Diode Effects in Current-Biased Josephson Junctions.

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 diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike 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.

Tuning a Two-Impurity Kondo System by a Moiré Superstructure.

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 interadatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moiré structure of the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moiré 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 moiré 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.

Diode effect in Josephson junctions with a single magnetic atom.

Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes1 and known as non-reciprocal charge transport2. 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 systems3-10. Here we investigate the ultimate limits of miniaturization by creating atomic-scale Pb-Pb Josephson junctions in a scanning tunnelling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behaviour, 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 by means of electron-hole asymmetric Yu-Shiba-Rusinov states inside the superconducting energy gap and identify a new mechanism for diode behaviour in Josephson junctions. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation.

Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor.

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 NbSe2. 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 NbSe2. 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.

Shot-noise measurements of single-atom junctions using a scanning tunneling microscope.

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 the thermal noise and 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.

Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains.

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.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111).

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of MoS_{2} on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer MoS_{2} as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Electronic Properties of Tetraazaperopyrene Derivatives on Au(111): Energy-Level Alignment and Interfacial Band Formation.

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 theory. 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 sp- and 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 leave the molecular frontier orbitals largely unperturbed, are a promising lead for the design of organic-metal interfaces with a low charge injection barrier.

Band Formation at Interfaces Between N-Heteropolycycles and Gold Electrodes.

Efficient charge injection at organic semiconductor/metal interfaces is crucial for the performance of organic field effect transistors. Interfacial hybrid band formation between electronic states of the organic compound and the metal electrode facilitates effective charge injection. Here, we show that a long-range ordered monolayer of a flat-lying N-heteropolycyclic aromatic compound on Au(111) leads to dispersing occupied and unoccupied interfacial hybrid bands. Using angle-resolved two-photon photoemission we determine their energy level alignment and dispersion relations. We suggest that band formation proceeds via hybridization of a localized occupied molecular state with the d-bands of the Au substrate, where the large effective mass of the d-bands is significantly reduced in the hybrid band. Hybridization of an unoccupied molecular state with the Au sp-band leads to a band with an even smaller effective mass.

Monolayers of MoS2 on Ag(111) as decoupling layers for organic molecules: resolution of electronic and vibronic states of TCNQ.

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 line shapes. Insertion of thin decoupling layers reduces the line widths 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 MoS2 on Ag(111) exhibits a semiconducting bandgap, which may prevent molecular states from strong interactions with the metal substrate. We show that the lowest unoccupied molecular orbital (LUMO) of tetracyanoquinodimethane (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.

Surface-orientation- and ligand-dependent quenching of the spin magnetic moment of Co porphyrins adsorbed on Cu substrates.

Porphyrin molecules are particularly interesting candidates for spintronic applications due to their bonding flexibility, which allows to modify their properties substantially by the addition or transformation of ligands. Here, we investigate the electronic and magnetic properties of cobalt octaethylporphyrin (CoOEP), deposited on copper substrates with two distinct crystallographic surface orientations, Cu(100) and Cu(111), with X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD). A significant magnetic moment is present in the Co ions of the molecules deposited on Cu(100), but it is completely quenched on Cu(111). Heating the molecules on both substrates to 500 K induces a ring-closure reaction with cobalt tetrabenzoporphyrin (CoTBP) as reaction product. In these molecules, the magnetic moment is quenched on both surfaces. Our XMCD and XAS measurements suggest that the filling of the dz2 orbital leads to a non-integer valence state and causes the quench of the spin moments on all samples except CoOEP/Cu(100), where the molecular conformation induces variations to the ligand field that lift the quench. We further employ density functional theory calculations, supplemented with on-site Coulomb correlations (DFT+U), to study the adsorption of these spin-bearing molecules on the Cu substrates. Our calculations show that charge transfer from the Cu substrates as well as charge redistribution within the Co 3d orbitals lead to the filling of the Co minority spin dz2 orbital, causing a 'turning off' of the exchange splitting and quenching of the spin moment at the Co magnetic centers. Our investigations suggest that, by this mechanism, molecule-substrate interactions can be used to control the quenching of the magnetic moments of the adsorbed molecules.

Vibrational Excitation Mechanism in Tunneling Spectroscopy beyond the Franck-Condon Model.

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 scanning tunneling microscope's tip over the molecule in great detail.

Interfering Tunneling Paths through Magnetic Molecules on Superconductors: Asymmetries of Kondo and Yu-Shiba-Rusinov Resonances.

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 line shapes.

Yu-Shiba-Rusinov States in the Charge-Density Modulated Superconductor NbSe2.

NbSe2 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 wave functions 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 NbSe2 a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.

π-Radical Formation by Pyrrolic H Abstraction of Phthalocyanine Molecules on Molybdenum Disulfide.

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 σ 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 favors the stabilization of this radical state.

Direct Imaging of the Induced-Fit Effect in Molecular Self-Assembly.

Molecular recognition is a crucial driving force for molecular self-assembly. In many cases molecules arrange in the lowest energy configuration following a lock-and-key principle. When molecular flexibility comes into play, the induced-fit effect may govern the self-assembly. Here, the self-assembly of dicyanovinyl-hexathiophene (DCV6T) molecules, a prototype specie for highly efficient organic solar cells, on Au(111) by using low-temperature scanning tunneling microscopy and atomic force microscopy is investigated. DCV6T molecules assemble on the surface forming either islands or chains. In the islands the molecules are straight-the lowest energy configuration in gas phase-and expose the dicyano moieties to form hydrogen bonds with neighbor molecules. In contrast, the structure of DCV6T molecules in the chain assemblies deviates significantly from their gas-phase analogues. The seemingly energetically unfavorable bent geometry is enforced by hydrogen-bonding intermolecular interactions. Density functional theory calculations of molecular dimers quantitatively demonstrate that the deformation of individual molecules optimizes the intermolecular bonding structure. The intermolecular bonding energy thus drives the chain structure formation, which is an expression of the induced-fit effect.

Electronic structure of an iron porphyrin derivative on Au(1 1 1).

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(1 1 1) 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.

Visualizing Intramolecular Distortions as the Origin of Transverse Magnetic Anisotropy.

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.

Tuning the Coupling of an Individual Magnetic Impurity to a Superconductor: Quantum Phase Transition and Transport.

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 (FeP) 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.

High-Resolution Vibronic Spectra of Molecules on Molybdenum Disulfide Allow for Rotamer Identification.

Tunneling spectroscopy is an important tool for the chemical identification of single molecules on surfaces. Here, we show that oligothiophene-based large organic molecules which only differ by single bond orientations can be distinguished by their vibronic fingerprint. These molecules were deposited on a monolayer of the transition metal dichalcogenide molybdenum disulfide (MoS2) on top of a Au(111) substrate. MoS2 features an electronic band gap for efficient decoupling of the molecular states. Furthermore, it exhibits a small electron-phonon coupling strength. Both of these material properties allow for the resolution of vibronic states in the range of the limit set by temperature broadening in our scanning tunneling microscope at 4.6 K. Using DFT calculations of the molecule in gas phase provides all details for an accurate simulation of the vibronic spectra of both rotamers.