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.

Highly customized 1010†nm, ns-pulsed Yb-doped fiber amplifier as a key tool for on-demand single-photon generation.

The development of highly customized technical devices is a decisive feature of technically complex setups, as frequently observed in quantum experiments. This paper describes the development and realization of an Yb-doped all-fiber amplifier system designed for such a special application, more specifically, an on-demand single-photon source based on four-wave mixing with rubidium Rydberg atoms. The laser is capable of generating bandwidth-limited configurable nanosecond pulses up to peak powers of >100 W and with pulse repetition frequencies (PRF) between 50 Hz and 1 MHz at selectable wavelengths (1008-1024 nm). Especially the amplification of the 1010 nm reference seed at the lower edge of the amplification range for Yb-based fibers is challenging and tends to produce amplified spontaneous emission (ASE) at higher wavelengths. To achieve high ASE suppression, particularly at low pulse repetition frequencies, two acousto-optical modulators (AOM) are utilized both for pulse picking and for temporal filtering. The synchronization between pulse repetition frequency and AOM driver signal allows pulse amplitude fluctuations to be kept below 1%, while ASE is suppressed by at least 85 dB (PRF = 1 MHz) and 65 dB (PRF = 1 kHz).

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.

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.

Wave-Function Hybridization in Yu-Shiba-Rusinov Dimers.

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.

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.

Exploring a Proximity-Coupled Co Chain on Pb(110) as a Possible Majorana Platform.

Linear 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 , S. et al., Science 2014 , 346 , 602 - 607 ]. 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 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.

Orbital Picture of Yu-Shiba-Rusinov Multiplets.

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.

Tuning the Magnetic Anisotropy of Single Molecules.

The magnetism of single atoms and molecules is governed by the atomic scale environment. In general, the reduced symmetry of the surrounding splits the d states and aligns the magnetic moment along certain favorable directions. Here, we show that we can reversibly modify the magnetocrystalline anisotropy by manipulating the environment of single iron(II) porphyrin molecules adsorbed on Pb(111) with the tip of a scanning tunneling microscope. When we decrease the tip-molecule distance, we first observe a small increase followed by an exponential decrease of the axial anisotropy on the molecules. This is in contrast to the monotonous increase observed earlier for the same molecule with an additional axial Cl ligand ( Nat. Phys. 2013 , 9 , 765 ). We ascribe the changes in the anisotropy of both species to a deformation of the molecules in the presence of the attractive force of the tip, which leads to a change in the d level alignment. These experiments demonstrate the feasibility of a precise tuning of the magnetic anisotropy of an individual molecule by mechanical control.

Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy.

The type I superconductor lead (Pb) has been theoretically predicted to be a two-band superconductor. We use scanning tunneling spectroscopy (STS) to resolve two superconducting gaps with an energy difference of 150 µeV. Tunneling into Pb(111), Pb(110), and Pb(100) crystals reveals a strong dependence of the two coherence peak intensities on the crystal orientation. We show that this is the result of a selective tunneling into the two bands at the energy of the two coherence peaks. This is further sustained by the observation of signatures of the Fermi sheets in differential conductance maps around subsurface defects. A modification of the density of states of the two bands by adatoms on the surface confirms the different orbital character of each of the two subbands.

End States and Subgap Structure in Proximity-Coupled Chains of Magnetic Adatoms.

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 smaller than previously extracted from experiment. 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.

Tunneling Processes into Localized Subgap States in Superconductors.

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 through impurity-induced Shiba bound states is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes, allowing us to extract information on quasiparticle transitions and lifetimes.

Change of the magnetic coupling of a metal-organic complex with the substrate by a stepwise ligand reaction.

The surface-assisted intramolecular ligand reaction of a porphyrin molecule adsorbed on Au(111) is studied by scanning tunneling microscopy and spectroscopy. The temperature-induced stepwise transformation of iron octaethylporphyrin proceeds via a concentric electrocyclic ring closure, with the final product iron tetrabenzoporphyrin being identified by its characteristic Kondo resonance. Along with the transformation of the organic ligand, changes in the magnetic fingerprint are observed, indicating an increasing coupling of the iron spin with the substrate electrons.

Magnetic coupling of Gd3N@C80 endohedral fullerenes to a substrate.

Using magnetic endohedral fullerenes for molecular spintronics requires control over their encapsulated magnetic moments. We show by field-dependent x-ray magnetic circular dichroism measurements of Gd3N@C80 endohedral fullerenes adsorbed on a Cu surface that the magnetic moments of the encapsulated Gd atoms lie in a 4f7 ground state and couple ferromagnetically to each other. When the molecules are in contact with a ferromagnetic Ni substrate, we detect two different Gd species. The more abundant one couples antiferromagnetically to the Ni, whereas the other one exhibits a stronger and ferromagnetic coupling to the substrate. Both of these couplings to the substrate can be explained by an indirect exchange mechanism mediated by the carbon cage. The origin of the distinctly different behavior may be attributed to different orientations and thus electronic coupling of the carbon cage to the substrate, as revealed by scanning tunneling microscopy of the fullerenes on Cu.

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.

Control of Oxidation and Spin State in a Single-Molecule Junction.

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.

Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime.

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 compared to the superconducting pairing energy Δ. When the experimental temperature suppresses Kondo screening, but preserves superconductivity, i.e., when Δ/k B > T > T K (k B is Boltzmann's constant and T K the Kondo temperature), this description fails. Here, we explore this temperature range in a set of manganese phthalocyanine molecules decorated with ammonia on Pb(111). We show that these molecules suffice the required energy conditions by exhibiting weak-coupling Kondo resonances. We correlate the Yu-Shiba-Rusinov bound states energy inside the superconducting gap with the intensity of the Kondo resonance. The observed correlation 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.

Magnetic anisotropy in Shiba bound states across a quantum phase transition.

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 tunnelling 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. Our results provide experimental insights into the phase diagram of a magnetic impurity on a superconducting host and shine light on the effects induced by magnetic anisotropy on many-body interactions.