Yu-Shiba-Rusinov bands in a self-assembled kagome lattice of magnetic molecules.

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 compelling platform for realizing 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 inside the superconducting energy gap allow for long-range coupling and induced pairing correlations, motivating further studies to resolve possible spin-liquid or Kondo-lattice-type behavior.

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.

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.

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.

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.

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.

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.

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.

Disentangling electron- and electric-field-induced ring-closing reactions in a diarylethene derivative on Ag(1 1 1).

Using scanning tunneling microscopy and spectroscopy we investigate the adsorption properties and ring-closing reaction of a diarylethene derivative (C5F-4Py) on a Ag(1 1 1) 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.

Visualizing the Role of Molecular Orbitals in Charge Transport through Individual Diarylethene Isomers.

Diarylethene molecules are prototype molecular switches with their two isomeric forms exhibiting strikingly different conductance, while maintaining similar length. We employed low-temperature scanning tunneling microscopy (STM) to resolve the energy and the spatial extend of the molecular orbitals of the open and closed isomers when lying on a Au(111) surface. We find an intriguing difference in the extension of the respective HOMOs and a peculiar energy splitting of the formerly degenerate LUMO of the open isomer. We then lift the two isomers with the tip of the STM and measure the current through the individual molecules. By a simple analytical model of the transport, we show that the previously determined orbital characteristics are essential ingredients for the complete understanding of the transport properties. We also succeeded in switching the suspended molecules by the current, while switching the ones which are in direct contact to the surface occurs nonlocally with the help of the electric field of the tip.

Electronic Structure and Luminescence of Quasi-Freestanding MoS2 Nanopatches on Au(111).

Monolayers of transition metal dichalcogenides are interesting materials for optoelectronic devices due to their direct electronic band gaps in the visible spectral range. Here, we grow single layers of MoS2 on Au(111) and find that nanometer-sized patches exhibit an electronic structure similar to their freestanding analogue. We ascribe the electronic decoupling from the Au substrate to the incorporation of vacancy islands underneath the intact MoS2 layer. Excitation of the patches by electrons from the tip of a scanning tunneling microscope leads to luminescence of the MoS2 junction and reflects the one-electron band structure of the quasi-freestanding layer.

Narrow-Line Single-Molecule Transducer between Electronic Circuits and Surface Plasmons.

A molecular wire containing an emitting molecular center is controllably suspended between the plasmonic electrodes of a cryogenic scanning tunneling microscope. Passing current through this circuit generates an ultranarrow-line emission at an energy of ≈1.5 eV which is assigned to the fluorescence of the molecular center. Control over the linewidth is obtained by progressively detaching the emitting unit from the surface. The recorded spectra also reveal several vibronic peaks of low intensities that can be viewed as a fingerprint of the emitter. Surface plasmons localized at the tip-sample interface are shown to play a major role in both excitation and emission of the molecular excitons.

Pulling and Stretching a Molecular Wire to Tune its Conductance.

A scanning tunnelling microscope is used to pull a polythiophene wire from a Au(111) surface while measuring the current traversing the junction. Abrupt current increases measured during the lifting procedure are associated with the detachment of molecular subunits, in apparent contradiction with the expected exponential decrease of the conductance with wire length. Ab initio simulations reproduce the experimental data and demonstrate that this unexpected behavior is due to release of mechanical stress in the wire, paving the way to mechanically gated single-molecule electronic devices.

Electroluminescence of a polythiophene molecular wire suspended between a metallic surface and the tip of a scanning tunneling microscope.

The electroluminescence of a polythiophene wire suspended between a metallic surface and the tip of a scanning tunneling microscope is reported. Under positive sample voltage, the spectral and voltage dependencies of the emitted light are consistent with the fluorescence of the wire junction mediated by localized plasmons. This emission is strongly attenuated for the opposite polarity. Both emission mechanism and polarity dependence are similar to what occurs in organic light emitting diodes (OLED) but at the level of a single molecular wire.

Oligothiophene nanorings as electron resonators for whispering gallery modes.

Structural and electronic properties of oligothiophene nanowires and rings synthesized on a Au(111) surface are investigated by scanning tunneling microscopy. The spectroscopic data of the linear and cyclic oligomers show remarkable differences which, to a first approximation, can be accounted by considering electronic state confinement to one-dimensional boxes having, respectively, fixed and periodic boundary conditions. A more detailed analysis shows that polythiophene must be treated as a ribbon (i.e., having an effective width) rather than a purely 1D structure. A fascinating consequence is that the molecular nanorings act as whispering gallery mode resonators for electrons, opening the way for new applications in quantum electronics.