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Magnetic adatoms on s-wave superconductors induce bound states inside the superconducting gap, called Yu-Shiba-Rusinov states (YSR). The anisotropy of the Fermi surface determines the spatial extension of bound states in a quasi-two-dimensional superconductor. This is especially important in the diluted impurity limit since the orbital overlap determines the coupling of YSR states of neighboring atoms and the formation of the collective YSR system. Here, we build diluted arrays of Mn atoms with different dimensionalities on the surface of $\beta$-Bi$_2$Pd, and we measure the evolution of their YSR spectra with the structure. We detect the coupling as a split of YSR peaks in subgap spectra and find that the split size increases with the number of atoms. The orientation of the structures along different directions of the \bipd substrate modulates the split and particle-hole asymmetry of the YSR states due to the anisotropic character of the Fermi surface, captured by the Green function model. With the aid of the model, we found multiple YSR excitations in an extended 2D array of 25 Mn atoms, and we identified that their spatial distribution reflects a chiral LDOS., Comment: 10 pages, 5 figures

Graphene nanostructures are a promising platform for engineering electronic states with tailored magnetic and quantum properties. Synthesis strategies on metallic substrates have made it possible to manufacture atomically precise nanographenes with controlled size, shape and edge geometry. In these nanographenes, finite spin magnetic moment can arise as a result of many-body interactions in molecular orbitals with $\pi$-conjugated character and subject to strong spatial confinement, for example at the zig-zag edges. However, owing to the mixing of the molecular orbitals and metallic states from the catalysing substrate, most of their expected quantum phenomenology is severely hindered. The use of in-situ ultra-thin decoupling layers can impede nanographene-metal hybridization and facilitate the expression of predicted properties. Here we show that the edges of narrow chiral graphene nanoribbons (GNRs) over MgO monolayers on Ag(001) can host integer charge and spin-1/2 frontier states. The electron occupation varies with the GNR length, which alternates even or odd number of electrons, thus resulting correspondingly in a non-magnetic closed-shell state or an open-shell paramagnetic system. For the latter, we found the spectral fingerprint of a narrow Coulomb correlation gap. Charged states, up to 19 additional electrons, were identified by comparing mean-field Hubbard (MFH) simulations of the density of states with experimental maps of the discretized molecular orbitals acquired with a scanning tunnelling microscope (STM). In consideration of the length-dependent magnetic moment and the discrete nature of the electronic structure, we envisage that GNRs supported by thin insulating films can be used as tailor-made active elements in quantum sensing and quantum information processing.

Unimolecular current rectifiers are fundamental building blocks in organic electronics. Rectifying behavior has been identified in numerous organic systems due to electron-hole asymmetries of orbital levels interfaced by a metal electrode. As a consequence, the rectifying ratio (RR) determining the diode efficiency remains fixed for a chosen molecule-metal interface. Here, we present a mechanically tunable molecular diode exhibiting an exceptionally large rectification ratio (>10^5) and reversible direction. The molecular system comprises a 7-armchair graphene nanoribbon (GNR) doped with a single unit of substitutional diboron within its structure, synthesized with atomic precision on a gold substrate by on-surface synthesis. The diboron unit creates half-populated in-gap bound states and splits the GNR frontier bands into two segments, localizing the bound state in a double barrier configuration. By suspending these GNRs freely between the tip of a low-temperature scanning tunneling microscope and the substrate, we demonstrate unipolar hole transport through the boron in-gap state's resonance. Strong current rectification is observed, associated with the varying widths of the two barriers, which can be tuned by altering the distance between tip and substrate. This study introduces an innovative approach for the precise manipulation of molecular electronic functionalities, opening new avenues for advanced applications in organic electronics., Comment: 9 pages, 4 figures; SI: 7 pages, 6 figures

Open-shell polycyclic aromatic hydrocarbons (PAHs) represent promising building blocks for carbon-based functional magnetic materials. Their magnetic properties stem from the presence of unpaired electrons localized in radical states of $\pi$ character. Consequently, these materials are inclined to exhibit spin delocalization, form extended collective states, and respond to the flexibility of the molecular backbones. However, they are also highly reactive, requiring structural strategies to protect the radical states from reacting with the environment. Here, we demonstrate that the open-shell ground state of the diradical 2-OS survives on a Au(111) substrate as a global singlet formed by two unpaired electrons with anti-parallel spins coupled through a conformational dependent interaction. The 2-OS molecule is a protected derivative of the Chichibabin's diradical, featuring a non-planar geometry that destabilizes the closed-shell quinoidal structure. Using scanning tunneling microscopy (STM), we localized the two interacting spins at the molecular edges, and detected an excited triplet state a few millielectronvolts above the singlet ground state. Mean-field Hubbard simulations reveal that the exchange coupling between the two spins strongly depends on the torsional angles between the different molecular moieties, suggesting the possibility of influencing the molecule's magnetic state through structural changes. This was demonstrated here using the STM tip to manipulate the molecular conformation, while simultaneously detecting changes in the spin excitation spectrum. Our work suggests the potential of these PAHs for a new class of all-carbon spin-crossover materials., Comment: 8 pages in the main manuscript, including 4 figures, 21 pages in the supporting info, including 19 figures

The differences on the thermal behavior (DTA-TG) of mica samples measured before and after sonication have been studied. Sonication treatment produces important modifications in the thermal behavior of muscovite and biotite samples. For muscovite, it produces a broadening and decrease in temperature of the dehydroxylation and crystallization effects, reaching a steady stage after 40 h treatment time. For biotite, the original single peak profile for the dehydroxylation of the untreated sample is converted into a two peaks profile after sonication, the intensity of the low temperature peak increases with sonication time, while the intensity of the high temperature peak decreases. The modification of the thermal behavior for sonicated samples has been correlated to the particle size distribution effect produced by the sonication treatment. It has been also observed that the cup tip of the sonication equipment contaminates the samples releasing titanium of its composition

Triangulenes are open-shell triangular graphene flakes with total spin increasing with their size. In the last years, on-surface-synthesis strategies have permitted fabricating and engineering triangulenes of various sizes and structures with atomic precision. However, direct proof of the increasing total spin with their size remains elusive. In this work, we report the combined in-solution and on-surface synthesis of a large nitrogen-doped triangulene (aza-[5]-triangulene) and the detection of its high spin ground state on a Au(111) surface. Bond-resolved scanning tunneling microscopy images uncovered radical states distributed along the zigzag edges, which were detected as weak zero-bias resonances in scanning tunneling spectra. These spectral features reveal the partial Kondo screening of a high spin state. Through a combination of several simulation tools, we find that the observed distribution of radical states is explained by a quintet ground state (S = 2), instead of the expected quartet state (S = 3/2), confirming the positively charged state of the molecule on the surface. We further provide a qualitative description of the change of (anti)aromaticity introduced by N-substitution, and its role in the charge stabilization on a surface, resulting in a S = 2 aza-[5]-triangulene on Au(111)., Comment: 8 pages with 4 figures

We argue that the formation of Yu-Shiba-Rusinov excitations in proximitized thin films is largely mediated by a type of Andreev-bound state named after de Gennes and Saint James. This is shown by studying an experimentally motivated model and computing the overlap of the wave functions of these two subgap states. We find the overlap stays close to unity even as the system moves away from weak coupling across the parity-changing quantum phase transition. Based on this observation, we introduce a single-site model of the bound state coupled to a quantum spin. The adequacy of this description is assessed by reintroducing the coupling to the continuum as a weak perturbation and studying its scaling flow using Anderson's poor man's scaling., Comment: 12 pages, 3 figures

Low dimensional carbon-based materials are interesting because they can show intrinsic $\pi$-magnetism associated to p-electrons residing in specific open-shell configurations. Consequently, during the last years there have been impressive advances in the field combining indirect experimental fingerprints of localized magnetic moments with theoretical models. In spite of that, a characterization of their spatial- and energy-resolved spin-moment has so far remained elusive. To obtain this information, we present an approach based on the stabilization of the magnetization of $\pi$-orbitals by virtue of a supporting substrate with ferromagnetic ground state. Remarkably, we go beyond localized magnetic moments in radical or faulty carbon sites: In our study, energy-dependent spin-moment distributions have been extracted from spatially extended one-dimensional edge states of chiral graphene nanoribbons. This method can be generalized to other nanographene structures, representing an essential validation of these materials for their use in spintronics and quantum technologies.

Network intrusion detection systems are evolving into intelligent systems that perform data analysis while searching for anomalies in their environment. Indeed, the development of deep learning techniques paved the way to build more complex and effective threat detection models. However, training those models may be computationally infeasible in most Edge or IoT devices. Current approaches rely on powerful centralized servers that receive data from all their parties - violating basic privacy constraints and substantially affecting response times and operational costs due to the huge communication overheads. To mitigate these issues, Federated Learning emerged as a promising approach, where different agents collaboratively train a shared model, without exposing training data to others or requiring a compute-intensive centralized infrastructure. This work presents GowFed, a novel network threat detection system that combines the usage of Gower Dissimilarity matrices and Federated averaging. Different approaches of GowFed have been developed based on state-of the-art knowledge: (1) a vanilla version; and (2) a version instrumented with an attention mechanism. Furthermore, each variant has been tested using simulation oriented tools provided by TensorFlow Federated framework. In the same way, a centralized analogous development of the Federated systems is carried out to explore their differences in terms of scalability and performance - across a set of designed experiments/scenarios. Overall, GowFed intends to be the first stepping stone towards the combined usage of Federated Learning and Gower Dissimilarity matrices to detect network threats in industrial-level networks., Comment: 16 pages, 12 figures, currently under review at Journal of Network and Computer Applications (JNCA). arXiv admin note: text overlap with arXiv:2204.12443

A magnetic impurity interacting with a superconductor develops a rich excitation spectrum formed by superposition of quasiparticles and spin states, which appear as Yu-Shiba-Rusinov and spin-flip excitations in tunneling spectra. Here, we show that tunneling electrons can also excite a superconducting pair-breaking transition in the presence of magnetic impurities, which is hidden for electrons on bare superconductors. Combining scanning tunneling spectroscopy with theoretical modeling, we map the excitation spectrum of a Fe-porphyrin molecule on the Au/V(100) proximitized surface into a manifold of many-body excitations and follow their behavior across a parity-changing transition. Pair excitations emerge in the tunneling spectra as peaks outside the gap in the strong interaction regime, scaling with the pair correlation. Our results unravel the quantum nature of magnetic impurities on superconductors and prove that pair excitations are parity detectors for magnetic impurities., Comment: 14 pages, 11 figures

Spin-hosting graphene nanostructures are promising metal-free systems for elementary quantum spintronic devices. Conventionally, spins are protected from quenching by electronic bandgaps, which also hinder electronic access to their quantum state. Here, we present a narrow graphene nanoribbon substitutionally doped with boron heteroatoms that combines a metallic character with the presence of localized spin 1/2 states in its interior. The ribbon was fabricated by on-surface synthesis on a Au(111) substrate. Transport measurements through ribbons suspended between the tip and the sample of a scanning tunnelling microscope revealed their ballistic behavior, characteristic of metallic nanowires. Conductance spectra show fingerprints of localized spin states in form of Kondo resonances and inelastic tunnelling excitations. Density functional theory rationalizes the metallic character of the graphene nanoribbon due to the partial depopulation of the valence band induced by the boron atoms. The transferred charge builds localized magnetic moments around the boron atoms. The orthogonal symmetry of the spin-hosting state's and the valence band's wavefunctions protects them from mixing, maintaining the spin states localized. The combination of ballistic transport and spin localization into a single graphene nanoribbon offers the perspective of electronically addressing and controlling carbon spins in real device architectures., Comment: 9 pages in the main manuscript, including 4 figures, 13 pages in the supporting info, including 13 figures

Intrusion detection systems are evolving into intelligent systems that perform data analysis searching for anomalies in their environment. The development of deep learning technologies opened the door to build more complex and effective threat detection models. However, training those models may be computationally infeasible in most Internet of Things devices. Current approaches rely on powerful centralized servers that receive data from all their parties -- violating basic privacy constraints and substantially affecting response times and operational costs due to the huge communication overheads. To mitigate these issues, Federated Learning emerged as a promising approach where different agents collaboratively train a shared model, neither exposing training data to others nor requiring a compute-intensive centralized infrastructure. This paper focuses on the application of Federated Learning approaches in the field of Intrusion Detection. Both technologies are described in detail and current scientific progress is reviewed and categorized. Finally, the paper highlights the limitations present in recent works and presents some future directions for this technology., Comment: Sent for publication in the Special Issue of Intrusion Detection for the Internet of Things - IEEE Internet of Things Journal: 9 pages, 3 figures, 1 table

Magnetic molecules deposited on surfaces are a promising platform to individually address and manipulate spins. Long spin excitation lifetimes are necessary to utilize them in quantum information processing and data storage. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations into the ground state. However, the presence of superconducting paring effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitations of a FeTPP-Cl molecule for more than 80ns. This long value was determined by studying inelastic spin excitations of the S=5/2 multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling spectroscopy. The spin lifetime decreases with increasing film thickness, in apparent connection with the gradual gap-closing of a pair of de Gennes-Saint James resonances found inside the superconducting gap. Our results elucidate the use of proximitized gold electrodes for addressing quantum spins on surfaces, envisioning new routes for tuning the value of their spin lifetime., Comment: 23 pages, 8 figures

Nitrogen heteroatom doping into a triangulene molecule allows tuning its magnetic state. However, the synthesis of the nitrogen-doped triangulene (aza-triangulene) has been challenging. Herein, we report the successful synthesis of aza-triangulene on the Au(111) and Ag(111) surfaces, along with their characterizations by scanning tunneling microscopy and spectroscopy in combination with density functional theory (DFT) calculations. Aza-triangulenes were obtained by reducing ketone-substituted precursors. Exposure to atomic hydrogen followed by thermal annealing and, when necessary, manipulations with the scanning probe, afforded the target product. We demonstrate that on Au(111) aza-triangulene donates an electron to the substrate and exhibits an open-shell triplet ground state. This is derived from the different Kondo resonances of the final aza-triangulene product and a series of intermediates on Au(111). Experimentally mapped molecular orbitals match perfectly with DFT calculated counterparts for a positively charged aza-triangulene. In contrast, aza-triangulene on Ag(111) receives an extra electron from the substrate and displays a closed-shell character. Our study reveals the electronic properties of aza-triangulene on different metal surfaces and offers an efficient approach for the fabrication of new hydrocarbon structures, including reactive open-shell molecules.

Magnetic impurities on a superconductor induce sub-gap Yu-Shiba-Rusinov (YSR) bound states, localized at the impurity site and fading away from it for distances up to several nanometers. In this article, we present a theoretical method to calculate the spatial distribution of the YSR spectrum of a two-dimensional superconductor with arbitrary Fermi contours (FCs) in the presence of magnetic impurities. Based on the Green's Function (GF) formalism, we obtain a general analytical expression by approximating an arbitrary contour shape to a regular polygon. This method allows us to show the connection between the spatial decay (and, hence, the extension) of YSR states and the shape of the FC of the host superconductor. We further apply this formalism to compute the evolution of YSR states in the presence of a nearby impurity atom, and compare the results with Scanning Tunneling Microscopy (STM) measurements on interacting manganese dimers on the $\beta$-Bi2Pd superconductor. The method can be easily extended to any arbitrary number of magnetically coupled impurities, thus, providing a useful tool for simulating the spectral properties of interacting YSR states in artificial atomic nanostructures., Comment: 10 pages, 4 figures

Chains of Na atoms and dicyanovinyl-quinquethiophene (DCV5T-Me2) molecules with ionic bonds form a superlattice on Au(111). Through a detailed analysis of the interchain distances obtained from scanning tunneling microscopy images at various molecular coverages, we found that the chain arrangement substantially deviates from a random distribution of noninteracting chains. Instead, the distribution of chain spacings provides evidence for the existence of an interchain long-range repulsive potential. Furthermore, the experimental results can be modeled by a repulsive potential with a 1/d distance dependence, characteristic of Coulomb interactions. Density functional theory calculations of free-standing molecular chains reveal a charge depletion at the periphery of the chains, which is attributed to the intrinsic polar property of the molecule and is responsible for the long-range repulsion.

Triangulene nanographenes are open-shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long-sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl-anthracene cyclic hexamer and the on-surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired {\pi}-electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S = 1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of a S = 1 spin ring, representing a unique system to test collective spin modes in cyclic systems., Comment: 8 pages Ms with 3 figures; 12 pages Supplementary Information

Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional $\pi$-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems: only armchair graphene nanoribbons (GNRs) show a band gap that, however, closes for any other GNR orientation. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergoes a topological phase transition, becoming first topological insulators, and transforming then into trivial band insulators for the narrowest chGNRs. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunnelling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. The first emerging gapped phases are topological, protected by a chiral interaction pattern between edges. For narrower ribbons, the symmetry of the interaction pattern changes, and the topological gap closes and re-opens again as a trivial band insulator. Our findings represent a new platform for producing topologically protected spin states and demonstrates the potential of connecting chiral edge and defect structure with band engineering., Comment: 12 pages, 5 figures

The electronic properties of graphene nanoribbons (GNRs) can be precisely tuned by chemical doping. Here we demonstrate that amino (NH$_2$) functional groups attached at the edges of chiral GNRs (chGNRs) can efficiently gate the chGNRs and lead to the valence band (VB) depopulation on a metallic surface. The NH$_2$-doped chGNRs are grown by on-surface synthesis on Au(111) using functionalized bianthracene precursors. Scanning tunneling spectroscopy resolves that the NH$_2$ groups significantly up-shift the bands of chGNRs, causing the Fermi level crossing of the VB onset of chGNRs. Through density functional theory simulations we confirm that the hole-doping behavior is due to an upward shift of the bands induced by the edge NH$_2$ groups., Comment: 7 pages with 5 figures and 4 page supplementary information. This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in ACS Nano, copyright American Chemical Society after peer review

A magnetic impurity on a superconductor induces Yu-Shiba-Rusinov (YSR) bound states, detected by tunneling spectroscopy as long-lived quasiparticle excitations inside the superconducting gap. Coupled YSR states constitute basic elements to engineer artificial superconducting states, but their substrate-mediated interactions are generally weak. In this paper, we report that intramolecular (Hund's like) exchange interactions produce coupled YSR states across a molecular platform. We measured YSR spectra along a magnetic iron-porphyrin on Pb(111) and found evidences of two orbital interaction channels, which invert their particle-hole asymmetry across the molecule. Numerical calculations show that the identical YSR asymmetry pattern of the two channels is caused by two spin-hosting orbitals with opposite potential scattering and coupled strongly. Both channels can be similarly excited by tunneling electrons into each orbital, depicting a new scenario for entangled superconducting bound states using molecular platforms., Comment: 6 pages, 5 figures, This document is the Author's version of an Accepted Work, copyright American Physical Society

Graphene nanoribbons (GNRs), low-dimensional platforms for carbon-based electronics, show the promising perspective to also incorporate spin polarization in their conjugated electron system. However, magnetism in GNRs is generally associated to localized states around zigzag edges, difficult to fabricate and with high reactivity. Here we demonstrate that magnetism can also be induced away from physical GNR zigzag edges through atomically precise engineering topological defects in its interior. A pair of substitutional boron atoms inserted in the carbon backbone breaks the conjugation of their topological bands and builds two spin-polarized boundary states around. The spin state was detected in electrical transport measurements through boron-substituted GNRs suspended between tip and sample of a scanning tunneling microscope. First-principle simulations find that boron pairs induce a spin 1, which is modified by tuning the spacing between pairs. Our results demonstrate a route to embed spin chains in GNRs, turning them basic elements of spintronic devices., Comment: 6 pages in main manuscript plus 9 pages Supplementary Material, 5 figures