresponding localized monomer orbitals, consistent with theoretical predictions.

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.

Evidence for ground state coherence in a two-dimensional Kondo lattice.

Kondo lattices are ideal testbeds for the exploration of heavy-fermion quantum phases of matter. While our understanding of Kondo lattices has traditionally relied on complex bulk f-electron systems, transition metal dichalcogenide heterobilayers have recently emerged as simple, accessible and tunable 2D Kondo lattice platforms where, however, their ground state remains to be established. Here we present evidence of a coherent ground state in the 1T/1H-TaSe2 heterobilayer by means of scanning tunneling microscopy/spectroscopy at 340 mK. Our measurements reveal the existence of two symmetric electronic resonances around the Fermi energy, a hallmark of coherence in the spin lattice. Spectroscopic imaging locates both resonances at the central Ta atom of the charge density wave of the 1T phase, where the localized magnetic moment is held. Furthermore, the evolution of the electronic structure with the magnetic field reveals a non-linear increase of the energy separation between the electronic resonances. Aided by ab initio and auxiliary-fermion mean-field calculations, we demonstrate that this behavior is inconsistent with a fully screened Kondo lattice, and suggests a ground state with magnetic order mediated by conduction electrons. The manifestation of magnetic coherence in TMD-based 2D Kondo lattices enables the exploration of magnetic quantum criticality, Kondo breakdown transitions and unconventional superconductivity in the strict two-dimensional limit.

Nontrivial Doping Evolution of Electronic Properties in Ising-Superconducting Alloys.

Transition metal dichalcogenides offer unprecedented versatility to engineer 2D materials with tailored properties to explore novel structural and electronic phase transitions. In this work, the atomic-scale evolution of the electronic ground state of a monolayer of Nb1- δ Moδ Se2 across the entire alloy composition range (0 < δ < 1) is investigated using low-temperature (300 mK) scanning tunneling microscopy and spectroscopy (STM/STS). In particular, the atomic and electronic structure of this 2D alloy throughout the metal to semiconductor transition (monolayer NbSe2 to MoSe2 ) is studied. The measurements enable extraction of the effective doping of Mo atoms, the bandgap evolution and the band shifts, which are monotonic with δ. Furthermore, it is demonstrated that collective electronic phases (charge density wave and superconductivity) are remarkably robust against disorder and further shown that the superconducting TC changes non-monotonically with doping. This contrasting behavior in the normal and superconducting state is explained using first-principles calculations. Mo doping is shown to decrease the density of states at the Fermi level and the magnitude of pair-breaking spin fluctuations as a function of Mo content. These results paint a detailed picture of the electronic structure evolution in 2D TMD alloys, which is of utmost relevance for future 2D materials design.

Observation of Superconducting Collective Modes from Competing Pairing Instabilities in Single-Layer NbSe2.

In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow the phase competition to be scrutinized. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. In this work, the existence of a soft collective mode in single-layer NbSe2 , observed as a characteristic resonance excitation in high-resolution tunneling spectra is reported. This resonance is observed along with higher harmonics, its frequency Ω/2Δ is anticorrelated with the local superconducting gap Δ, and its amplitude gradually vanishes by increasing the temperature and upon applying a magnetic field up to the critical values (TC and HC2 ), which sets an unambiguous link to the superconducting state. Aided by a microscopic model that captures the main experimental observations, this resonance is interpreted as a collective Leggett mode that represents the fluctuation toward a proximate f-wave triplet state, due to subleading attraction in the triplet channel. These findings demonstrate the fundamental role of correlations in superconducting 2D transition metal dichalcogenides, opening a path toward unconventional superconductivity in simple, scalable, and transferable 2D superconductors.

Observation of shell effects in superconducting nanoparticles of Sn.

In a zero-dimensional superconductor, quantum size effects (QSE) not only set the limit to superconductivity, but are also at the heart of new phenomena such as shell effects, which have been predicted to result in large enhancements of the superconducting energy gap. Here, we experimentally demonstrate these QSE through measurements on single, isolated Pb and Sn nanoparticles. In both systems superconductivity is ultimately quenched at sizes governed by the dominance of the quantum fluctuations of the order parameter. However, before the destruction of superconductivity, in Sn nanoparticles we observe giant oscillations in the superconducting energy gap with particle size leading to enhancements as large as 60%. These oscillations are the first experimental proof of coherent shell effects in nanoscale superconductors. Contrarily, we observe no such oscillations in the gap for Pb nanoparticles, which is ascribed to the suppression of shell effects for shorter coherence lengths. Our study paves the way to exploit QSE in boosting superconductivity in low-dimensional systems.

Magnetic correlations in single-layer NbSe2.

By means of spin-resolved density functional theory calculations using both atomic orbitals and plane-wave basis codes, we study the electronic and magnetic ground state of single-layer NbSe2. We find that, for all the functionals considered, the most stable solution in this two-dimensional (2D) superconductor is the ferrimagnetic ground state with a magnetic moment of 1.09 µBat the Nb atoms and of 0.05 µBat the Se atoms pointing in the opposite direction. Our calculations show that the ferrimagnetic state precludes the development of charge density wave (CDW) order and their coexistence in the single-layer limit, unless graphene is considered as a substrate. The spin-resolved calculated density of states (DOS), a key fingerprint of the electronic and magnetic structure of a material, unambiguously reproduces the experimental DOS measured by scanning tunneling spectroscopy in single-layer NbSe2. Our work sets magnetism into play in this prototypical correlated 2D material, which is crucial to understand the formation mechanisms of 2D superconductivity and CDW order.

Proximity Effects on the Charge Density Wave Order and Superconductivity in Single-Layer NbSe2.

Collective electronic states such as the charge density wave (CDW) order and superconductivity (SC) respond sensitively to external perturbations. Such sensitivity is dramatically enhanced in two dimensions (2D), where 2D materials hosting such electronic states are largely exposed to the environment. In this regard, the ineludible presence of supporting substrates triggers various proximity effects on 2D materials that may ultimately compromise the stability and properties of the electronic ground state. In this work, we investigate the impact of proximity effects on the CDW and superconducting states in single-layer (SL) NbSe2 on four substrates of diverse nature, namely, bilayer graphene (BLG), SL-boron nitride (h-BN), Au(111), and bulk WSe2. By combining low-temperature (340 mK) scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we compare the electronic structure of this prototypical 2D superconductor on each substrate. We find that, even when the electronic band structure of SL-NbSe2 remains largely unaffected by the substrate except when placed on Au(111), where a charge transfer occurs, both the CDW and SC show disparate behaviors. On the insulating h-BN/Ir(111) substrate and the metallic BLG/SiC(0001) substrate, both the 3 × 3 CDW and superconducting phases persist in SL-NbSe2 with very similar properties, which reveals the negligible impact of graphene on these electronic phases. In contrast, these collective electronic phases are severely weakened and even absent on the bulk insulating WSe2 substrate and the metallic single-crystal Au(111) substrate. Our results provide valuable insights into the fragile stability of such electronic ground states in 2D materials.

Identifying substitutional oxygen as a prolific point defect in monolayer transition metal dichalcogenides.

Chalcogen vacancies are generally considered to be the most common point defects in transition metal dichalcogenide (TMD) semiconductors because of their low formation energy in vacuum and their frequent observation in transmission electron microscopy studies. Consequently, unexpected optical, transport, and catalytic properties in 2D-TMDs have been attributed to in-gap states associated with chalcogen vacancies, even in the absence of direct experimental evidence. Here, we combine low-temperature non-contact atomic force microscopy, scanning tunneling microscopy and spectroscopy, and state-of-the-art ab initio density functional theory and GW calculations to determine both the atomic structure and electronic properties of an abundant chalcogen-site point defect common to MoSe2 and WS2 monolayers grown by molecular beam epitaxy and chemical vapor deposition, respectively. Surprisingly, we observe no in-gap states. Our results strongly suggest that the common chalcogen defects in the described 2D-TMD semiconductors, measured in vacuum environment after gentle annealing, are oxygen substitutional defects, rather than vacancies.

Electronic Properties of Transferable Atomically Thin MoSe2/h-BN Heterostructures Grown on Rh(111).

Vertically stacked two-dimensional (2D) heterostructures composed of 2D semiconductors have attracted great attention. Most of these include hexagonal boron nitride (h-BN) as either a substrate, an encapsulant, or a tunnel barrier. However, reliable synthesis of large-area and epitaxial 2D heterostructures incorporating BN remains challenging. Here, we demonstrate the epitaxial growth of nominal monolayer (ML) MoSe2 on h-BN/Rh(111) by molecular beam epitaxy, where the MoSe2/h-BN layer system can be transferred from the growth substrate onto SiO2. The valence band structure of ML MoSe2/h-BN/Rh(111) revealed by photoemission electron momentum microscopy ( kPEEM) shows that the valence band maximum located at the K point is 1.33 eV below the Fermi level ( EF), whereas the energy difference between K and Γ points is determined to be 0.23 eV, demonstrating that the electronic properties, such as the direct band gap and the effective mass of ML MoSe2, are well preserved in MoSe2/h-BN heterostructures.

Observation of topologically protected states at crystalline phase boundaries in single-layer WSe2.

Transition metal dichalcogenide materials are unique in the wide variety of structural and electronic phases they exhibit in the two-dimensional limit. Here we show how such polymorphic flexibility can be used to achieve topological states at highly ordered phase boundaries in a new quantum spin Hall insulator (QSHI), 1T'-WSe2. We observe edge states at the crystallographically aligned interface between a quantum spin Hall insulating domain of 1T'-WSe2 and a semiconducting domain of 1H-WSe2 in contiguous single layers. The QSHI nature of single-layer 1T'-WSe2 is verified using angle-resolved photoemission spectroscopy to determine band inversion around a 120 meV energy gap, as well as scanning tunneling spectroscopy to directly image edge-state formation. Using this edge-state geometry we confirm the predicted penetration depth of one-dimensional interface states into the two-dimensional bulk of a QSHI for a well-specified crystallographic direction. These interfaces create opportunities for testing predictions of the microscopic behavior of topologically protected boundary states.

Mapping the orbital structure of impurity bound states in a superconductor.

A magnetic atom inside a superconductor locally distorts superconductivity. It scatters Cooper pairs as a potential with broken time-reversal symmetry, leading to localized bound states with subgap excitation energies, named Shiba states. Most conventional approaches regarding Shiba states treat magnetic impurities as point scatterers with isotropic exchange interaction. Here, we show that the number and the shape of Shiba states are correlated to the spin-polarized atomic orbitals of the impurity, hybridized with the superconductor. Using scanning tunnelling spectroscopy, we spatially map the five Shiba excitations found on subsurface chromium atoms in Pb(111), resolving their particle and hole components. While particle components resemble d orbitals of embedded Cr atoms, hole components differ strongly from them. Density functional theory simulations correlate the orbital shapes to the magnetic ground state of the atom, and identify scattering channels and interactions, all valuable tools for designing atomic-scale superconducting devices.