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Artificial quantum systems have emerged as platforms to realize topological matter in a well-controlled manner. So far, experiments have mostly explored non-interacting topological states, and the realization of many-body topological phases in solid-state platforms with atomic resolution has remained challenging. Here we construct topological quantum Heisenberg spin lattices by assembling spin chains and two-dimensional spin arrays from spin-1/2 Ti atoms on an insulating MgO film in a scanning tunnelling microscope. We engineer both topological and trivial phases of the quantum spin model and thereby realize first- and second-order topological quantum magnets. We probe the many-body excitations of the quantum magnets by single-atom electron spin resonance with an energy resolution better than 100 neV. Making use of the atomically localized magnetic field of the scanning tunnelling microscope tip, we visualize various many-body topological bound modes including topological edge states, topological defects and higher-order corner modes. Our results provide a bottom-up approach for the simulation of exotic quantum many-body phases of interacting spins., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

Persistent currents circulate continuously without requiring external power sources. Here, we extend their theory to include dissipation within the framework of non-Hermitian quantum Hamiltonians. Using Green's function formalism, we introduce a non-Hermitian Fermi-Dirac distribution and derive an analytical expression for the persistent current that relies solely on the complex spectrum. We apply our formula to two dissipative models supporting persistent currents: (i) a phase-biased superconducting-normal-superconducting junction; (ii) a normal ring threaded by a magnetic flux. We show that the persistent currents in both systems exhibit no anomalies at any emergent exceptional points, whose signatures are only discernible in the current susceptibility. We validate our findings by exact diagonalization and extend them to account for finite temperatures and interaction effects. Our formalism offers a general framework for computing quantum many-body observables of non-Hermitian systems in equilibrium, with potential extensions to nonequilibrium scenarios.

Two-dimensional van der Waals materials have become an established platform to engineer flat bands which can lead to strongly-correlated emergent phenomena. In particular, the family of Ta dichalcogenides in the 1T phase presents a star-of-David charge density wave that creates a flat band at the Fermi level. For TaS 2 and TaSe 2 this flat band is at half filling leading to a magnetic insulating phase. In this work, we theoretically demonstrate that ligand substitution in the TaSe2-xTe x system produces a transition from the magnetic insulator to a non-magnetic metal in which the flat band gets doped away from half-filling. Forx∈[0.846,1.231]the spin-polarized flat band is self-doped and the system becomes a magnetic metal. In this regime, we show that attractive interactions promote three different spin-triplet superconducting phases as a function of x , corresponding to a nodal f-wave and two topologically-different chiral p-wave superconducting phases. Our results establish monolayer TaSe2-xTe x as a promising platform for correlated flat band physics leading to unconventional superconducting states., (Creative Commons Attribution license.)

Progress in layered van der Waals materials has resulted in the discovery of ferromagnetic and ferroelectric materials down to the monolayer limit. Recently, evidence of the first purely 2D multiferroic material was reported in monolayer NiI 2 . However, probing multiferroicity with scattering-based and optical bulk techniques is challenging on 2D materials, and experiments on the atomic scale are needed to fully characterize the multiferroic order at the monolayer limit. Here, scanning tunneling microscopy (STM) supported by density functional theory (DFT) calculations is used to probe and characterize the multiferroic order in monolayer NiI 2 . It is demonstrated that the type-II multiferroic order displayed by NiI 2 , arising from the combination of a magnetic spin spiral order and a strong spin-orbit coupling, allows probing the multiferroic order in the STM experiments. Moreover, the magnetoelectric coupling of NiI 2 is directly probed by external electric field manipulation of the multiferroic domains. The findings establish a novel point of view to analyze magnetoelectric effects at the microscopic level, paving the way toward engineering new multiferroic orders in van der Waals materials and their heterostructures., (© 2024 The Authors. Advanced Materials published by Wiley‐VCH GmbH.)

A valley filter capable of generating a valley-polarized current is a crucial element in valleytronics, yet its implementation remains challenging. Here, we propose a valley filter made of a graphene bilayer which exhibits a 1D moiré pattern in the overlapping region of the two layers controlled by heterostrain. In the presence of a lattice modulation between layers, electrons propagating in one layer can have valley-dependent dissipation due to valley asymmetric interlayer coupling, thus giving rise to a valley-polarized current. Such a process can be described by an effective non-Hermitian theory, in which the valley filter is driven by a valley-resolved non-Hermitian skin effect. Nearly 100% valley polarization can be achieved within a wide parameter range and the functionality of the valley filter is electrically tunable. The non-Hermitian topological scenario of the valley filter ensures high tolerance against imperfections such as disorder and edge defects. Our work opens a new route for efficient and robust valley filters while significantly relaxing the stringent implementation requirements.

CeSiI has been recently isolated in the ultrathin limit, establishing CeSiI as the first intrinsic two-dimensional van der Waals heavy-fermion material up to 85 K. We show that, due to the strong spin-orbit coupling, the local moments develop a multipolar real-space magnetic texture, leading to local pseudospins with a nearly vanishing net moment. To elucidate its Kondo-screened regime, we extract from first-principles the parameters of the Kondo lattice model describing this material. We develop a pseudofermion methodology in combination with ab initio calculations to reveal the nature of the heavy-fermion state in CeSiI. We analyze the competing magnetic interactions leading to an unconventional heavy-fermion order as a function of the magnetic exchange between the localized f-electrons and the strength of the Kondo coupling. Our results show that the magnetic exchange interactions promote an unconventional momentum-dependent Kondo-screened phase, establishing the nature of the heavy-fermion state observed in CeSiI.

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena., (Creative Commons Attribution license.)

Synthesis of one-dimensional molecular arrays with tailored stereoisomers is challenging yet has great potential for application in molecular opto-, electronic- and magnetic-devices, where the local array structure plays a decisive role in the functional properties. Here, we demonstrate the construction and characterization of dehydroazulene isomer and diradical units in three-dimensional organometallic compounds on Ag(111) with a combination of low-temperature scanning tunneling microscopy and density functional theory calculations. Tip-induced voltage pulses firstly result in the formation of a diradical species via successive homolytic fission of two C-Br bonds in the naphthyl groups, which are subsequently transformed into chiral dehydroazulene moieties. The delicate balance of the reaction rates among the diradical and two stereoisomers, arising from an in-line configuration of tip and molecular unit, allows directional azulene-to-azulene and azulene-to-diradical local probe structural isomerization in a controlled manner. Furthermore, our theoretical calculations suggest that the diradical moiety hosts an open-shell singlet with antiferromagnetic coupling between the unpaired electrons, which can undergo an inelastic spin transition of 91 meV to the ferromagnetically coupled triplet state., (© 2023. The Author(s).)

Unconventional superconductors represent one of the fundamental directions in modern quantum materials research. In particular, nodal superconductors are known to appear naturally in strongly correlated systems, including cuprate superconductors and heavy-fermion systems. Van der Waals materials hosting superconducting states are well known, yet nodal monolayer van der Waals superconductors have remained elusive. Here, using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) experiments, it is shown that pristine monolayer 1H-TaS 2 realizes a nodal superconducting state. Non-magnetic disorder drives the nodal superconducting state to a conventional gapped s-wave state. Furthermore, many-body excitations emerge close to the gap edge, signalling a potential unconventional pairing mechanism. The results demonstrate the emergence of nodal superconductivity in a van der Waals monolayer, providing a building block for van der Waals heterostructures exploiting unconventional superconducting states., (© 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH.)

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Quantum magnets provide a powerful platform to explore complex quantum many-body phenomena. One example is triplon excitations, exotic many-body modes emerging from propagating singlet-triplet transitions. We engineer a minimal quantum magnet from organic molecules and demonstrate the emergence of dispersive triplon modes in one- and two-dimensional assemblies probed with scanning tunneling microscopy and spectroscopy. Our results provide the first demonstration of dispersive triplon excitations from a real-space measurement.

Two-dimensional magnetic materials provide an ideal platform to explore collective many-body excitations associated with spin fluctuations. In particular, it should be feasible to explore, manipulate, and ultimately design magnonic excitations in two-dimensional van der Waals magnets in a controllable way. Here we demonstrate the emergence of moiré magnon excitations, stemming from the interplay of spin-excitations in monolayer CrBr 3 and the moiré pattern arising from the lattice mismatch with the underlying substrate. The existence of moiré magnons is further confirmed via inelastic quasiparticle interference, showing the appearance of a dispersion pattern correlated with the moiré length scale. Our results provide a direct visualization in real-space of the dispersion of moiré magnons, demonstrating the versatility of moiré patterns in creating emergent many-body excitations.

Scattering processes in quantum materials emerge as resonances in electronic transport, including confined modes, Andreev states, and Yu-Shiba-Rusinov states. However, in most instances, these resonances are driven by a single scattering mechanism. Here, we show the appearance of resonances due to the combination of two simultaneous scattering mechanisms, one from superconductivity and the other from graphene p-n junctions. These resonances stem from Andreev reflection and Klein tunneling that occur at two different interfaces of a hole-doped region of graphene formed at the boundary with superconducting graphene due to proximity effects from Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+δ}. The resonances persist with gating from p^{+}-p and p-n configurations. The suppression of the oscillation amplitude above the bias energy which is comparable to the induced superconducting gap indicates the contribution from Andreev reflection. Our experimental measurements are supported by quantum transport calculations in such interfaces, leading to analogous resonances. Our results put forward a hybrid scattering mechanism in graphene-high-temperature superconductor heterojunctions of potential impact for graphene-based Josephson junctions.

Spectral functions of non-Hermitian Hamiltonians can reveal the existence of topologically nontrivial line gaps and the associated topological edge modes. However, the computation of spectral functions in a non-Hermitian many-body system remains an open challenge. Here, we put forward a numerical approach to compute spectral functions of a non-Hermitian many-body Hamiltonian based on the kernel polynomial method and the matrix-product state formalism. We show that the local spectral functions computed with our algorithm reveal topological spin excitations in a non-Hermitian spin model, faithfully reflecting the nontrivial line gap topology in a many-body model. We further show that the algorithm works in the presence of the non-Hermitian skin effect. Our method offers an efficient way to compute local spectral functions in non-Hermitian many-body systems with tensor networks, allowing us to characterize line gap topology in non-Hermitian quantum many-body models.

2D ferroelectric materials provide a promising platform for the electrical control of quantum states. In particular, due to their 2D nature, they are suitable for influencing the quantum states of deposited molecules via the proximity effect. Here, electrically controllable molecular states in phthalocyanine molecules adsorbed on monolayer ferroelectric material SnTe are reported. The strain and ferroelectric order in SnTe are found to create a transition between two distinct orbital orders in the adsorbed phthalocyanine molecules. By controlling the polarization of the ferroelectric domain using scanning tunneling microscopy (STM), it is successfully demonstrated that orbital order can be manipulated electrically. The results show how ferroelastic coupling in 2D systems allows for control of molecular states, providing a starting point for ferroelectrically switchable molecular orbital ordering and ultimately, electrical control of molecular magnetism., (© 2023 The Authors. Advanced Materials published by Wiley-VCH GmbH.)

Ferroelectric van der Waals heterostructures provide a natural platform to design a variety of electrically controllable devices. In this work, we demonstrate that AB bilayer graphene encapsulated in MoTe 2 acts as a valley valve that displays a switchable built-in topological gap, leading to ferroelectrically driven topological channels. Using a combination of ab initio calculations and low energy models, we show that the ferroelectric order of MoTe 2 allows the control of the gap opening in bilayer graphene and leads to topological channels between different ferroelectric domains. Moreover, we analyze the effect that the moiré modulation between MoTe 2 and graphene layers has in the topological modes, demonstrating that the edge states are robust against moiré modulations of the ferroelectrically-induced electric potential. Our results put forward ferroelectric/graphene heterostructures as versatile platforms to engineer switchable built-in topological channels without requiring an external electric bias.

Magnetic frustrations in two-dimensional materials provide a rich playground to engineer unconventional phenomena. However, despite intense efforts, a realization of tunable frustrated magnetic order in two-dimensional materials remains an open challenge. Here we propose Coulomb engineering as a versatile strategy to tailor magnetic ground states in layered materials. Using the frustrated van der Waals monolayer 1T-TaS 2 as an example, we show how long-range Coulomb interactions renormalize the low energy nearly flat band structure, leading to a Heisenberg model which depends on the Coulomb interactions. Based on this, we show that superexchange couplings in the material can be precisely tailored by means of environmental dielectric screening, ultimately allowing to externally drive the material towards a tunable frustrated regime. Our results put forward Coulomb engineering as a powerful tool to manipulate magnetic properties of van der Waals materials., (Creative Commons Attribution license.)

Direct detection of superconductivity has long been a key strength of point-contact Andreev reflection. However, its applicability to atomic-scale imaging is limited by the mechanical contact of the Andreev probe. To this end, we present a new method to probe Andreev reflection in a tunnel junction, leveraging tunneling spectroscopy and junction tunability to achieve quantitative detection of Andreev scattering. This method enables unambiguous assignment of superconducting origins of current-carrying excitations, as well as detection of higher order Andreev processes in atomic-scale junctions. We furthermore revealed distinct sensitivity of Andreev reflection to natural defects, such as step edges, even in classical superconductors. The methodology opens a new path to nano- and atomic-scale imaging of superconducting properties, including disordered superconductors and proximity to phase transitions.

Transition metal dichalcogenides (TMDC) are a rich family of two-dimensional materials displaying a multitude of different quantum ground states. In particular, d 3 TMDCs are paradigmatic materials hosting a variety of symmetry broken states, including charge density waves, superconductivity, and magnetism. Among this family, NbSe 2 is one of the best-studied superconducting materials down to the monolayer limit. Despite its superconducting nature, a variety of results point toward strong electronic repulsions in NbSe 2 . Here, we control the strength of the interactions experimentally via quantum confinement and use low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to demonstrate that NbSe 2 is in close proximity to a correlated insulating state. This reveals the coexistence of competing interactions in NbSe 2 , creating a transition from a superconducting to an insulating quantum correlated state by confinement-controlled interactions. Our results demonstrate the dramatic role of interactions in NbSe 2 , establishing NbSe 2 as a correlated superconductor with competing interactions.

The search for artificial topological superconductivity has been limited by the stringent conditions required for its emergence. As exemplified by the recent discoveries of various correlated electronic states in twisted van der Waals materials, moiré patterns can act as a powerful knob to create artificial electronic structures. Here, we demonstrate that a moiré pattern between a van der Waals superconductor and a monolayer ferromagnet creates a periodic potential modulation that enables the realization of a topological superconducting state that would not be accessible in the absence of the moiré. The magnetic moiré pattern gives rise to Yu-Shiba-Rusinov minibands and periodic modulation of the Majorana edge modes that we detect using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Moiré patterns and, more broadly, periodic potential modulations are powerful tools to overcome the conventional constraints for realizing and controlling topological superconductivity.

Moiré patterns in van der Waal materials can be used for designing magnetic structures.

Heavy-fermion systems represent one of the paradigmatic strongly correlated states of matter 1-5 . They have been used as a platform for investigating exotic behaviour ranging from quantum criticality and non-Fermi liquid behaviour to unconventional topological superconductivity 4-12 . The heavy-fermion phenomenon arises from the exchange interaction between localized magnetic moments and conduction electrons leading to Kondo lattice physics, and represents one of the long-standing open problems in quantum materials 3 . In a Kondo lattice, the exchange interaction gives rise to a band with heavy effective mass. This intriguing phenomenology has so far been realized only in compounds containing rare-earth elements with 4f or 5f electrons 1,4,13,14 . Here we realize a designer van der Waals heterostructure where artificial heavy fermions emerge from the Kondo coupling between a lattice of localized magnetic moments and itinerant electrons in a 1T/1H-TaS 2 heterostructure. We study the heterostructure using scanning tunnelling microscopy and spectroscopy and show that depending on the stacking order of the monolayers, we can reveal either the localized magnetic moments and the associated Kondo effect, or the conduction electrons with a heavy-fermion hybridization gap. Our experiments realize an ultimately tunable platform for future experiments probing enhanced many-body correlations, dimensional tuning of quantum criticality and unconventional superconductivity in two-dimensional artificial heavy-fermion systems 15-17 ., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)

Twisted van der Waals materials have been shown to host a variety of tunable electronic structures. Here we put forward twisted trilayer graphene (TTG) as a platform to emulate heavy fermion physics. We demonstrate that TTG hosts extended and localized modes with an electronic structure that can be controlled by interlayer bias. In the presence of interactions, the existence of localized modes leads to the development of local moments, which are Kondo coupled to coexisting extended states. By electrically controlling the effective exchange between local moments, the system can be driven from a magnetic into a heavy fermion regime, passing through a quantum critical point, allowing one to electrically explore a generalized Doniach phase diagram. Our results put forward twisted graphene multilayers as a platform for the realization of strongly correlated heavy fermion physics in a purely carbon-based platform.

When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes suitable for topological quantum computing. Here, the first observation of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms, is reported. Superconductivity in graphene is induced by proximity effect brought by adsorbing nanometer-scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy the superconducting proximity gap is measured in graphene, and Yu-Shiba-Rusinov states are visualized in graphene grain boundaries. The results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long-sought experimental confirmation that graphene grain boundaries host local magnetic moments and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system., (© 2021 Wiley-VCH GmbH.)

Van der Waals heterostructures provide a rich platform for emergent physics due to their tunable hybridization of layers, orbitals, and spin. Here, we find that twisted bilayer graphene stacked between antialigned ferromagnetic insulators can feature flat electronic bands due to the interplay between twist, exchange proximity, and spin-orbit coupling. These flat bands are nearly degenerate in valley only and are effectively described by a triangular superlattice model. At half filling, we find that interactions induce spontaneous valley correlations that favor spiral order and derive a low-energy valley-Heisenberg model with symmetric and antisymmetric exchange couplings. We also show how electric interlayer bias broadens the bands and tunes these couplings. Our results put forward magnetic van der Waals heterostructures as a platform to explore valley-correlated states.

Van der Waals (VdW) materials have opened new directions in the study of low dimensional magnetism. A largely unexplored arena is the intrinsic tuning of VdW magnets toward new ground states. Chromium trihalides provided the first such example with a change of interlayer magnetic coupling emerging upon exfoliation. Here, we take a different approach to engineer previously unknown ground states, not by exfoliation, but by tuning the spin-orbit coupling (SOC) of the nonmagnetic ligand atoms (Cl, Br, I). We synthesize a three-halide series, CrCl 3 - x - y Br x I y , and map their magnetic properties as a function of Cl, Br, and I content. The resulting triangular phase diagrams unveil a frustrated regime near CrCl 3 . First-principles calculations confirm that the frustration is driven by a competition between the chromium and halide SOCs. Furthermore, we reveal a field-induced change of interlayer coupling in the bulk of CrCl 3 - x - y Br x I y crystals at the same field as in the exfoliation experiments., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or quantization of energy levels. However, creating confining structures with nanometer precision in shape, size, and location remains an experimental challenge, both for top-down and bottom-up approaches. Moreover, Klein tunneling, offering an escape route to graphene electrons, limits the efficiency of electrostatic confinement. Here, a scanning tunneling microscope (STM) is used to create graphene nanopatterns, with sub-nanometer precision, by the collective manipulation of a large number of H atoms. Individual graphene nanostructures are built at selected locations, with predetermined orientations and shapes, and with dimensions going all the way from 2 nm up to 1 µm. The method permits the patterns to be erased and rebuilt at will, and it can be implemented on different graphene substrates. STM experiments demonstrate that such graphene nanostructures confine very efficiently graphene Dirac quasiparticles, both in 0D and 1D structures. In graphene quantum dots, perfectly defined energy bandgaps up to 0.8 eV are found that scale as the inverse of the dot's linear dimension, as expected for massless Dirac fermions., (© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Crystal fields occur due to a potential difference between chemically different atomic species. In van der Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions, and elastic relaxations, but crystal fields have not received the attention they deserve. Here, we show that the band structure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic band gap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer [Formula: see text] = 0.13 V/nm ≈ [Formula: see text] = 0.12 V/nm. We show both by means of first-principles calculations and low energy models that crystal fields open a band gap in the ground state. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers.

Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles (α≈0.3°) and flat bands at magic angles (α≈1°). We show that tuning the twist angle to α^{*}≈0.8° generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with ±6 electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-broken ground state (Stoner instability) with spin-polarized regions that order ferromagnetically. Application of an interlayer electric field breaks inversion symmetry and introduces valley-dependent dispersion that quenches the magnetic order. With these results, we propose a solid-state platform that realizes electrically tunable strong correlations.

Shrinking spintronic devices to the nanoscale ultimately requires localized control of individual atomic magnetic moments. At these length scales, the exchange interaction plays important roles, such as in the stabilization of spin-quantization axes, the production of spin frustration, and creation of magnetic ordering. Here, we demonstrate the precise control of the exchange bias experienced by a single atom on a surface, covering an energy range of 4 orders of magnitude. The exchange interaction is continuously tunable from milli-eV to micro-eV by adjusting the separation between a spin-1/2 atom on a surface and the magnetic tip of a scanning tunneling microscope. We seamlessly combine inelastic electron tunneling spectroscopy and electron spin resonance to map out the different energy scales. This control of exchange bias over a wide span of energies provides versatile control of spin states, with applications ranging from precise tuning of quantum state properties, to strong exchange bias for local spin doping. In addition, we show that a time-varying exchange interaction generates a localized ac magnetic field that resonantly drives the surface spin. The static and dynamic control of the exchange interaction at the atomic scale provides a new tool to tune the quantum states of coupled-spin systems.

Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumheadlike surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction drives a Stoner ferromagnetic instability in the DSS while the bulk remains nonmagnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each piece of DSS carries a half-integer topological charge, which for systems containing two pieces of DSS yield a net Chern number C=-1. We show that this phenomenology is robust against chiral-symmetry breaking, which gives a finite dispersion to the DSS. Our results show that nodal line semimetals are a promising platform to implement surface Chern insulators and dissipationless electron transport by exploiting enhanced interaction effects of the DSS.

Nuclear spins serve as sensitive probes in chemistry 1 and materials science 2 and are promising candidates for quantum information processing 3-6 . NMR, the resonant control of nuclear spins, is a powerful tool for probing local magnetic environments in condensed matter systems, which range from magnetic ordering in high-temperature superconductors 7,8 and spin liquids 9 to quantum magnetism in nanomagnets 10,11 . Increasing the sensitivity of NMR to the single-atom scale is challenging as it requires a strong polarization of nuclear spins, well in excess of the low polarizations obtained at thermal equilibrium, as well as driving and detecting them individually 4,5,12 . Strong nuclear spin polarization, known as hyperpolarization, can be achieved through hyperfine coupling with electron spins 2 . The fundamental mechanism is the conservation of angular momentum: an electron spin flips and a nuclear spin flops. The nuclear hyperpolarization enables applications such as in vivo magnetic resonance imaging using nanoparticles 13 , and is harnessed for spin-based quantum information processing in quantum dots 14 and doped silicon 15-17 . Here we polarize the nuclear spins of individual copper atoms on a surface using a spin-polarized current in a scanning tunnelling microscope. By employing the electron-nuclear flip-flop hyperfine interaction, the spin angular momentum is transferred from tunnelling electrons to the nucleus of individual Cu atoms. The direction and magnitude of the nuclear polarization is controlled by the direction and amplitude of the current. The nuclear polarization permits the detection of the NMR of individual Cu atoms, which is used to sense the local magnetic environment of the Cu electron spin.

Taking advantage of nuclear spins for electronic structure analysis, magnetic resonance imaging, and quantum devices hinges on knowledge and control of the surrounding atomic-scale environment. We measured and manipulated the hyperfine interaction of individual iron and titanium atoms placed on a magnesium oxide surface by using spin-polarized scanning tunneling microscopy in combination with single-atom electron spin resonance. Using atom manipulation to move single atoms, we found that the hyperfine interaction strongly depended on the binding configuration of the atom. We could extract atom- and position-dependent information about the electronic ground state, the state mixing with neighboring atoms, and properties of the nuclear spin. Thus, the hyperfine spectrum becomes a powerful probe of the chemical environment of individual atoms and nanostructures., (Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, α≪1°, the application of a perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field leads to the development of highly localized modes associated with flat bands close to charge neutrality, which form an emergent kagome lattice in real space. Our findings indicate that for tiny angles biased twisted bilayer graphene is a promising platform that can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.

Two-dimensional topological superconductivity has attracted great interest due to the emergence of Majorana modes bound to vortices and propagating along edges. However, due to its rare appearance in natural compounds, experimental realizations rely on a delicate artificial engineering involving materials with helical states, magnetic fields, and conventional superconductors. Here we introduce an alternative path using a class of three-dimensional antiferromagnets to engineer a two-dimensional topological superconductor. Our proposal exploits the appearance of solitonic states at the interface between a topologically trivial antiferromagnet and a conventional superconductor, which realize a topological superconducting phase when their spectrum is gapped by intrinsic spin-orbit coupling. We show that these interfacial states do not require fine-tuning, but are protected by asymptotic boundary conditions.

Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises varied magnetic states, including ultrathin insulating multiferroics, spin liquids, and ferromagnets, but device-oriented characterization methods are needed to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI 3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and interlayer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI 3 barriers, respectively. We further measure inelastic tunneling spectra for our junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI 3 ., (Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Quantum spin networks having engineered geometries and interactions are eagerly pursued for quantum simulation and access to emergent quantum phenomena such as spin liquids. Spin-1/2 centers are particularly desirable, because they readily manifest coherent quantum fluctuations. Here we introduce a controllable spin-1/2 architecture consisting of titanium atoms on a magnesium oxide surface. We tailor the spin interactions by atomic-precision positioning using a scanning tunneling microscope (STM) and subsequently perform electron spin resonance on individual atoms to drive transitions into and out of quantum eigenstates of the coupled-spin system. Interactions between the atoms are mapped over a range of distances extending from highly anisotropic dipole coupling to strong exchange coupling. The local magnetic field of the magnetic STM tip serves to precisely tune the superposition states of a pair of spins. The precise control of the spin-spin interactions and ability to probe the states of the coupled-spin network by addressing individual spins will enable the exploration of quantum many-body systems based on networks of spin-1/2 atoms on surfaces.

Two-dimensional (2D) semiconducting materials are particularly appealing for many applications. Although theory predicts a large number of 2D materials, experimentally only a few of these materials have been identified and characterized comprehensively in the ultrathin limit. Lead iodide, which belongs to the transition metal halides family and has a direct bandgap in the visible spectrum, has been known for a long time and has been well characterized in its bulk form. Nevertheless, studies of this material in the nanometer thickness regime are rather scarce. In this article we demonstrate an easy way to synthesize ultrathin, highly crystalline flakes of PbI 2 by precipitation from a solution in water. We thoroughly characterize the produced thin flakes with different techniques ranging from optical and Raman spectroscopy to temperature-dependent photoluminescence and electron microscopy. We compare the results to ab initio calculations of the band structure of the material. Finally, we fabricate photodetectors based on PbI 2 and study their optoelectronic properties.

Twisted graphene bilayers develop highly localized states around AA-stacked regions for small twist angles. We show that interaction effects may induce either an antiferromagnetic or a ferromagnetic (FM) polarization of said regions, depending on the electrical bias between layers. Remarkably, FM-polarized AA regions under bias develop spiral magnetic ordering, with a relative 120° misalignment between neighboring regions due to a frustrated antiferromagnetic exchange. This remarkable spiral magnetism emerges naturally without the need of spin-orbit coupling, and competes with the more conventional lattice-antiferromagnetic instability, which interestingly develops at smaller bias under weaker interactions than in monolayer graphene, due to Fermi velocity suppression. This rich and electrically controllable magnetism could turn twisted bilayer graphene into an ideal system to study frustrated magnetism in two dimensions.

The advent of devices based on single dopants, such as the single-atom transistor, the single-spin magnetometer and the single-atom memory, has motivated the quest for strategies that permit the control of matter with atomic precision. Manipulation of individual atoms by low-temperature scanning tunnelling microscopy provides ways to store data in atoms, encoded either into their charge state, magnetization state or lattice position. A clear challenge now is the controlled integration of these individual functional atoms into extended, scalable atomic circuits. Here, we present a robust digital atomic-scale memory of up to 1 kilobyte (8,000 bits) using an array of individual surface vacancies in a chlorine-terminated Cu(100) surface. The memory can be read and rewritten automatically by means of atomic-scale markers and offers an areal density of 502 terabits per square inch, outperforming state-of-the-art hard disk drives by three orders of magnitude. Furthermore, the chlorine vacancies are found to be stable at temperatures up to 77 K, offering the potential for expanding large-scale atomic assembly towards ambient conditions.

The inelastic portion of the tunnel current through an individual magnetic atom grants unique access to read out and change the atom's spin state, but it also provides a path for spontaneous relaxation and decoherence. Controlled closure of the inelastic channel would allow for the latter to be switched off at will, paving the way to coherent spin manipulation in single atoms. Here, we demonstrate complete closure of the inelastic channels for both spin and orbital transitions due to a controlled geometric modification of the atom's environment, using scanning tunneling microscopy (STM). The observed suppression of the excitation signal, which occurs for Co atoms assembled into chains on a Cu2N substrate, indicates a structural transition affecting the dz(2) orbital, effectively cutting off the STM tip from the spin-flip cotunneling path.

The independent predictions of edge ferromagnetism and the quantum spin Hall phase in graphene have inspired the quest of other two-dimensional honeycomb systems, such as silicene, germanene, stanene, iridates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but a larger spin-orbit coupling. Here, we study the interplay of ferromagnetic order and spin-orbit interactions at the zigzag edges of these graphenelike systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conducting edge channels that should result in large changes of electronic properties upon rotation of the magnetization.