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Quantum state preparation is a key step in all digital quantum simulation algorithms. Here we propose methods to initialize on a gate-based quantum computer a general class of quantum spin wave functions, the so-called Valence-Bond-Solid (VBS) states, that are important for two reasons. First, VBS states are the exact ground states of a class of interacting quantum spin models introduced by Affleck, Kennedy, Lieb and Tasaki (AKLT). Second, the two-dimensional VBS states are universal resource states for measurement-based quantum computing. We find that schemes to prepare VBS states based on their tensor-network representations yield quantum circuits that are too deep to be within reach of noisy intermediate-scale quantum (NISQ) computers. We then apply the general non-deterministic method herein proposed to the preparation of the spin-1 and spin-3/2 VBS states, the ground states of the AKLT models defined in one dimension and in the honeycomb lattice, respectively. Shallow quantum circuits of depth independent of the lattice size are explicitly derived for both cases, making use of optimization schemes that outperform standard basis gate decomposition methods. Given the probabilistic nature of the proposed routine, two strategies that achieve a quadratic reduction of the repetition overhead for any VBS state defined on a bipartite lattice are devised. Our approach should permit to use NISQ processors to explore the AKLT model and variants thereof, outperforming conventional numerical methods in the near future., Comment: Main text: 17 pages, 7 figures. Appendices: 10 pages, 5 figures. QASM files to be added in next version of preprint

Magnetic 2D materials hold promise to change the miniaturization paradigm of unidirectional photonic components. However, the integration of these materials in devices hinges on the accurate determination of the optical properties down to the monolayer limit, which is still missing. By using hyperspectral wide-field imaging at room temperature, we reveal a nonmonotonic thickness dependence of the complex optical dielectric function in the archetypal magnetic 2D material CrI3 extending across different length scales: onsetting at the mesoscale, peaking at the nanoscale, and decreasing again down to the single layer. These results portray a modification of the electronic properties of the material and align with the layer-dependent magnetism in CrI3, shedding light on the long-standing structural conundrum in this material. The unique modulation of the complex dielectric function from the monolayer up to more than 100 layers will be instrumental for understanding mesoscopic effects in layered materials and tuning light-matter interactions in magnetic 2D materials. The project that gave rise to these results received the financial support of a fellowship from the “la Caixa” Foundation (ID No. 100010434, fellowship codes LCF/BQ/PR21/11840011 and LCF/BQ/DI22/11940022) and Grant No. PID2020-118938GA-100 from the Spanish Ministerio de Ciencia e Innovación (MICINN). E. N. M. acknowledges the European Research Council (ERC) under the Horizon 2020 research and innovation program (ERC StG, Grant Agreement No. 803092). E. N. M. and M. G. acknowledge the MICINN and the European Union NextGenerationEU for financial support from the Ramon y Cajal program (Grants No. RYC2018-024736-I and No. RYC2021-034609-I). F. C. P. also acknowledges the MICINN for the FPU program (Grant No. FPU17/01587). F. R. M. acknowledges the MICINN for financial support (Grant No. PID2021-123163OB-I00). This work was also supported by the Spanish Unidad de Excelencia “María de Maeztu” (Grant No. CEX2019-000919-M) and is part of the Advanced Materials program supported by MICINN with funding from European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat Valenciana. D. S. and A.C. acknowledge Generalitat Valenciana for financial support (from the CIDEGENT program Grant No. CIDEGENT/2021/052 and PROMETEO2020-016 respectively) and computational resources at University of Pisa.

Electron-spin resonance carried out with scanning tunneling microscopes (ESR-STM) is a recently developed experimental technique that is attracting enormous interest on account of its potential to carry out single-spin on-surface resonance with subatomic resolution. Here we carry out a theoretical study of the role of tip-adatom interactions and provide guidelines for choosing the experimental parameters in order to optimize spin resonance measurements. We consider the case of the Fe adatom on a MgO surface and its interaction with the spin-polarized STM tip. We address three problems: first, how to optimize the tip-sample distance to cancel the effective magnetic field created by the tip on the surface spin, in order to carry out proper magnetic field sensing. Second, how to reduce the voltage dependence of the surface-spin resonant frequency, in order to minimize tip-induced decoherence due to voltage noise. Third, we propose an experimental protocol to infer the detuning angle between the applied field and the tip magnetization, which plays a crucial role in the modeling of the experimental results., 10 pages, 5 Figures

Spin-orbit coupling gives rise to a range of spin-charge interconversion phenomena in non-magnetic systems where certain spatial symmetries are reduced or absent. Chirality-induced spin selectivity (CISS), a term that generically refers to a spin-dependent electron transfer in non-magnetic chiral systems, is one such case, appearing in a variety of seemingly unrelated situations ranging from inorganic materials to molecular devices. In particular, the origin of CISS in molecular junctions is a matter of an intense current debate. Here we derive a set of geometrical conditions for this effect to appear, hinting at the fundamental role of symmetries beyond otherwise relevant quantitative issues. Our approach, which draws on the use of point-group symmetries within the scattering formalism for transport, shows that electrode symmetries are as important as those of the molecule when it comes to the emergence of a spin-polarization and, by extension, to the possible appearance of CISS. It turns out that standalone metallic nanocontacts can exhibit spin-polarization when relative rotations which reduce the symmetry are introduced. As a corollary, molecular junctions with $\textbf{achiral}$ molecules can also exhibit spin-polarization along the direction of transport, provided that the whole junction is chiral in a specific way. This formalism also allows the prediction of qualitative changes of the spin-polarization upon substitution of a chiral molecule in the junction with its enantiomeric partner. Quantum transport calculations based on density functional theory corroborate all of our predictions and provide further quantitative insight within the single-particle framework., 34 pages, 4 figures, 1 table

Low-temperature scanning tunneling microscopy is used here to study the dynamic bonding of gold atoms on surfaces under low coordination conditions. In the experiments, using an atomically sharp gold tip, a gold adatom is deposited onto a gold surface with atomic precision either on the first hollow site near a step edge or far away from it. Classical molecular dynamics simulations at 4.2 K and density-functional theory calculations serve to elucidate the difference in the bonding behavior between these two different placements, while also providing information on the crystalline classification of the STM tips based on their experimental performance. This work was supported by the Generalitat Valenciana through Grants No. CDEIGENT/2018/028, No. PROMETEO/2017/139, and No. PROMETEO/2021/017. The authors also acknowledge financial support from Spanish MICIN through Grant No. PID2019-109539 GB-C43, the María de Maeztu Program for Units of Excellence in R&D (Grant No. CEX2018-000805-M), the Comunidad Autónoma de Madrid through the Nanomag COST-CM Program (Grant No. S2018/NMT-4321). The theoretical modeling was performed on the high-performance computing facilities of the University of South Africa and the University of Alicante. Netherlands Organization for Scientific Research (NWO/OCW) supported the experiments.

We study the emergence of magnetism and its interplay with structural properties in a two-dimensional molecular crystal of cyclacenes, using density functional theory (DFT). Isolated cyclacenes with an even number of fused benzenes host two unpaired electrons in two topological protected zero modes, at the top and bottom carbon rings that form the molecule. We show that, in the gas phase, electron repulsion promotes an open-shell singlet with strong intramolecular antiferromagnetic exchange. We consider a closed packing triangular lattice crystal phase and we find a strong dependence of the band structure and magnetic interactions on the rotation angle of the cyclacenes with respect to the crystal lattice vectors. The orientational ground state maximizes the intermolecular hybridization, yet local moments survive. Intermolecular exchange is computed to be antiferromagnetic, and DFT predicts a broken symmetry 120∘ spin phase reflecting the frustration of the intermolecular spin coupling. Thus, the cyclacene crystal realizes a bilayer of two antiferromagnetically coupled S = 1/2 triangular lattices. Our results provide a bottom-up route towards carbon based strongly correlated platforms in two dimensions. We acknowledge funding support from Ministry of Science and Innovation of Spain (Grants No. PID2019-106114GB-I00 and No. PID2019-109539GB), Generalitat Valenciana and Fondo Social Europeo (Grant No. ACIF/2018/175), Generalitat Valenciana (Grant No. Prometeo2017/139), and FEDER/Junta de Andalucía Consejería de Transformación Económica, Industria, Conocimiento y Universidades, Grant No. PY18-4834.

The Haldane phase for antiferromagnetic spin-1 chains is a celebrated topological state of matter, featuring gapped excitations and fractional spin-1/2 edge states. Here, we provide numerical evidence that this phase can be realized with a Hubbard model at half filling, where each $s=1$ spin is stored in a four-site fermionic structure. We find that the noninteracting limit of our proposed model describes a one-dimensional topological insulator, and we conjecture it to be adiabatically connected to the Haldane phase. Our work suggests a route to build spin-1 networks using Hubbard model quantum simulators., Revised version, including Supplemental Material

Paramagnons are the collective modes that govern the spin response of nearly magnetic conductors. In some cases they mediate electron pairing leading to superconductivity. This scenario may occur in 2H-NbSe$_2$ monolayers, that feature spin-valley coupling on account of spin-orbit interactions and their lack of inversion symmetry. Here we explore spin anisotropy of paramagnons both for non-centrosymmetric Kane-Mele-Hubbard models for 2H-NbSe$_2$ monolayers described with a DFT-derived tight-binding model. In the infinite wavelength limit we find spatially uniform paramagnons with energies around $1$~meV that feature a colossal off-plane uniaxial magnetic anisotropy, with quenched transversal spin response. At finite wave vectors, longitudinal and transverse channels reverse roles: XY fluctuations dominate within a significant portion of the Brillouin zone. Our results show that 2H-NbSe$_2$ is close to a Coulomb-driven in-plane (XY) spin density wave instability., Comment: 10 pages (6 main text, 4 supplementary material), 10 figures (4 in the main text, 6 in the SM)

Detection is most often the main impediment to reduce the number of spins in paramagnetic resonance experiments. Here we propose a new route to carry out electrically-detected spin resonance of an individual spin, placed at the edge of a quantum spin Hall insulator (QSHI). The edges of a QSHI host a one dimensional electron gas with perfect spin-momentum locking. Therefore, the spin relaxation induced by emission of an electron-hole pair at the edge state of the QSHI can generate current. Here we demonstrate that driving the system with an $AC$ signal, a nonequilibrium occupation can be induced in the absence of applied bias voltage, resulting in a $DC$ measurable current. We compute the $DC$ current as a function of the Rabi frequency $\Omega$, the spin relaxation and decoherence times, $T_1$ and we discuss the feasibility of this experiment with state-of-the-art instrumentation., Comment: 5 pages, 1 figure

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by J. Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level., Comment: 4 pages

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect, solitons in one-dimensional conducting polymers and Majorana states in topological superconductors. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk and, remarkably, S = 1/2 edge states at the chain termini, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order. Here, we use on-surface synthesis to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunneling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated quantum spin liquid phases in purely organic materials, with the potential for the realization of measurement-based quantum computation., 23 pages, 4 main figures and 7 extended data figures; supplementary information containing additional data is included

We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter, i.e. cyclic oligoacene or oligophenacene molecules, and disclosing how adding layers and/or end-caps (i.e. hemifullerenes) can modify their (poly)radicaloid nature. We mostly used tight-binding and finite-temperature density-based methods, the former providing a simple but intuitive picture about their electronic structure, and the latter dealing effectively with strong correlation effects by relying on a fractional occupation number weighted electron density (ρFOD), with additional RAS-SF calculations backing up the latter results. We also explore how minor structural modifications of nanotube end-caps might influence the results, showing that topology, together with the chemical nature of the systems, is pivotal for the understanding of the electronic properties of these and other related systems. A. J. P. J. and J. C. S. G acknowledge the project CTQ2014-55073-P from the Spanish Government (MINECO/FEDER) and the project AICO/2018/175 from the Regional Government (GVA/FSE). J. F. R. acknowledges the projects MAT2016-78625 from the Spanish Government (MINECO/FEDER) and projects No. PTDC/FIS-NAN/4662/2014 and No. PTDC/FIS-NAN/3668/2014 from the Portuguese Government (Fundaçao para a Ciencia e Tecnologia). D. C. is thankful to projects IT588-13 (Eusko Jaurlaritza) and CTQ2016-80955 from the Spanish Government (MINECO/FEDER). M. E. S.-S. acknowledges CONACyT-México for a PhD fellowship (ref. 591700). R. O. C. acknowledges “Generalitat Valenciana” and “Fondo Social Europeo” for a PhD fellowship (ACIF/2018/198).

Under the challenge of growing a single bilayer of Bi oriented in the (111) crystallographic direction over amorphous substrates, we have studied different thicknesses of Bi thermally evaporated onto silicon oxide in order to shed light on the dominant atomic structures and their oxidation. We have employed atomic force microscope, X-ray diffraction, and scanning electron microscope approaches to demonstrate that Bi is crystalline and oriented in the (111) direction for thicknesses over 20 nm. Surprisingly, Raman spectroscopy indicates that the rhombohedral structure is preserved even for ultra-thin layers of Bi, down to $\sim 5$ nm. Moreover, the signals also reveal that bismuth films exposed to ambient conditions do not suffer major surface oxidation., 6 pages,4 figures

We study spin excitations and Kondo effect in open-shell nanographenes, motivated by recent scanning tunneling inelastic spectroscopy experiments. Specifically, we consider three systems, the triangulene, the extended triangulene with rocket shape, both with an $S=1$ ground state, and a triangulene dimer with $S=0$ on account of intermolecular exchange. We focus on the consequences of hybridization of the nanographene zero-modes with a conducting substrate on the $dI/dV$ lineshapes associated with spin excitations. The partially filled nanographene zero-modes coupled to the conduction electrons in the substrate constitute multi-orbital Anderson impurity models that we solve in the one-crossing approximation which treats the coupling to the substrate to infinite order. We find that the coupling to the substrate leads to (i) renormalization of the spin flip excitation energies of the bare molecule, (ii) broadening of the spectral features and (iii) the emergence of zero bias Kondo peaks for the $S=1$ ground states. The calculated substrate induced shift of the spin excitation energies is found to be significantly larger than their broadening, which implies that this effect has to be considered when comparing experimental results and theory., Comment: 9 pages, 4 figures; replaced with revised version, accepted in Phys. Rev. B

For the past three decades, nanoscience has widely affected many areas in physics, chemistry, and engineering, and has led to numerous fundamental discoveries as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds a burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this manuscript according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system such as charge, spin, mechanical motion, and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations., Comment: 34 pages, 6 figures, 2 boxes

The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically-motivated ans\"{a}tze on quantum hardware is therefore important to achieve quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller Wave Function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the $U = 0$ limit of the model is prepared. In the second, the non-unitary Gutzwiller projection that selectively removes states with doubly-occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the $|0\rangle$ state confirms the projection was made. Due to its non-deterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength $U/t$. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed., Comment: 5 pages + Supplemental Material

We study the electronic properties of the heterobilayer of vanadium and iron oxychlorides, VOCl and FeOCl, two layered air stable van der Waals insulating oxides with different types of antiferromagnetic order in bulk: VOCl monolayers are ferromagnetic (FM) whereas the FeOCl monolayers are antiferromagnetic (AF). We use density functional theory (DFT) calculations, with Hubbard correction that is found to be needed to describe correctly the insulating nature of these compounds. We compute the magnetic anisotropy and propose a spin model Hamiltonian. Our calculations show that interlayer coupling in weak and ferromagnetic so that magnetic order of the monolayers is preserved in the heterobilayers providing thereby a van der Waals heterostructure that combines two monolayers with different magnetic order. Interlayer exchange should lead both to exchange bias and to the emergence of hybrid collective modes that that combine FM and AF magnons. The energy band of the heterobilayer show a type II band alignment, and feature spin-splitting of the states of the AF layer due to the breaking of the inversion symmetry., Comment: 6 pages, 3 figures

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 as 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 nanometers up to 1 micron. The method permits to erase and rebuild the patterns 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 zero and one dimensional structures. In graphene quantum dots, perfectly defined energy band gaps up to 0.8 eV are found, that scale as the inverse of the dots linear dimension, as expected for massless Dirac fermions, Main Manuscript and Supporting Information

Nonreciprocal spin waves have a chiral asymmetry so that their energy is different for two opposite wave vectors. They are found in atomically thin ferromagnetic overlayers with in-plane magnetization and are linked to the antisymmetric Dzyaloshinskii-Moriya surface exchange. We use an itinerant fermion theory based on first-principles calculations to predict that nonreciprocal magnons can occur in Fe3GeTe2, the first stand-alone metallic two-dimensional crystal with out-of-plane magnetization. We find that both the energy and lifetime of magnons are nonreciprocal, and we predict that acoustic magnons can have lifetimes up to hundreds of picoseconds, orders of magnitude larger than in other conducting magnets., N.M.R.P. acknowledges support from the European Commission through the project Graphene-Driven Revolutions in ICT and Beyond (Ref. No. 881603 -Core 3), and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2013, COMPETE2020, PORTUGAL2020, FEDER, and the Portuguese Foundation for Science and Technology (FCT) through Projects No. PTDC/FISNAN/3668/2013 and No. POCI-01-0145-FEDER-028114. J.F.-R. acknowledges financial support from FCT for Project No. UTAP-EXPL/NTec/0046/2017, as well as Generalitat Valenciana funding Prometeo2017/139 and MINECO-Spain (Grant No. MAT2016-78625-C2). A.T.C. acknowledges the use of computer resources at MareNostrum and technical support provided by the Barcelona Supercomputing Center (RES-FI-2019-2-0034, RES-FI-2019-3-0019).

Nanographenes with zigzag edges are predicted to manifest non-trivial pi-magnetism resulting from the interplay of hybridization of localized frontier states and Coulomb repulsion between valence electrons. This provides a chemically tunable platform to explore quantum magnetism at the nanoscale and opens avenues toward organic spintronics. The magnetic stability in nanographenes is thus far limited by the weak magnetic exchange coupling which remains below the room temperature thermal energy. Here, we report the synthesis of large rhombus-shaped nanographenes with zigzag periphery on gold and copper surfaces. Single-molecule scanning probe measurements unveil an emergent magnetic spin-singlet ground state with increasing nanographene size. The magnetic exchange coupling in the largest nanographene, determined by inelastic electron tunneling spectroscopy, exceeds 100 meV or 1160 K, which outclasses most inorganic nanomaterials and remarkably survives on a metal electrode., 4 figures plus supplementary information

Triangular zigzag nanographenes, such as triangulene and its π‐extended homologues, have received widespread attention as organic nanomagnets for molecular spintronics, and may serve as building blocks for high‐spin networks with long‐range magnetic order, which are of immense fundamental and technological relevance. As a first step towards these lines, we present the on‐surface synthesis and a proof‐of‐principle experimental study of magnetism in covalently bonded triangulene dimers. On‐surface reactions of rationally designed precursor molecules on Au(111) lead to the selective formation of triangulene dimers in which the triangulene units are either directly connected through their minority sublattice atoms, or are separated via a 1,4‐phenylene spacer. The chemical structures of the dimers have been characterized by bond‐resolved scanning tunneling microscopy. Scanning tunneling spectroscopy and inelastic electron tunneling spectroscopy measurements reveal collective singlet–triplet spin excitations in the dimers, demonstrating efficient intertriangulene magnetic coupling., The on‐surface synthesis of covalently bonded triangulene dimers with or without a 1,4‐phenylene spacer was achieved on Au(111). Scanning tunneling spectroscopy measurements revealed collective magnetism in the dimers in the form of singlet–triplet spin excitations, demonstrating efficient and tunable intertriangulene magnetic coupling.

We address the coexistence of massless and massive topological edge states at the interface between two materials with different topological phases. We modify the well-known Bernevig-Hughes-Zhang model to introduce a smooth function describing the band inversion and the band bending due to electrostatic effects between the bulk of the quantum well and the vacuum. Within this minimal model we identify distinct parameter sets that can lead to the coexistence of the two types of edge states and that determine their number and characteristics. We propose several experimental setups that could demonstrate their presence in two-dimensional topological systems, as well as ways to regulate or tune the contribution of the massive edge states to the conductance of associated electronic devices. Our results suggest that such states may also be present in novel two-dimensional van der Waals topological materials., The work of T.L.v.d.B. and D.B. was supported by the Spanish Ministerio de Economía y Competitividad (MINECO) through Project No. FIS2014-55987-P, by Spanish Ministerio de Ciecia, Innovation y Universidades (MICINN) through Project No. FIS2017-82804-P, and by the Transnational Common Laboratory Quantum-ChemPhys. M.R.C. acknowledges funding from the Spanish Government through Project No. MAT2017-88377-C2-2-R (AEI/FEDER UE) and the Generalitat Valenciana through Grant No. Cidegent2018004.

Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate the Berry phase and use it to classify the topological order of both single-particle and interacting models, highlighting the differences between the two. This algorithm is immediately extensible to any interacting topological system. Our results evidence the potential of near-term quantum hardware for the topological classification of quantum matter., Comment: Main text: 4 pages, 3 figures; Supplemental material: 9 pages, 9 figures

The emergence of local moments in graphene zigzag edges, grain boundaries, vacancies and sp3 defects has been widely studied theoretically. However, conclusive experimental evidence is scarce. Recent progress in on-surface synthesis has made it possible to create nanographenes, such as triangulenes, with local moments in their ground states, and to probe them using scanning tunneling microscope (STM) spectroscopy. Here we review the application of the theory of sequential and cotunneling transport to relate the dI/dV spectra with the spin properties of nanographenes probed by STM. This approach permits us to connect the dI/dV with the many-body energies and wavefunctions of the graphene nanostructures. We apply this method describing the electronic states of the nanographenes by means of exact diagonalization of the Hubbard model within a restricted Active Space. This permits us to provide a proper quantum description of the emergence of local moments in graphene and its interplay with transport. We discuss the results of this theory in the case of diradical nanographenes, such as triangulene, rectangular ribbons and the Clar’s goblet, that have been recently studied experimentally by means of STM spectroscopy. This approach permits us to calculate both the dI/dV spectra, that yields excitation energies, as well as the atomically resolved conductivity maps, that provide information on the wavefunctions of the collective spin modes. We acknowledge financial support from Ministry of Science and Innovation of Spain (grant numbers PID2019-106114GB-I00 and PID2019- 109539GB), from MINECO-Spain (Grant No. MAT2016-78625-C2) and from the Portuguese Fundação para a Ciência e a Tecnologia (FCT) for the projects P2020-PTDC/FIS-NAN/4662/2014, P2020-PTDC/FIS-NAN/3668/2014 and UTAPEXPL/NTec/0046/2017 projects. JFR acknowledges Generalitat Valenciana funding (Prometeo2017/139). R. O. acknowledge ACIF/2018/175 (Generalitat Valenciana and Fondo Social Europeo).

In topological systems, a modulation in the gap onset near interfaces can lead to the appearance of massive edge states, as were first described by Volkov and Pankratov. In this work, we study graphene nanoribbons in the presence of intrinsic spin-orbit coupling smoothly modulated near the system edges. We show that this space modulation leads to the appearance of Volkov-Pankratov states, in addition to the topologically protected ones. We obtain this result by means of two complementary methods, one based on the effective low-energy Dirac equation description and the other on a fully numerical tight-binding approach, finding excellent agreement between the two. We then show how transport measurements might reveal the presence of Volkov-Pankratov states, and discuss possible graphene-like structures in which such states might be observed., Comment: 12 pages, 8 figures

The discovery of ferromagnetic order in monolayer 2D crystals has opened a new venue in the field of two dimensional (2D) materials. 2D magnets are not only interesting on their own, but their integration in van der Waals heterostructures allows for the observation of new and exotic effects in the ultrathin limit. The family of Chromium trihalides, CrI$_3$, CrBr$_3$ and CrCl$_3$, is, so far, the most studied among magnetic 2D crystals. In this mini-review, we provide a perspective of the state of the art of the theoretical understanding of magnetic 2D trihalides, most of which will also be relevant for other 2D magnets, such as vanadium trihalides. We discuss both the well-established facts, such as the origin of the magnetic moment and magnetic anisotropy and address as well open issues such as the nature of the anisotropic spin couplings and the magnitude of the magnon gap. Recent theoretical predictions on Moir\' e magnets and magnetic skyrmions are also discussed. Finally, we give some prospects about the future interest of these materials and possible device applications., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright \c{opyright} American Chemical Society after peer review

Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number $\pm 1/2$, that entails both a quantized dc Hall response and a subgap full-quarter Kerr rotation. The observation of these effects in 2D massive Dirac materials such as gapped graphene, hexagonal boron nitride or transition metal dichalcogenides (TMDs) is obscured by the fact that Dirac cones come in pairs with opposite sign Berry curvatures, leading to a vanishing Chern number. Here, we show that the presence of spin-orbit interactions, combined with an exchange spin splitting induced either by diluted magnetic impurities or by proximity to a ferromagnetic insulator, gives origin to a net magneto-optical Kerr effect in such systems. We focus on the case of TMD monolayers and study the dependence of Kerr rotation on frequency and exchange spin splitting. The role of the substrate is included in the theory and found to critically affect the results. Our calculations indicate that state-of-the-art magneto-optical Kerr spectroscopy can detect a single magnetic impurity in diluted magnetic TMDs., 8 pages, 3 figures

Efficient and versatile spin-to-charge current conversion is crucial for the development of spintronic applications, which strongly rely on the ability to electrically generate and detect spin currents. In this context, the spin Hall effect has been widely studied in heavy metals with strong spin-orbit coupling. While the high crystal symmetry in these materials limits the conversion to the orthogonal configuration, unusual configurations are expected in low symmetry transition metal dichalcogenide semimetals, which could add flexibility to the electrical injection and detection of pure spin currents. Here, we report the observation of spin-to-charge conversion in MoTe$_2$ flakes, which are stacked in graphene lateral spin valves. We detect two distinct contributions arising from the conversion of two different spin orientations. In addition to the conventional conversion where the spin polarization is orthogonal to the charge current, we also detect a conversion where the spin polarization and the charge current are parallel. Both contributions, which could arise either from bulk spin Hall effect or surface Edelstein effect, show large efficiencies comparable to the best spin Hall metals and topological insulators. Our finding enables the simultaneous conversion of spin currents with any in-plane spin polarization in one single experimental configuration., 14 pages, 4 figures, and Supporting Information

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. Fil: Yang, Kai. Ibm Research; Estados Unidos Fil: Paul, William. Ibm Research; Estados Unidos Fil: Natterer, Fabian D.. Ibm Research; Estados Unidos. Universitat Zurich; Suiza Fil: Lado, Jose Luis. Eidgenössische Technische Hochschule; Suiza Fil: Bae, Yujeong. Ewha Womans University; Corea del Sur. Ibm Research; Estados Unidos Fil: Willke, Philip. Ibm Research; Estados Unidos. Institute for Basic Science; Corea del Sur Fil: Choi, Taeyoung. Institute for Basic Science; Corea del Sur. Ewha Womans University; Corea del Sur Fil: Ferrón, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina Fil: Fernandez Rossier, Joaquín. Universidad de Alicante; España. International Iberian Nanotechnology Laboratory; Portugal Fil: Heinrich, Andreas. Institute for Basic Science; Corea del Sur. Ewha Womans University; Corea del Sur Fil: Lutz, Christopher. Ibm Research; Estados Unidos

We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change of sign in the group velocity. Second, a surface plasmon-magnon polariton formed as a linear superposition of graphene surface plasmon and the antiferromagnetic bare magnon. This polariton has a dispersion with two branches, formed by the anticrossing between the dispersive surface plasmon and the magnon. We discuss the potential these new modes have for combining photons, magnons, and plasmons to reach new functionalities., Comment: 12 pages, 4 figures

We propose a method to realize a broad class of tunable fermionic Hamiltonians in graphene bilayer. For that matter, we consider graphene bilayer functionalized with sp3 defects that induce zero-energy resonances hosting an individual electron each. The application of an off-plane electric field opens up a gap, so that the zero-energy resonance becomes an in-gap bound state whose confinement scales inversely with the gap. Controlling both the distance among the defects and the applied electric field, we can define fermionic models, even lattices, whose hoppings and Coulomb interactions can be tuned. We consider in detail the case of triangular and honeycomb artificial lattices and we show how, for a given arrangement of the sp3 centers, these lattices can undergo an electrically controlled transition between the weak and strong coupling regimes. We acknowledge Grant No. P2020-PTDC/FIS-NAN/3668/2014, financial support Generalitat Valenciana funding Prometeo2017/139 and MINECO Spain (Grant No. MAT2016-78625-C2).

We study the optical properties of semiconducting transition metal dichalcogenide monolayers under the influence of strong out-of-plane magnetic fields, using the effective massive Dirac model. We pay attention to the role of spin-orbit-coupling effects, doping level, and electron-electron interactions, treated at the Hartree-Fock level. We find that optically induced valley and spin imbalance, commonly attained with circularly polarized light, can also be obtained with linearly polarized light in the doped regime. Additionally, we explore an exchange-driven mechanism to enhance the spin-orbit splitting of the conduction band, in n -doped systems, controlling both the carrier density and the intensity of the applied magnetic field., We thank A. J. Chaves and L. Brey for fruitful discussions. G.C. thanks Departamento de Fisica Aplicada at Universidad de Alicante for their hospitality. G.C. and J.F.-R. acknowledge financial support from Fundacao para a Ciencia e a Tecnologia (FCT) for the Grant No. P2020-PTDC/FIS-NAN/4662/2014. J.H. acknowledges financial support by the QUSCOPE Center, sponsored by the Villum foundation. J.F.-R. acknowledges financial support from FCT for the Grants No. P2020-PTDC/FIS-NAN/3668/2014 and No. UTAP-EXPL/NTec/0046/2017, as well as Generalitat Valenciana funding Prometeo2017/139 and MINECO-Spain (Grant No. MAT2016-78625-C2). N.M.R.P. acknowledges financial support from the European Commission through the project "Graphene-Driven Revolutions in ICT and Beyond" (Ref. No. 785219) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing Grant No. UID/FIS/04650/2013. Additionally, N.M.R.P. acknowledges COMPETE2020, PORTUGAL2020, FEDER and the Portuguese Foundation for Science and Technology (FCT) for the Grants No. PTDC/FIS-NAN/3668/2013 and No. POCI-01-0145-FEDER-028114., info:eu-repo/semantics/publishedVersion

Magnons dominate the magnetic response of the recently discovered insulating ferromagnetic two dimensional crystals such as CrI$_3$. Because of the arrangement of the Cr spins in a honeycomb lattice, magnons in CrI$_3$ bear a strong resemblance with electronic quasiparticles in graphene. Neutron scattering experiments carried out in bulk CrI$_3$ show the existence of a gap at the Dirac points, that has been conjectured to have a topological nature. Here we propose a theory for magnons in ferromagnetic CrI$_3$ monolayers based on an itinerant fermion picture, with a Hamiltonian derived from first principles. We obtain the magnon dispersion for 2D CrI$_3$ with a gap at the Dirac points with the same Berry curvature in both valleys. For CrI$_3$ ribbons, we find chiral in-gap edge states. Analysis of the magnon wave functions in momentum space further confirms their topological nature. Importantly, our approach does not require to define a spin Hamiltonian, and can be applied to both insulating and conducting 2D materials with any type of magnetic order., Includes supplementary material

A scanning tunneling microscope is used to explore the evolution of electron and Cooper-pair transport across single Mn-phthalocyanine molecules adsorbed on Pb(111) from tunneling to contact ranges. Normal-metal as well as superconducting tips give rise to a gradual transition of the Bardeen-Cooper-Schrieffer energy gap in the tunneling range into a zero-energy resonance close to and at contact. Supporting transport calculations show that in the normal-metal–superconductor junctions this resonance reflects the merging of in-gap Yu-Shiba-Rusinov states as well as the onset of Andreev reflection. For the superconductor-superconductor contacts, the zero-energy resonance is rationalized in terms of a finite Josephson current that is carried by phase-dependent Andreev and Yu-Shiba-Rusinov levels. Financial support by the Deutsche Forschungsgemeinschaft through Grant No. KR 2912/10-1, the FCT (Projects No. PTDC/FIS-NAN/4662/2014 and No. P2020-PTDC/FISNAN/3668/2014), and the MINECO-Spain (MAT2016-78625-C2) is acknowledged. J.L.L. acknowledges financial support from the ETH Zurich Postdoctoral Fellowship program.

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 CrI₃ as a function of temperature and applied magnetic field.We electrically detect the magnetic ground state and interlayer coupling and observe a fieldinducedmetamagnetic transition.The metamagnetic transition results in magnetoresistances of 95, 300, and 550% for bilayer, trilayer, and tetralayer CrI₃ barriers, respectively.We further measure inelastic tunneling spectra for our junctions, unveiling a rich spectrum consistent with collective magnetic excitations (magnons) in CrI₃., Gordon and Betty Moore Foundation (Grant GBMF4541)

We propose spin valves where a 2D non-magnetic conductor is intercalated between two ferromagnetic insulating layers. In this setup, the relative orientation of the magnetizations of the insulating layers can have a strong impact on the in-plane conductivity of the 2D conductor. We first show this for a graphene bilayer, described with a tight-binding model, placed between two ferromagnetic insulators. In the anti-parallel configuration, a band gap opens at the Dirac point, whereas in the parallel configuration, the graphene bilayer remains conducting. We then compute the electronic structure of graphene bilayer placed between two monolayers of the ferromagnetic insulator CrI$_3$, using density functional theory. Consistent with the model, we find that a gap opens at the Dirac point only in the antiparallel configuration., 5 pages, 4 figures

Topological invariants allow to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wavefunctions under twisted boundary conditions. However, those procedures do not allow to calculate a topological invariant by evaluating the system locally, and thus require information about the wavefunctions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a 1-D topological superconductor and a 2-D quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the Kernel Polynomial Method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system., Comment: 9 pages, 6 figures

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 tunnelling microscopy (STM). The observed suppression of the excitation signal, which occurs for Co atoms assembled into chain on a Cu$_2$N substrate, indicates a structural transition affecting the d$_z$$^2$ orbital, effectively cutting off the STM tip from the spin-flip cotunnelling path., Comment: 4 figures plus 4 supplementary figures

We propose a new universal mechanism that makes it possible to drive an individual atomic spin using a spin polarized scanning tunnel microscope (STM) with an oscillating electric signal. We show that the combination of the distance dependent exchange with the magnetic tip and the electrically driven mechanical oscillation of the surface spins permits to control their quantum state. Based on a combination of density functional theory and multiplet calculations, we show that the proposed mechanism is essential to account for the recently observed electrically driven paramagnetic spin resonance (ESR) of an individual Fe atom on a MgO/Ag(100) surface. Our findings set the foundation to deploy the ESR-STM quantum sensing technique to a much broader class of systems., Comment: 7 pages, 3 figures

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. Fil: Yang, Kai. Ibm Research; Estados Unidos Fil: Bae, Yujeong. Ibm Research; Estados Unidos. Center for Quantum Nanoscience, Institute for Basic Science (IBS); Corea del Sur. Ewha Womans University; Corea del Sur Fil: Paul, William. Ibm Research; Estados Unidos Fil: Natterer, Fabian D.. Ibm Research; Estados Unidos. Ecole Polytechnique Federale de Lausanne; Suiza Fil: Willke, Philip. Ibm Research; Estados Unidos. Center for Quantum Nanoscience, Institute for Basic Science (IBS); Corea del Sur. Ewha Womans University; Corea del Sur Fil: Lado, Jose Luis. International Iberian Nanotechnology Laboratory; Portugal Fil: Ferrón, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina Fil: Choi, Taeyoung. Center for Quantum Nanoscience, Institute for Basic Science (IBS); Corea del Sur. Ewha Womans University; Corea del Sur Fil: Fernandez Rossier, Joaquín. International Iberian Nanotechnology Laboratory; Portugal. Universidad de Alicante; España Fil: Heinrich, Andreas J.. Center for Quantum Nanoscience, Institute for Basic Science (IBS); Corea del Sur. Ewha Womans University; Corea del Sur Fil: Lutz, Christopher P.. Ibm Research; Estados Unidos

Our analysis of the contact formation processes undergone by Au, Ag and Cu nanojunctions, reveals that the distance at which the two closest atoms on a pair of opposing electrodes jump into contact is, on average, two times longer for Au than either Ag or Cu. This suggests the existence of a longer range interaction between those two atoms in the case of Au, a result of the significant relativistic energy contributions to the electronic structure of this metal, as confirmed by ab initio calculations. Once in the contact regime, the differences between Au, Ag and Cu are subtle, and the conductance of single-atom contacts for metals of similar chemical valence is mostly determined by geometry and coordination., 4 pages, 4 figures

We study a graphene Hall probe located on top of a magnetic surface as a detector of skyrmions, using as working principle the anomalous Hall effect produced by the exchange interaction of the graphene electrons with the non-coplanar magnetization of the skyrmion. We study the magnitude of the effect as a function of the exchange interaction, skyrmion size and device dimensions. Our calculations for multiterminal graphene nanodevices, working in the ballistic regime, indicate that for realistic exchange interactions a single skyrmion would give Hall voltages well within reach of the experimental state of the art. The proposed device could act as an electrical transducer that marks the presence of a single skyrmion in a nanoscale region, paving the way towards the integration of skyrmion-based spintronics and graphene electronics., 8 pages, 6 figures

We propose a mechanism to drive singlet-triplet spin transitions electrically in a wide class of graphene nanostructures that present pairs of in-gap zero modes, localized at opposite sublattices. Examples are rectangular nanographenes with short zigzag edges, armchair ribbon heterojunctions with topological in-gap states, and graphene islands with sp3 functionalization. The interplay between the hybridization of zero modes and the Coulomb repulsion leads to symmetric exchange interaction that favors a singlet ground state. Application of an off-plane electric field to the graphene nanostructure generates an additional Rashba spin-orbit coupling, which results in antisymmetric exchange interaction that mixes S=0 and S=1 manifolds. We show that modulation in time of either the off-plane electric field or the applied magnetic field permits performing electrically driven spin resonance in a system with very long spin-relaxation times. This work has been financially supported, in part, by FEDER funds. We acknowledge financial support from Marie-Curie-ITN Grant No. 607904-SPINOGRAPH, FCT, under the Projects No. PTDC/FIS-NAN/4662/2014 and No. PTDC/FISNAN/3668/2014, and MINECO-Spain (Grant No. MAT2016-78625-C2).

We review the problem of spin decoherence of magnetic atoms deposited on a surface. Recent breakthroughs in scanning tunnelling microscopy (STM) make it possible to probe the spin dynamics of individual atoms, either isolated or integrated in nanoengineered spin structures. Transport pump and probe techniques with spin polarized tips permit measuring the spin relaxation time T, while novel demonstration of electrically driven STM single spin resonance has provided a direct measurement of the spin coherence time T of an individual magnetic adatom. Here we address the problem of spin decoherence from the theoretical point of view. First we provide a short general overview of decoherence in open quantum systems and we discuss with some detail ambiguities that arise in the case of degenerate spectra, relevant for magnetic atoms. Second, we address the physical mechanisms that allows probing the spin coherence of magnetic atoms on surfaces. Third, we discuss the main spin decoherence mechanisms at work on a surface, most notably, Kondo interaction, but also spin–phonon coupling and dephasing by Johnson noise. Finally, we briefly discuss the implications in the broader context of quantum technologies., JFR acknowledges financial supported by MEC-Spain (FIS2013-47328-C2-2-P) and Generalitat Valenciana (ACOMP/2010/070), Prometeo. This work is funded by ERDF funds through the Portuguese Operational Program for Competitiveness and Internationalization COMPETE 2020, and National Funds through FCT – The Portuguese Foundation for Science and Technology, under the project “PTDC/FIS-NAN/4662/2014” (016656). FD acknowledges funding by the Ministerio de Economía y Competitividad (MINECO, Spain), with grant MAT2015-66888-C3-2-R., and Gobierno Vasco by grant IT986-16. We thank J. Sinova for financial support in the SPICE workshop on “Magnetic adatoms as building blocks for quantum magnetism”.

Two-dimensional semiconducting materials are particularly appealing for many applications. Although theory predicts a large number of two-dimensional 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 PbI2 by precipitation from a solution in water. We thoroughly characterize the produced thin flakes with different techniques ranging from optical and Raman spectros-copy 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 PbI2 and study their optoelectronic properties., main text 20 pages + 10 figures, supporting information 16 pages + 17 figures

We report on the fabrication, transport measurements, and density functional theory (DFT) calculations of atomic-size contacts made of gadolinium (Gd). Gd is known to have local moments mainly associated with f electrons. These coexist with itinerant s and d bands that account for its metallic character. Here we explore whether and how the local moments influence electronic transport properties at the atomic scale. Using both scanning tunneling microscope and lithographic mechanically controllable break junction techniques under cryogenic conditions, we study the conductance of Gd when only few atoms form the junction between bulk electrodes made of the very same material. Thousands of measurements show that Gd has an average lowest conductance, attributed to single-atom contact, below 2e2h. Our DFT calculations for monostrand chains anticipate that the f bands are fully spin polarized and insulating and that the conduction may be dominated by s, p, and d bands. We also analyze the electronic transport for model nanocontacts using the nonequilibrium Green's function formalism in combination with DFT. We obtain an overall good agreement with the experimental results for zero bias and show that the contribution to the electronic transport from the f channels is negligible and that from the d channels is marginal. B.O., C.S., J.F.R., J.J.P., and C.U. acknowledge financial support by MEC-Spain (Grant No. FIS2013-47328-C2 and MAT2016-78625-C2) and the Generalitat Valenciana under Grant No. PROMETEO/2012/011. C.S. and J.J.P. acknowledge the EU structural funds and the Comunidad de Madrid under NANOFRONTMAG-CM program Grant No. S2013/MIT-2850. J.L.L. and J.F.R. acknowledge Marie Curie ITN SPINOGRAPH FP7 under REA Grant Agreement No. 607904-13. B.O. acknowledges financial support by MEC Spain (Grant No. FIS2010-21883-C02-01) under brief stays abroad scholarship.

The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of the tight-binding model, however not many experimental approaches exist that allow to tailor artificial crystal lattices using a bottom-up approach. The ability to engineer and study atomically crafted designer materials by scanning tunnelling microscopy and spectroscopy (STM/STS) helps to understand the emergence of material properties. Here, we use atom manipulation of individual vacancies in a chlorine monolayer on Cu(100) to construct one- and two-dimensional structures of various densities and sizes. Local STS measurements reveal the emergence of quasiparticle bands, evidenced by standing Bloch waves, with tuneable dispersion. The experimental data are understood in terms of a tight-binding model combined with an additional broadening term that allows an estimation of the coupling to the underlying substrate., 7 figures, 12 pages, main text and supplementary material

Scattering of electrons by localized spins is the ultimate process enabling detection and control of the magnetic state of a spin-doped material. At the molecular scale, scattering is mediated by the orbitals hosting the spin. Here we report the selective excitation of a molecular spin by tunneling through different molecular orbitals. Spatially resolved tunneling spectra on iron-porphyrins reveal that the inelastic spin excitation extends beyond the iron site, changing shape and symmetry along the molecule. Combining density functional theory simulations with a phenomenological scattering model, we show that the extension and lineshape of the inelastic signal are due to excitation pathways assisted by different frontier orbitals. By selecting the intramolecular site for electron injection, the relative weight of iron and pyrrole orbitals in the tunneling process is modified. Thus, the excitation mechanism, reflected by its spectral lineshape, depends on the degree of localization and energy alignment of the chosen molecular orbital., This work has been funded by the COST 15128 Molecular Spintronics project, by Marie Curie IF ARTE, by the Spanish Ministerio de Economía y Competitividad (MINECO) through the cooperative grant No. MAT2016-78293 and grant No. FIS2016-75862-P, and by the Basque Government (Dep. Industry, Grant PI-2015-1-42, Dep. Education, Grant PI-2016-1-27 and Grant IT-756-13), the EU project PAMS (610446), and the European Regional Development Fund (ERDF).

We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp3 covalent functionalizations. We describe graphene with the single-orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. To circumvent artifacts related to periodic unit cells, we use either huge simulation cells of up to 8×105 sites, or an embedding scheme that allows the modeling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment (m) in this system. First, in the noninteracting (U=0) zero-temperature (T=0) case, the m(B) is a continuous smooth curve with divergent susceptibility, different from the stepwise constant function found for single unpaired spins in a gapped system. Second, for U=0 and T>0, the linear susceptibility follows a power law ∝T−α with an exponent of α=0.77 different from the conventional Curie law. For U>0, in the mean-field approximation, the integrated moment is smaller than m=1μB, in contrast with results using periodic unit cells. These three results highlight the fact that the magnetic response of the local moment induced by sp3 functionalizations in graphene is different from that of local moments in gapped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which linear susceptibility can be defined at T=0. The authors acknowledge financial support by Marie-Curie-ITN 607904-SPINOGRAPH. J.F.-R. acknowledges financial supported by MEC-Spain (GrantsNo. FIS2013-47328-C2-2-P and No. MAT2016-78625-C2) and Generalitat Valenciana (Grant No. ACOMP/2010/070), Prometeo, by European Regional Development Fund (ERDF) funds through the Portuguese Operational Program for Competitiveness and Internationalization COMPETE 2020, and National Funds through FCT, under the Project No. PTDC/FIS-NAN/4662/2014 (016656) [Portuguese Foundation for Science and Technology]. This work has been financially supported in part by FEDER funds.

We consider spin relaxation of finite-size spin chains exchanged coupled with a one dimensional (1D) electron gas at the edge of a Quantum Spin Hall (QSH) insulator. Spin lifetimes can be enhanced due to two independent mechanisms. First, the suppression of spin-flip forward scattering inherent in the spin momentum locking of the QSH edges. Second, the reduction of spin-flip backward scattering due to destructive interference of the quasiparticle exchange, modulated by $k_F d$, where $d$ is the inter-spin distance and $k_F$ is the Fermi wavenumber of the electron gas. We show that the spin lifetime of the $S=1/2$ ground state of odd-numbered chains of antiferromagnetically (AFM) coupled $S=1/2$ spins can be increased more than 4 orders of magnitude by properly tuning the product $k_Fd$ and the spin size $N$, in strong contrast with the 1D case. Possible physical realizations together with some potential issues are also discussed., 11 pages, 3 figures