2D Lateral Heterojunction Arrays with Tailored Interface Band Bending.

Two-dimensional (2D) lateral heterojunction arrays, characterized by well-defined electronic interfaces, hold significant promise for advancing next-generation electronic devices. Despite this potential, the efficient synthesis of high-density lateral heterojunctions with tunable interfacial band alignment remains a challenging. Here, a novel strategy is reported for the fabrication of lateral heterojunction arrays between monolayer Si2Te2 grown on Sb2Te3 (ML-Si2Te2@Sb2Te3) and one-quintuple-layer Sb2Te3 grown on monolayer Si2Te2 (1QL-Sb2Te3@ML-Si2Te2) on a p-doped Sb2Te3 substrate. The site-specific formation of numerous periodically arranged 2D ML-Si2Te2@Sb2Te3/1QL-Sb2Te3@ML-Si2Te2 lateral heterojunctions is realized solely through three epitaxial growth steps of thick-Sb2Te3, ML-Si2Te2, and 1QL-Sb2Te3 films, sequentially. More importantly, the precisely engineering of the interfacial band alignment is realized, by manipulating the substrate's p-doping effect with lateral spatial dependency, on each ML-Si2Te2@Sb2Te3/1QL-Sb2Te3@ML-Si2Te2 junction. Atomically sharp interfaces of the junctions with continuous lattices are observed by scanning tunneling microscopy. Scanning tunneling spectroscopy measurements directly reveal the tailored type-II band bending at the interface. This reported strategy opens avenues for advancing lateral epitaxy technology, facilitating practical applications of 2D in-plane heterojunctions.

Phase Coexistence of Mn Trimer Clusters and Antiferromagnetic Mn Islands on Ir(111).

Clusters supported by solid substrates are prime candidates for heterogeneous catalysis and can be prepared in various ways. While mass-selected soft-landing methods are often used for the generation of monodisperse particles, self-assembly typically leads to a range of different cluster sizes. Here we show by scanning tunneling microscopy measurements that in the initial stages of growth, Mn forms trimers on a close-packed hexagonal Ir surface, providing a route for self-organized monodisperse cluster formation on an isotropic metallic surface. For an increasing amount of Mn, first a phase with reconstructed monolayer islands is formed, until at full coverage a pseudomorphic Mn phase evolves, which is the most densely packed one of the three different observed Mn phases on Ir(111). The magnetic state of both the reconstructed islands and the pseudomorphic film is found to be the prototypical antiferromagnetic Néel state with a 120° spin rotation between all nearest neighbors in the hexagonal layer.

Experimental Realization of Monolayer α-Tellurene.

2D materials emerge as a versatile platform for developing next-generation devices. The experimental realization of novel artificial 2D atomic crystals, which does not have bulk counterparts in nature, is still challenging and always requires new physical or chemical processes. Monolayer α-tellurene is predicted to be a stable 2D allotrope of tellurium (Te), which has great potential for applications in high-performance field-effect transistors. However, the synthesis of monolayer α-tellurene remains elusive because of its complex lattice configuration, in which the Te atoms are stacked in tri-layers in an octahedral fashion. Here, a self-assemble approach, using three atom-long Te chains derived from the dynamic non-equilibrium growth of an a-Si:Te alloy as building blocks, is reported for the epitaxial growth of monolayer α-tellurene on a Sb2 Te3 substrate. By combining scanning tunneling microscopy/spectroscopy with density functional theory calculations, the surface morphology and electronic structure of monolayer α-tellurene are revealed and the underlying growth mechanism is determined. The successful synthesis of monolayer α-tellurene opens up the possibility for the application of this new single-element 2D material in advanced electronic devices.

Proximity superconductivity in atom-by-atom crafted quantum dots.

Gapless materials in electronic contact with superconductors acquire proximity-induced superconductivity in a region near the interface1,2. Numerous proposals build on this addition of electron pairing to originally non-superconducting systems and predict intriguing phases of matter, including topological3-7, odd-frequency8, nodal-point9 or Fulde-Ferrell-Larkin-Ovchinnikov10 superconductivity. Here we investigate the most miniature example of the proximity effect on only a single spin-degenerate quantum level of a surface state confined in a quantum corral11 on a superconducting substrate, built atom by atom by a scanning tunnelling microscope. Whenever an eigenmode of the corral is pitched close to the Fermi energy by adjusting the size of the corral, a pair of particle-hole symmetric states enters the gap of the superconductor. We identify these as spin-degenerate Andreev bound states theoretically predicted 50 years ago by Machida and Shibata12, which had-so far-eluded detection by tunnel spectroscopy but were recently shown to be relevant for transmon qubit devices13,14. We further find that the observed anticrossings of the in-gap states are a measure of proximity-induced pairing in the eigenmodes of the quantum corral. Our results have direct consequences on the interpretation of impurity-induced in-gap states in superconductors, corroborate concepts to induce superconductivity into surface states and further pave the way towards superconducting artificial lattices.

Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors.

Spin chains proximitized by s-wave superconductors are predicted to enter a mini-gapped phase with topologically protected Majorana modes (MMs) localized at their ends. However, the presence of non-topological end states mimicking MM properties can hinder their unambiguous observation. Here, we report on a direct method to exclude the non-local nature of end states via scanning tunneling spectroscopy by introducing a locally perturbing defect on one of the chain's ends. We apply this method to particular end states observed in antiferromagnetic spin chains within a large minigap, thereby proving their topologically trivial character. A minimal model shows that, while wide trivial minigaps hosting end states are easily achieved in antiferromagnetic spin chains, unrealistically large spin-orbit coupling is required to drive the system into a topologically gapped phase with MMs. The methodology of perturbing candidate topological edge modes in future experiments is a powerful tool to probe their stability against local disorder.

Antiferromagnetism-driven two-dimensional topological nodal-point superconductivity.

Magnet/superconductor hybrids (MSHs) hold the promise to host emergent topological superconducting phases. Both one-dimensional (1D) and two-dimensional (2D) magnetic systems in proximity to s-wave superconductors have shown evidence of gapped topological superconductivity with zero-energy end states and chiral edge modes. Recently, it was proposed that the bulk transition-metal dichalcogenide 4Hb-TaS2 is a gapless topological nodal-point superconductor (TNPSC). However, there has been no experimental realization of a TNPSC in a MSH system yet. Here we present the discovery of TNPSC in antiferromagnetic (AFM) monolayers on top of an s-wave superconductor. Our calculations show that the topological phase is driven by the AFM order, resulting in the emergence of a gapless time-reversal invariant topological superconducting state. Using low-temperature scanning tunneling microscopy we observe a low-energy edge mode, which separates the topological phase from the trivial one, at the boundaries of antiferromagnetic islands. As predicted by the calculations, we find that the relative spectral weight of the edge mode depends on the edge's atomic configuration. Our results establish the combination of antiferromagnetism and superconductivity as a novel route to design 2D topological quantum phases.

Nano-scale collinear multi-Q states driven by higher-order interactions.

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

Correlation of Magnetism and Disordered Shiba Bands in Fe Monolayer Islands on Nb(110).

Two-dimensional (2D) magnet-superconductor hybrid systems are intensively studied due to their potential for the realization of 2D topological superconductors with Majorana edge modes. It is theoretically predicted that this quantum state is ubiquitous in spin-orbit-coupled ferromagnetic or skyrmionic 2D spin-lattices in proximity to an s-wave superconductor. However, recent examples suggest that the requirements for topological superconductivity are complicated by the multiorbital nature of the magnetic components and disorder effects. Here, we investigate Fe monolayer islands grown on a surface of the s-wave superconductor with the largest gap of all elemental superconductors, Nb, with respect to magnetism and superconductivity using spin-resolved scanning tunneling spectroscopy. We find three types of islands which differ by their reconstruction inducing disorder, the magnetism and the subgap electronic states. All three types are ferromagnetic with different coercive fields, indicating diverse exchange and anisotropy energies. On all three islands, there is finite spectral weight throughout the substrate's energy gap at the expense of the coherence peak intensity, indicating the formation of Shiba bands overlapping with the Fermi energy. A strong lateral variation of the spectral weight of the Shiba bands signifies substantial disorder on the order of the substrate's pairing energy with a length scale of the period of the three different reconstructions. There are neither signs of topological gaps within these bands nor of any kind of edge modes. Our work illustrates that a reconstructed growth mode of magnetic layers on superconducting surfaces is detrimental for the formation of 2D topological superconductivity.

Spin revolution breaks time reversal symmetry of rolling magnets.

The classical laws of physics are usually invariant under time reversal. Here, we reveal a novel class of magnetomechanical effects rigorously breaking time-reversal symmetry. These effects are based on the mechanical rotation of a hard magnet around its magnetization axis in the presence of friction and an external magnetic field, which we call spin revolution. The spin revolution leads to a variety of symmetry breaking phenomena including upward propulsion on vertical surfaces defying gravity as well as magnetic gyroscopic motion that is perpendicular to the applied force. The angular momentum of spin revolution differs from those of the magnetic field, the magnetic torque, the rolling axis, and the net torque about the rolling axis. The spin revolution emerges spontaneously, without external rotations, and offers various applications in areas such as magnetism, robotics and energy harvesting.

Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions.

Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers, where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Néel walls and quantify the DMI induced by the Pd capping layer. We also observe the chiral evolution of a skyrmion during the DMI switching, where no significant topological protection is found as the skyrmion winding number varies. This corresponds to a minimum energy cost of <1 attojoule during the skyrmion chirality switching. Our results demonstrate the detailed chirality evolution within skyrmions during the DMI sign switching, which is relevant to practical applications of skyrmionic devices.

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains.

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 µeV in chains of at least 35 nm length, corresponding to 70 atoms.

Correlation of Yu-Shiba-Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor.

Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu-Shiba-Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle-hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.

Discovery and characterization of a new type of domain wall in a row-wise antiferromagnet.

Antiferromagnets have recently moved into the focus of application-related research, with the perspective to use them in future spintronics devices. At the same time the experimental determination of the detailed spin texture remains challenging. Here we use spin-polarized scanning tunneling microscopy to investigate the spin structure of antiferromagnetic domain walls. Comparison with spin dynamics simulations allows the identification of a new type of domain wall, which is a superposition state of the adjacent domains. We determine the relevant magnetic interactions and derive analytical formulas. Our experiments show a pathway to control the number of domain walls by boundary effects, and demonstrate the possibility to change the position of domain walls by interaction with movable adsorbed atoms. The knowledge about the exact spin structure of the domain walls is crucial for an understanding and theoretical modelling of their properties regarding, for instance, dynamics, response in transport experiments, and manipulation.

Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers.

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles' edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

Anomalous Flexural Elasticities of Graphene Membranes Unveiled by Manipulating Topology.

Mechanical behavior of atomically thin membranes is governed by bending rigidity and the Gaussian modulus. However, owing to methodological drawbacks, these two parameters have not been investigated sufficiently. We employed atomic force microscopy to demonstrate that the bending rigidity can be extracted from a quadratic relationship of adhesion energy with monolayer curvatures of rolled and unrolled graphene. The tip-induced topological defects revealed the Gaussian modulus; to the best of our knowledge, this is the first study on these parameters. Our study may hold great significance because existing investigations have been performed only on flat graphene. The configurational (strain) energy was evaluated via changes in the surface geometry, with subatomic resolution, by three-dimensional analyses of attractive interatomic forces. The mechanical parameters, evaluated at the hollow sites of the honeycomb lattice, were consistent with the isotropic elastic attributes. The remarkably large negative Gaussian modulus, observed when a single carbon atom was located at the center of the tip-induced bump, revealed attractive interactions between the topological defects and geometric potentials of the Gaussian curvature. Our approach will aid in developing two-dimensional materials and understanding cell biology.

Spin-Polarized Yu-Shiba-Rusinov States in an Iron-Based Superconductor.

Yu-Shiba-Rusinov (YSR) bound states appear when a magnetic atom interacts with a superconductor. Here, we report on spin-resolved spectroscopic studies of YSR states related with Fe atoms deposited on the surface of the topological superconductor FeTe_{0.55}Se_{0.45} using a spin-polarized scanning tunneling microscope. We clearly identify the spin signature of pairs of YSR bound states at finite energies within the superconducting gap having opposite spin polarization as theoretically predicted. In addition, we also observe zero-energy bound states for some of the adsorbed Fe atoms. In this case, a spin signature is found to be absent indicating the absence of Majorana bound states associated with Fe adatoms on FeTe_{0.55}Se_{0.45}.

Atomic-scale spin-polarization maps using functionalized superconducting probes.

A scanning tunneling microscope (STM) with a magnetic tip that has a sufficiently strong spin polarization can be used to map the sample's spin structure down to the atomic scale but usually lacks the possibility to absolutely determine the value of the sample's spin polarization. Magnetic impurities in superconducting materials give rise to pairs of perfectly, i.e., 100%, spin-polarized subgap resonances. In this work, we functionalize the apex of a superconducting Nb STM tip with such impurity states by attaching Fe atoms to probe the spin polarization of atom-manipulated Mn nanomagnets on a Nb(110) surface. By comparison with spin-polarized STM measurements of the same nanomagnets using Cr bulk tips, we demonstrate an extraordinary spin sensitivity and the possibility to measure the sample's spin-polarization values close to the Fermi level quantitatively with our new functionalized probes.

Rotating edge-field driven processing of chiral spin textures in racetrack devices.

Topologically distinct magnetic structures like skyrmions, domain walls, and the uniformly magnetized state have multiple applications in logic devices, sensors, and as bits of information. One of the most promising concepts for applying these bits is the racetrack architecture controlled by electric currents or magnetic driving fields. In state-of-the-art racetracks, these fields or currents are applied to the whole circuit. Here, we employ micromagnetic and atomistic simulations to establish a concept for racetrack memories free of global driving forces. Surprisingly, we realize that mixed sequences of topologically distinct objects can be created and propagated over far distances exclusively by local rotation of magnetization at the sample boundaries. We reveal the dependence between chirality of the rotation and the direction of propagation and define the phase space where the proposed procedure can be realized. The advantages of this approach are the exclusion of high current and field densities as well as its compatibility with an energy-efficient three-dimensional design.

Long-range focusing of magnetic bound states in superconducting lanthanum.

Quantum mechanical systems with long-range interactions between quasiparticles provide a promising platform for coherent quantum information technology. Superconductors are a natural choice for solid-state based quantum devices, while magnetic impurities inside superconductors give rise to quasiparticle excitations of broken Cooper pairs that provide characteristic information about the host superconductor. Here, we reveal that magnetic impurities embedded below a superconducting La(0001) surface interact via quasiparticles extending to very large distances, up to several tens of nanometers. Using low-temperature scanning probe techniques, we observe the corresponding anisotropic and giant oscillations in the LDOS. Theoretical calculations indicate that the quasi-two-dimensional surface states with their strongly anisotropic Fermi surface play a crucial role for the focusing and long-range extension of the magnetic bound states. The quasiparticle focusing mechanism should facilitate the design of versatile magnetic structures with tunable and directed magnetic interactions over large distances, thereby paving the way toward the design of low-dimensional magnet-superconductor hybrid systems exhibiting topologically non-trivial quantum states as possible elements of quantum computation schemes based on Majorana quasiparticles.

Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors.

Chains of magnetic atoms with either strong spin-orbit coupling or spiral magnetic order which are proximity-coupled to superconducting substrates can host topologically non-trivial Majorana bound states. The experimental signature of these states consists of spectral weight at the Fermi energy which is spatially localized near the ends of the chain. However, topologically trivial Yu-Shiba-Rusinov in-gap states localized near the ends of the chain can lead to similar spectra. Here, we explore a protocol to disentangle these contributions by artificially augmenting a candidate Majorana spin chain with orbitally-compatible nonmagnetic atoms. Combining scanning tunneling spectroscopy with ab-initio and tight-binding calculations, we realize a sharp spatial transition between the proximity-coupled spiral magnetic order and the non-magnetic superconducting wire termination, with persistent zero-energy spectral weight localized at either end of the magnetic spiral. Our findings open a new path towards the control of the spatial position of in-gap end states, trivial or Majorana, via different chain terminations, and the realization of designer Majorana chain networks for demonstrating topological quantum computation.