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Charge-density waves (CDWs) are correlated states of matter, where the electronic density is modulated periodically as a consequence of electronic and phononic interactions. Often, CDW phases coexist with other correlated states, such as superconductivity, spin-density waves or Mott insulators. Controlling CDW phases may therefore enable the manipulation of the energy landscape of these interacting states. 2H-NbSe$_2$ is a prime example of a transition metal dichalcogenide (TMDC) hosting CDW order and superconductivity. The CDW is of incommensurate nature resulting in different CDW-to-lattice alignments at the atomic scale. Here, we use the tip of a scanning tunneling microscope (STM) to position adatoms on the surface and induce reversible switching of the CDW domains. We show that the domain structure critically affects other local interactions, namely the hybridization of Yu-Shiba-Rusinov (YSR) states, which arise from exchange interactions of magnetic Fe atoms with the superconductor. Our results suggest that CDW manipulation could also be used to introduce domain walls in coupled spin chains on superconductors, potentially also affecting topological superconductivity.

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultra-low temperature scanning tunneling microscopy/spectroscopy, the Yu-Shiba-Rusinov (YSR) states of individual manganese phthalocyanine molecules with high spin character on the surface of an ultra-thin lead film in variable transverse magnetic field. We observe two types of YSR excitations, depending on the adsorption geometry of the molecule. Using a zero-bandwidth model, we detail the role of the magnetic anisotropy, spin-spin exchange, and Kondo exchange. We illustrate that one molecular type can be treated as an individual spin akin to an isolated spin on the metal center, whereas the other molecular type invokes a coupled spin system represented by a spin on the center and the ligand. Using the field-dependent evolution of the YSR excitations and comparisons to modeling, we describe the quantum phase of each of the molecules. These results provide an insight into the quantum nature of YSR excitations in magnetic field, and a platform to study spin impurity models on superconductors in magnetic field.

Magnetic adatoms on superconductors give rise to Yu-Shiba-Rusinov (YSR) states that hold considerable interest for the design of topological superconductivity. Here, we show that YSR states are also an ideal platform to engineer structures with intricate wave-function symmetries. We assemble structures of iron atoms on the quasi-two-dimensional superconductor $2H$-NbSe$_2$. The Yu-Shiba-Rusinov wave functions of individual atoms extend over several nanometers enabling hybridization even at large adatom spacing. We show that the substrate can be exploited to deliberately break symmetries of the adatom structure in ways unachievable in the gas phase. We highlight this potential by designing chiral wave functions of triangular adatom structures confined within a plane. Our results significantly expand the range of interesting quantum states that can be engineered using arrays of magnetic adatoms on superconductors.

Sulphur vacancies in MoS$_2$ on Au(111) have been shown to be negatively charged as reflected by a Kondo resonance. Here, we use scanning tunneling microscopy to show that these vacancies serve as anchoring sites for thiol-based molecules (CF$_3$-3P-SH) with two distinct reaction products, one of them showing a Kondo resonance. Based on comparisons with density-functional theory (DFT) calculations, including a random structure search and computation of energies and electronic properties at a hybrid exchange-correlation functional level, we conclude that both anchored molecules are charge neutral. One of them is an anchored intact CF$_3$-3P-SH molecule while the other one is the result of catalytically activated dehydrogenation to CF$_3$-3P-S with subsequent anchoring. Our investigations highlight a perspective of functionalizing defects with thiol-terminated molecules that can be equipped with additional functional groups, such as charge donor- or acceptor-moieties, switching units or magnetic centers.

Two-dimensional (2D) transition-metal dichalcogenides (TMDC) are considered highly promising platforms for next-generation optoelectronic devices. Owing to its atomically thin structure, device performance is strongly impacted by a minute amount of defects. Although defects are usually considered to be disturbing, defect engineering has become an important strategy to control and design new properties of 2D materials. Here, we produce single S vacancies in a monolayer of MoS$_2$ on Au(111). Using a combination of scanning tunneling and atomic force microscopy, we show that these defects are negatively charged and give rise to a Kondo resonance, revealing the presence of an unpaired electron spin exchange coupled to the metal substrate. The strength of the exchange coupling depends on the density of states at the Fermi level, which is modulated by the moir\'e structure of the MoS$_2$ lattice and the Au(111) substrate. In the absence of direct hybridization of MoS$_2$ with the metal substrate, the S vacancy remains charge-neutral. Our results suggest that defect engineering may be used to induce and tune magnetic properties of otherwise non-magnetic materials.

Kagome lattices constitute versatile platforms for studying paradigmatic correlated phases. While molecular self-assembly of kagome structures on metallic substrates is promising, it is challenging to realize pristine kagome properties because of hybridization with the bulk degrees of freedom and modified electron-electron interactions. We suggest that a superconducting substrate offers an ideal support for a magnetic kagome lattice. Exchange coupling induces kagome-derived bands at the interface, which are protected from the bulk by the superconducting energy gap. We realize a magnetic kagome lattice on a superconductor by depositing Fe-porphin-chloride molecules on Pb(111) and using temperature-activated de-chlorination and self-assembly. This allows us to control the formation of smaller kagome precursors and long-range ordered kagome islands. Using scanning tunneling microscopy and spectroscopy at 1.6 K, we identify Yu-Shiba-Rusinov states inside the superconducting energy gap and track their hybridization from the precursors to larger islands, where the kagome lattice induces extended YSR bands. These YSR-derived kagome bands are protected inside the superconducting energy gap, motivating further studies to resolve possible spin-liquid or Kondo-lattice-type behavior.

Electrostatic potentials strongly affect molecular energy levels and charge states, providing the fascinating opportunity of molecular gating. Their influence on molecular vibrations remains less explored. Here, we investigate Ethyl-Diaminodicyanoquinone molecules on a monolayer of MoS$_2$ on Au(111) using scanning tunneling and atomic force microscopy and spectroscopy. These molecules exhibit a large dipole moment in gas phase, which we find to (partially) persist on the MoS$_2$ monolayer. The self-assembled structures consist of chains, where the dipoles of neighboring molecules are aligned anti-parallel. Thanks to the decoupling efficiency of the molecular states from the metal by the MoS$_2$ interlayer, we resolve vibronic states of the molecules, which vary in intensity depending on the molecular surrounding. We suggest that the vibrations are strongly damped by electrostatic interactions with the environment.

Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems. Working with Mn atoms on Au(111) covered by a monolayer of MoS$_2$, we tune the inter-adatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moir\'e structure of the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moir\'e structure. Mn dimers spaced by a few atomic lattice sites exhibit split Kondo resonances. In contrast, adatoms in closely spaced dimers couple antiferromagnetically, resulting in a molecular-singlet ground state. Exciting the singlet-triplet transition by tunneling electrons, we find that the singlet-triplet splitting is surprisingly sensitive to the moir\'e structure. We interpret our results theoretically by relating the variations in the singlet-triplet splitting to the heights of the Kondo peaks of single adatoms, finding evidence for coupling of the adatom spin to multiple conduction electron channels.

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diode-like effects in the switching and retrapping currents of weakly-damped Josephson junctions. We find that while the diode-like behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions., Comment: 6+12 pages, 3 figures

Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes and known as non-reciprocal charge transport. The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems. Probing the ultimate limits of miniaturization, we have created atomic-scale Pb--Pb Josephson junctions in a scanning tunneling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behavior, confirming the high quality of the junctions, but no asymmetry between the bias directions. Non-reciprocal supercurrents emerge when inserting a single magnetic atom into the junction, with the preferred direction depending on the atomic species. Aided by theoretical modelling, we trace the non-reciprocity to quasiparticle currents flowing via Yu-Shiba-Rusinov (YSR) states inside the superconducting energy gap. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation.

Molecules consisting of a donor and an acceptor moiety can exhibit large intrinsic dipole moments. Upon deposition on a metal surface, the dipole may be effectively screened and the charge distribution altered due to hybridization with substrate electronic states. Here, we deposit Ethyl-Diaminodicyanoquinone molecules, which exhibit a large dipole moment in gas phase, on a Au(111) surface. Employing a combination of scanning tunneling microscopy and non-contact atomic force microscopy, we find that a significant dipole moment persists in the flat-lying molecules. Density-functional theory calculations reveal that the dipole moment is even increased on the metal substrate as compared to the gas phase. We also show that the local contact potential across the molecular islands is decreased by several tens of meV with respect to the bare metal. We explain this by the induced charge-density redistribution due to the adsorbed molecules, which confine the substrate's wavefunction at the interface. Our local measurements provide direct evidence of this so-called push-back or cushion effect at the scale of individual molecules., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Journal of Physical Chemistry C

Magnetic adatoms on a superconducting substrate undergo a quantum phase transition as their exchange coupling to the conduction electrons increases. For quantum spins, this transition is accompanied by screening of the adatom spin. Here, we explore the consequences of this screening for the phase diagrams and subgap excitation spectra of dimers of magnetic adatoms coupled by hybridization of their Yu-Shiba-Rusinov states and spin-spin interactions. We specifically account for higher spins, single-ion anisotropy, Ruderman-Kittel-Kasuya-Yosida coupling, and Dzyaloshinsky-Moriya interactions relevant in transition-metal and rare-earth systems. Our flexible approach based on a zero-bandwidth approximation provides detailed physical insight and is in excellent qualitative agreement with available numerical-renormalization group calculations on monomers and dimers. Remarkably, we find that even in the limit of large impurity spins or strong single-ion anisotropy, the phase diagrams for dimers of quantum spins remain qualitatively distinct from phase diagrams based on classical spins, highlighting the need for a theory of quantum Yu-Shiba-Rusinov dimers., Comment: 17 pages, 12 figures

The interplay between disorder and interactions can dramatically influence the physical properties of thin-film superconductors. In the most extreme case, strong disorder is able to suppress superconductivity as an insulating phase emerges. Due to the known pair-breaking potential of magnetic disorder on superconductors, the research focus is on the influence of non-magnetic disorder. Here we provide direct evidence that magnetic disorder is also present at the surface of amorphous superconducting films. This magnetic disorder is present even in the absence of magnetic impurity atoms and is intimately related to the surface termination itself. While bulk superconductivity survives in sufficiently thick films, we suggest that magnetic disorder may crucially affect the superconductor-to-insulator transition in the thin-film limit.

Current fluctuations related to the discreteness of charge passing through small constrictions are termed shot noise. This unavoidable noise provides both advantages - being a direct measurement of the transmitted particles' charge, and disadvantages - a main noise source in nanoscale devices operating at low temperature. While better understanding of shot noise is desired, the technical difficulties in measuring it result in relatively few experimental works, especially in single-atom structures. Here we describe a local shot-noise measurement apparatus, and demonstrate successful noise measurements through single-atom junctions. Our apparatus, based on a scanning tunneling microscope operates at liquid helium temperatures. It includes a broadband commercial amplifier mounted in close proximity to the tunnel junction, thus reducing both thermal noise and the input capacitance that limit traditional noise measurements. The full capabilities of the microscope are maintained in the modified system and a quick transition between different measurement modes is possible.

N-Heteropolycyclic aromatic compounds are promising organic electron-transporting semiconductors for applications in field effect transistors. Here, we investigated the electronic properties of 1,3,8,10-tetraazaperopyrene derivatives adsorbed on Au(111) using a complementary experimental approach, namely scanning tunneling spectroscopy and two-photon photoemission combined with state-of-the-art density functional calculations. We find signatures of weak physisorption of the molecular layers, such as the absence of charge transfer, a nearly unperturbed surface state and an intact herringbone reconstruction underneath the molecular layer. Interestingly, molecular states in the energy region of the \emph{sp}- and \emph{d}-bands of the Au(111) substrate exhibit hole-like dispersive character. We ascribe this band character to hybridization with the delocalized states of the substrate. We suggest that such bands, which effectively leave the molecular frontier orbitals largely unperturbed, to be a promising lead for the design of organic-metal interfaces with a low charge injection barrier.

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.

Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe$_2$. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe$_2$. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity.

Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended $t-J$ model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures., Comment: 16 pages including supplementary information; 4 figures

Theoretical descriptions of Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities inside the gap of a superconductor typically rely on a classical spin model or are restricted to spin-1/2 quantum spins. These models fail to account for important aspects of YSR states induced by transition-metal impurities, including the effects of higher quantum spins coupled to several conduction-electron channels, crystal or ligand-field effects, and magnetic anisotropy. We introduce and explore a zero-bandwidth model, which incorporates these aspects, is readily solved numerically, and analytically tractable in several limiting cases. The principal simplification of the model is to neglect Kondo renormalizations of the exchange couplings between impurity spin and conduction electrons. Nevertheless, we find excellent correspondence in those cases, in which we can compare our results to existing numerical-renormalization-group calculations. We apply the model to obtain and understand phase diagrams as a function of pairing strength and magnetic anisotropy as well as subgap excitation spectra. The single-channel case is most relevant for transition-metal impurities embedded into metallic coordination complexes on superconducting substrates, while the multi-channel case models transition-metal adatoms., Comment: 23 pages, 10 figures, to appear in Phys. Rev. B

Magnetic adatoms on surfaces are exchange coupled to their environment, inducing fast relaxation of excited spin states and decoherence. These interactions can be suppressed by inserting decoupling layers between the magnetic adsorbate and the metallic substrate. Using low-temperature scanning tunneling microscopy and spectroscopy, we investigate the magnetic properties of single Fe atoms on Au(111) covered by a monolayer of MoS$_2$ and explore the influence of the moir\'e structure on the spin excitation spectra. Fe adatoms absorbed at minima of the moir\'e structure exhibit almost pure inelastic spin excitations. Kondo correlations develop for adsorption sites off the moir\'e minimum, culminating in fully developed Kondo resonances on moir\'e maxima. The increase in Kondo correlations is accompanied by a decrease in the single-ion anisotropy, which we rationalize by poor-person's scaling. Local variations in the tunneling spectra indicate pronounced interference between tunneling paths involving the spin-carrying orbitals and a hybrid Fe-S orbital, which forms despite the nominally inert nature of the terminating S layer.

Photon-assisted tunneling frequently provides detailed information on the underlying charge-transfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a systematic Keldysh calculation of the subgap conductance and provides a detailed analytical understanding of photon-assisted tunneling into subgap states, in excellent agreement with a recent experiment. We focus on tunneling from superconducting electrodes and into Yu-Shiba-Rusinov states associated with magnetic impurities or adatoms, but we also explicitly extend our results to include normal-metal electrodes or other types of subgap states in superconductors. In particular, we argue that photon-assisted Andreev reflections provide a high-accuracy method to measure small, but nonzero energies of subgap states which can be important for distinguishing conventional subgap states from Majorana bound states., Comment: 20 pages, 8 figures

Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111). We show that both asymmetries originate in interfering tunneling paths via a spin-carrying orbital and the highest occupied molecular orbital (HOMO). Strong evidence for this model comes from nodal planes of the HOMO, where tunneling reveals symmetric Kondo and YSR resonances. Our results establish an important mechanism for the asymmetries of Kondo and YSR lineshapes.

The electronic structure of molecules on metal surfaces is largely determined by hybridization and screening by the substrate electrons. As a result, the energy levels are significantly broadened and molecular properties, such as vibrations are hidden within the spectral lineshapes. Insertion of thin decoupling layers reduces the linewidths and may give access to the resolution of electronic and vibronic states of an almost isolated molecule. Here, we use scanning tunneling microscopy and spectroscopy to show that a single layer of MoS$_{2}$ on Ag(111) provides a semiconducting band gap that may prevent molecular states from strong interactions with the metal substrate. We show that the lowest unoccupied molecular orbital (LUMO) of tetra-cyano-quino-dimethane (TCNQ) molecules is significantly narrower than on the bare substrate and that it is accompanied by a characteristic satellite structure. Employing simple calculations within the Franck-Condon model, we reveal their vibronic origin and identify the modes with strong electron-phonon coupling.

Vibronic spectra of molecules are typically described within the Franck-Condon model. Here, we show that highly resolved vibronic spectra of large organic molecules on a single layer of MoS$_{2}$ on Au(111) show spatial variations in their intensities, which cannot be captured within this picture. We explain that vibrationally mediated perturbations of the molecular wave functions need to be included into the Franck-Condon model. Our simple model calculations reproduce the experimental spectra at arbitrary position of the STM tip over the molecule in great detail.

Tunneling across superconducting junctions proceeds by a rich variety of processes, which transfer single electrons, Cooper pairs, or even larger numbers of electrons by multiple Andreev reflections. Photon-assisted tunneling combined with the venerable Tien-Gordon model has long been a powerful tool to identify tunneling processes between superconductors. Here, we probe superconducting tunnel junctions including an impurity-induced Yu-Shiba-Rusinov (YSR) state by exposing a scanning tunneling microscope with a superconducting tip to microwave radiation. We find that a simple Tien-Gordon description describes tunneling of single electrons and Cooper pairs into the bare substrate, but breaks down for tunneling via YSR states by resonant Andreev reflections. We develop an improved theoretical description which is in excellent agreement with the data. Our results establish photon-assisted tunneling as a powerful tool to analyze tunneling processes at the atomic scale which should be particularly informative for unconventional and topological superconductors.

Scanning tunneling spectroscopy requires the application of a potential difference between the sample and a tip. In metal-vacuum-metal junctions, one can safely assume that the potential is constant along the metallic substrate. Here, we show that the inhomogeneous shape of the electric potential has to be taken into account when probing spatially extended molecules on a decoupling layer. To this end, oligothiophene-based molecules were deposited on a monolayer of molybdenum disulfide (MoS$_2$) on a Au(111) surface. By probing the delocalized molecular orbital along the thiophene-backbone, we found an apparent intramolecular shift of the positive ion resonance, which can be ascribed to a perturbation potential caused by the tip. Using a simple model for the electrostatic landscape, we show that such a perturbation is caused by the inhomogeneity of the applied bias potential in the junction and may be further modified by an electric dipole of a functionalized tip. The two effects can be disentangled in tunneling spectra by probing the apparent energy shift of vibronic resonances along the molecular backbone. We suggest that extended molecules on MoS$_2$ can be used as a sensor for the shape of the electrostatic potential of arbitrary tips.

For a molecular radical to be stable, the environment needs to be inert. Furthermore, an unpaired electron is less likely to react chemically, when it is placed in an extended orbital. Here, we use the tip of a scanning tunneling microscope to abstract one of the pyrrolic hydrogen atoms from phthalocyanine (H2Pc) deposited on a single layer of molybdenum disulfide (MoS2) on Au(111). We show the successful dissociation reaction by current-induced three-level fluctuations reflecting the inequivalent positions of the remaining H atom in the pyrrole center. Tunneling spectroscopy reveals two narrow resonances inside the semiconducting energy gap of MoS2 with their spatial extent resembling the highest occupied molecular orbital (HOMO) of H2Pc. By comparison to simple density functional calculations of the isolated molecule, we show that these correspond to a single occupation of the Coulomb-split highest molecular orbital of HPc. We conclude that the dangling $\sigma$ bond after N-H bond cleavage is filled by an electron from the delocalized HOMO. The extended nature of the HOMO together with the inert nature of the MoS2 layer favor the stabilization of this radical state.

NbSe$_2$ is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wavefunctions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make NbSe$_2$ a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.

The detection of vibrational excitations of individual molecules on surfaces by scanning tunneling spectroscopy does not obey strict selection rules but rather propensity rules. The experimental verification of these is challenging because it requires the independent variation of specific parameters, such as the electronic structure, while keeping the vibrational modes the same. Here, we make use of the versatile self-assembled structures of Fe-tetra-pyridyl-porphyrin molecules on a Au(111) surface. These exhibit different energy-level alignments of the frontier molecular orbitals, thus allowing the correlation of electronic structure and detection of vibrations. We identify up to seven vibrational modes in the tunneling spectra of the molecules in some of the arrangements, whereas we observe none in other structures. We find that the presence of vibrational excitations and their distribution along the molecule correlates with the observation of energetically low-lying molecular states. This correlation allows to explain the different numbers of vibrational signatures for molecules embedded within different structures as well as the bias asymmetry of the vibrational intensities within an individual molecule. Our observations are in agreement with a resonant enhancement of vibrations by the virtual excitation of electronic states.

Surface-bound porphyrins are promising candidates for molecular switches, electronics and spintronics. Here, we studied the structural and the electronic properties of Fe-tetra-pyridil-porphyrin adsorbed on Au(111) in the monolayer regime. We combined scanning tunneling microscopy/spectroscopy, ultraviolet photoemission, and two-photon photoemission to determine the energy levels of the frontier molecular orbitals. We also resolved an excitonic state with a binding energy of 420 meV, which allowed us to compare the electronic transport gap with the optical gap.

The magnetic properties of metal-organic complexes are strongly influenced by conformational changes in the ligand. The flexibility of Fe-tetra-pyridyl-porphyrin molecules leads to different adsorption configurations on a Au(111) surface. By combining low-temperature scanning tunneling spectroscopy and atomic force microscopy, we resolve a correlation of the molecular configuration with different spin states and magnitudes of magnetic anisotropy. When the macrocycle exhibits a laterally-undistorted saddle shape, the molecules lie in a S=1 state with axial anisotropy arising from a square-planar ligand field. If the symmetry in the molecular ligand field is reduced by a lateral distortion of the molecule, we find a finite contribution of transverse anisotropy. Some of the distorted molecules lie in a S=2 state, again exhibiting substantial transverse anisotropy.

A Kondo resonance has been observed on purely organic molecules in several combinations of charge transfer complexes on a metal surface. It has been regarded as a fingerprint of the transfer of one electron from the donor to the extended $\pi$ orbital of the acceptor's LUMO. Here, we investigate the stoichiometric checkerboard structure of tetrathiafulvalene (TTF) and tetracyanoethylene (TCNE) on a Au(111) surface using scanning tunneling and atomic force microscopy at 4.8 K. We find a bistable state of the TCNE molecules with distinct structural and electronic properties. The two states represent different conformations of the TCNE within the structure. One of them exhibits a Kondo resonance, whereas the other one does not, despite of both TCNE types being singly charged.

The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states. We find that the FeP moment is screened in the pristine adsorption state. Approaching the tip of a scanning tunneling microscope, we exert a sufficiently strong attractive force to tune the molecule through the quantum phase transition into the free-spin state. We ascertain and characterize the transition by investigating the transport processes as function of tip-molecule distance, exciting the YSR states by single-electron tunneling as well as (multiple) Andreev reflections.

Monolayer islands of molybdenum disulfide (MoS$_2$) on Au(111) form a characteristic moir\'e structure, leading to locally different stacking sequences at the S-Mo-S-Au interface. Using low-temperature scanning tunneling microscopy (STM) and atomic force microscopy (AFM), we find that the moir\'e islands exhibit a unique orientation with respect to the Au crystal structure. This indicates a clear preference of MoS$_2$ growth in a regular stacking fashion. We further probe the influence of the local atomic structure on the electronic properties. Differential conductance spectra show pronounced features of the valence band and conduction band, some of which undergo significant shifts depending on the local atomic structure. We also determine the tunneling decay constant as a function of the bias voltage by a height-modulated spectroscopy method. This allows for an increased sensitivity of states with non-negligible parallel momentum $k_\parallel$ and the identification of the origin of the states from different areas in the Brillouin zone., Comment: in honor of K.-H. Rieder

The oxidation and spin state of a metal-organic molecule determine its chemical reactivity and magnetic properties. Here, we demonstrate the reversible control of the oxidation and spin state in a single Fe-porphyrin molecule in the force field of the tip of a scanning tunneling microscope. Within the regimes of half-integer and integer spin state, we can further track the evolution of the magnetocrystalline anisotropy. Our experimental results are corroborated by density functional theory and wave function theory. This combined analysis allows us to draw a complete picture of the molecular states over a large range of intramolecular deformations., Comment: Manuscript + Supplementary Information

Magnetic adsorbates on superconductors induce local bound states within the superconducting gap. These Yu-Shiba-Rusinov (\YSR) states decay slowly away from the impurity compared to atomic orbitals, even in 3d bulk crystals. Here, we use scanning tunneling spectroscopy to investigate their hybridization between two nearby magnetic Mn adatoms on a superconducting Pb(001) surface. We observe that the hybridization leads to the formation of symmetric and antisymmetric combinations of \YSR states. We investigate how the structure of the dimer wave functions and the energy splitting depend on the shape of the underlying monomer orbitals and the orientation of the dimer with respect to the Pb lattice.

The competition of the free spin state of a paramagnetic impurity on a superconductor with its screened counterpart is characterized by the energy scale of Kondo screening $k_BT_K$ compared to the superconducting pairing energy $\Delta$. When the experimental temperature suppresses Kondo screening, but preserves superconductivity, i.e., when $\Delta/k_B > T > T_K$, this description fails. Here, we explore this temperature range in a set of manganese phthalocyanine molecules decorated with ammonia (MnPc-NH$_3$) on Pb(111). We show that these molecules suffice the required energy conditions by exhibiting weak-coupling Kondo resonances. We correlate the energy of the Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap with the intensity of the Kondo resonance. We reveal that the bound state energy follows the expectations for a classical spin on a superconductor. This finding is important in view of many theoretical predictions using a classical spin model, in particular for the description of Majorana bound states in magnetic nanostructures on superconducting substrates.

In superconductors, magnetic impurities induce a pair-breaking potential for Cooper pairs, which locally affects the Bogoliubov quasiparticles and gives rise to Yu-Shiba-Rusinov (YSR or Shiba, in short) bound states in the density of states (DoS). These states carry information on the magnetic coupling strength of the impurity with the superconductor, which determines the many-body ground state properties of the system. Recently, the interest in Shiba physics was boosted by the prediction of topological superconductivity and Majorana modes in magnetically coupled chains and arrays of Shiba impurities. Here, we review the physical insights obtained by scanning tunneling microscopy into single magnetic adsorbates on the $s$-wave superconductor lead (Pb). We explore the tunneling processes into Shiba states, show how magnetic anisotropy affects many-body excitations, and determine the crossing of the many-body groundstate through a quantum phase transition. Finally, we discuss the coupling of impurities into dimers and chains and their relation to Majorana physics., Comment: 18 pages, 17 figures, review

Using scanning tunneling microscopy and spectroscopy we investigate the adsorption properties and ring-closing reaction of a diarylethene derivative (C5F-4Py) on a Ag(111) surface. We identify an electron-induced reaction mechanism, with a quantum yield varying from $10^{-14}-10^{-9}$ per electron upon variation of the bias voltage from $1-2$ V. We ascribe the drastic increase in switching efficiency to a resonant enhancement upon tunneling through molecular orbitals. Additionally, we resolve the ring-closing reaction even in the absence of a current passing through the molecule. In this case the electric-field can modify the reaction barrier, leading to a finite switching probability at 4.8 K. A detailed analysis of the switching events shows that a simple plate-capacitor model for the tip-surface junction is insufficient to explain the distance dependence of the switching voltage. Instead, describing the tip as a sphere is in agreement with the findings. We resolve small differences in the adsorption configuration of the closed isomer, when comparing the electron- and field-induced switching product.

Linear, suspended chains of magnetic atoms proximity coupled to an s-wave superconductor are predicted to host Majorana zero modes at the chain ends in the presence of strong spin-orbit coupling. Specifically, iron (Fe) chains on Pb(110) have been explored as a possible system to exhibit topological superconductivity and host Majorana zero-modes [Nadj-Perge, et al., Science 346, 602 (2014)]. Here, we study chains of the transition metal cobalt (Co) on Pb(110) and check for topological signatures. Using spin-polarized scanning tunneling spectroscopy, we resolve ferromagnetic order in the $d$ bands of the chains. Interestingly, also the subgap Yu-Shiba-Rusinov (YSR) bands carry a spin polarization as was predicted decades ago. Superconducting tips allow us to resolve further details of the YSR bands and in particular resonances at zero energy. We map the spatial distribution of the zero-energy signal and find it delocalized along the chain. Hence, despite of the ferromagnetic coupling within the chains and the strong-spin orbit coupling in the superconductor, we do not find clear evidence of Majorana modes. Simple tight-binding calculations suggest that the spin-orbit-split bands may cross the Fermi level four times which suppresses the zero-energy modes., Comment: 5 pages, 5 figures, 13 pages supplementary material

Single-ion lanthanide-organic complexes can provide stable magnetic moments with well-defined orientation for spintronic applications on the atomic level. Here, we show by a combined experimental approach of scanning tunneling microscopy and X-ray absorption spectroscopy that dysprosium-tris(1,1,1-trifluoro-4-(2-thienyl)-2,4butanedionate) (Dy(tta)$_3$) complexes deposited on a Au(111) surface undergo a molecular distortion, resulting in distinct crystal field symmetry imposed on the Dy ion. This leads to an easy-axis magnetization direction in the ligand plane. Furthermore, we show that tunneling electrons hardly couple to the spin excitations, which we ascribe to the shielded nature of the $4f$ electrons.

We investigate the nature of Yu-Shiba-Rusinov (YSR) subgap states induced by single Manganese (Mn) atoms adsorbed on different surface orientations of superconducting lead (Pb). Depending on the adsorption site, we detect a distinct number and characteristic patterns of YSR states around the Mn atoms. We suggest that the YSR states inherit their properties from the Mn $d$-levels, which are split by the surrounding crystal field. The periodicity of the long-range YSR oscillations allows us to identify a dominant coupling of the d-states to the outer Fermi sheet of the two-band superconductor Pb., Comment: 5 pages, 4 figures + supplemental material

We use scanning tunneling microscopy and spectroscopy to investigate structural and electronic properties of tetracyanonaphtho-quinodimethane (TNAP) based metal-organic networks on a superconducting Pb(111) surface. At low temperatures, the TNAP molecules form densely packed islands. When deposited at room temperature, Pb adatoms are incorporated into fourfold bonding nodes with the TNAP molecules leading to long-range ordered porous structures. Co-deposition of NaCl with TNAP yields a Na source for an ionically bonded Na-TNAP structure. Fourfold bonding motifs are also created by Fe atoms with the cyano terminations of TNAP. However, the structures are irregular and do not sustain the formation of long-range ordered networks. Some Fe centers with molecules surrounded in a local C2 symmetry exhibit Shiba states as a fingerprint of a magnetic interaction with the superconducting surface., Comment: 8 pages, 5 figures

The exchange coupling between magnetic adsorbates and a superconducting substrate leads to Shiba states inside the superconducting energy gap and a Kondo resonance outside the gap. The exchange coupling strength determines whether the quantum many-body ground state is a Kondo singlet or a singlet of the paired superconducting quasiparticles. Here, we use scanning tunneling spectroscopy to identify the different quantum ground states of Manganese phthalocyanine on Pb(111). We observe Shiba states, which are split into triplets by magnetocrystalline anisotropy. Their characteristic spectral weight yields an unambiguous proof of the nature of the quantum ground state., Comment: 6 pages, 4 figures

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] provides evidence for Majorana zero modes in iron (Fe) chains on the superconducting Pb(110) surface. Here, we study this system by scanning tunneling microscopy using superconducting tips. This high-resolution technique resolves a rich subgap structure, including zero-energy excitations in some chains. We compare the symmetry properties of the data under voltage reversal against theoretical expectations and provide evidence that the putative Majorana signature overlaps with a previously unresolved low-energy resonance. Interpreting the data within a Majorana framework suggests that the topological gap is significantly smaller than previously believed. Aided by model calculations, we also analyze higher-energy features of the subgap spectrum and their relation to high-bias peaks which we associate with the Fe d-bands., Comment: 5+5 pages, 5+6 figures

We combine scanning-tunneling-spectroscopy experiments probing magnetic impurities on a superconducting surface with a theoretical analysis of the tunneling processes between (superconducting) tip and substrate. We show that the current is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes between the impurity-induced Shiba bound state and the quasiparticle continuum, allowing us to extract information on such relaxation processes from our analysis., Comment: 4+ pages, 3 figures; supplementary material: 18 pages, 9 figures