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Publication# Scanning Tunneling Spectroscopy with Superconducting Junctions

Abstract

This thesis contains two major topics, the restriction of tunneling to only a few channels in the scanning tunneling microscope (STM) and the interaction of local magnetic impurities with superconductivity. At a temperature of 15mK, the quantum back-action of the electromagnetic environment in an STM junction becomes prominent. It influences the tunneling process, and by that inevitably also the spectroscopy of physical phenomena. We demonstrate that the macroscopic tip shape strongly defines this back-action. It can be reduced by increasing the tip wire diameter. This increases the capacitance of the junction, and thereby significantly enhances the spectroscopic energy resolution. Modeling this effect with P(E)-theory, we extrapolate that the electromagnetic environment of the junction influences measurements in the STM up to a temperature of 1K. This result helps establish a direct correspondence between the P(E)-model and the energy resolution of the STM. We further study the tunneling process by constructing a single-channel junction of an Al adatom on an Al(100) crystal and the single apex atom of an Al tip. We provide proof that the transport in this junction is strongly limited to a single channel by analyzing Andreev reflection spectra over a wide conductance range up to the quantum of conductance. With this junction we show how the Josephson effect deviates from the many channel and low transmission model by Ambegaokar and Baratoff. We also present a model, based on the full Andreev bound state relation for the few channel limit, which accounts for transmission dependencies and multiple Cooper pair tunneling. Modeling the Josephson effect in our junction this model reproduces the experimental data in great detail. Regarding the determination of the Josephson coupling energy in STM-experiments, we expect at least 0.6% and up to 2.6% deviation from the linear model at a conductance of 0.1G0 and up to 17% at 0.5G0. In the normal conducting state of this junction the environmental back-action manifests as a transmission reduction around zero bias, known as the dynamical Coulomb blockade (DCB). Here we test the predicted vanishing of the DCB for transmissions towards unity. Our data support this expectation. These results suggest that the transport process becomes less sensitive to the environmental back-action with increasing channel transmission. Concerning pair breaking potentials in a multi-band superconductor, we study Fe-doped NbSe2 with a V-tip. We demonstrate that Yu-Shiba-Rusinov (YSR) resonances emerge not only in the energy-gap but also outside of it, at the position of coherence peaks, where they are significantly broadened. We demonstrate a correspondence of the YSR-state lifetime to the imaginary part of the superconducting order parameter. To do so we compare the experimental peak-width to peak-energy-position dependence with a T-matrix scattering model, taking into account the two-band superconductivity of NbSe2, with inter-band coupling and magnetic background scattering. Our results show that YSR-resonances can be used to probe the imaginary part of the superconducting order parameter. We suspect that many asymmetries observed in spectra of the superconducting gap are related to this effect. We collate some early results of the local Josephson critical current in NbSe2. We find local variations around the embedded Fe impurities suggesting that the order parameter is reduced by about 20%.

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Scanning tunneling microscope

A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IB

Superconductivity

Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these

Scanning probe microscopy

Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans the specimen. SPM was founded in 1981, with the invention of the scanning tunn

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This thesis reports measurements concerning quantum size effects of single crystalline metallic islands by using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Different sample systems are presented in the following chapters. In chapter 2, several aspects of quantum well states (QWS) of Pb ultrathin islands grown on Si(111) substrate are reported. The differential conductance spectra of QWS can be understood by discrete energy levels with linewidth broadening because of finite quasiparticle lifetime. Using low temperature scanning tunneling spectroscopy, we studied the linewidth of unoccupied quantum-well states (QWS) in Pb islands, grown on Si(111) on two different Pb/Si interfaces, of thicknesses between 7 and 22 monolayers. A quantitative analysis of the differential conductance spectra allowed us to determine the QWS lifetime broadening as a function of energy, showing agreement with 3D Fermi-liquid theory, as well as the electron-phonon (e-ph) contribution between 5 and 50 K. Layer-dependent ab initio calculations of the e-ph linewidth contributions are in excellent agreement with the data. Importantly, the sum of the calculated e-e and e-ph lifetime broadening follows the experimentally observed quadratic energy dependence. In chapter 3, studies investigating reduction of the superconducting gap of ultrathin Pb islands are presented. The energy gap Δ of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Δ was found to decrease from its bulk value as a function of inverse island thickness. Corresponding Tc values, estimated using bulk gap-to-Tc ratio, are in quantitative agreement with ex situ magnetic susceptibility measurements, however, in strong contrast to previous scanning probe results. Layer-dependent ab initio density functional calculations for free-standing Pb films show that the electron-phonon coupling constant, determining Tc, decreases with diminishing film thickness. In chapter 4, we present preliminary results on single electron tunneling and Coulomb blockade phenomena of metallic islands decoupled from a Ag(111) substrate by dielectric NaCl layers. Using low temperature STM/STS, the geometry of the metallic island can be determined unambiguously and the single electron tunneling properties are characterized. Using orthodox theory of single electron tunneling, the tunneling spectra can be reproduced qualitatively. Despite minor quantitative disagreement between data and simulations, the parameters of the double barrier tunneling junction, including the capacitances and the resistances of both junctions, as well as the residual charge, can be determined.

Magnetic impurities generate a wealth of phenomena on surfaces. On metals, conducting electrons screen the magnetic moment giving rise to the Kondo effect. On superconductors, the Yu-Shiba-Rusinov (YSR) states emerge inside the superconducting gap due to the exchange coupling. In this thesis, we use a scanning tunneling microscope (STM) with a base temperature of 10mK to study magnetic impurities on surfaces. This thesis contains two parts, the interplay between magnetic impurities and superconductivity as well as the tunneling processes between YSR states.Concerning the interplay between magnetic impurities and superconductivity, the single impurity Anderson model (SIAM) offers a consistent picture, in which the impurity substrate coupling is a central parameter of experimental relevance. For YSR phenomena, the mean field (MF) approximation is usually sufficient which gives analytical results for a quantitative interpretation of the experimental data. We tune the coupling by the atomic forces in the junction and quantitatively identify the key role of the coupling in the YSR energy. We further investigate multiple Andreev reflections (MARs) involving a single YSR state, confirming the absence of a spin forbidden family of MARs thereby proving the spin non-degeneracy of the YSR states experimentally.The presence of YSR impurities not only gives rise to peaks in the tunneling spectra, but also influences the superconducting ground state. At a small coupling, the impurity spin is unscreened, which results in a pi phase shift in the Josephson transport. At a large coupling, the impurity spin is screened and the phase is 0. The change of the YSR ground state qualifies as a quantum phase transition (QPT). We observe a significant step in the Josephson current when tuning the coupling across the QPT, which signals the 0-pi transition and the change of the ground state.We then go beyond the MF approximation and include correlation effects in the SIAM to fit the Kondo effect in the magnetic field. We present the scaling between the YSR energy and the Kondo temperature connected by the SIAM. Despite the close relation between the two phenomena, the question remains that to which extent the correlation effects persist in the superconducting state. On this, we show that the correlation effects manifest as an offset current in the YSR measurements.Conventionally, the STM tip only serves as a probe to unravel the sample properties. However, in principle the tip, sample and junction form one quantum system. With the capability to controllably introduce YSR states of desired properties on the tip apex (the YSR-STM), we construct a minimal tunnel junction between two discrete levels, a YSR state on the sample and a YSR state on the tip apex. The tunneling between two YSR states, Shiba-Shiba tunneling, features sharp current peaks, the area of which reveals the relaxation dynamics. We further show that the spin plays an important role in Shiba-Shiba tunneling and we find a behavior consistent with paramagnetic impurities. To conclude, this thesis presents multiple experimental aspects of a single YSR state quantitatively explained by the SIAM, both on the MF level and in the fully correlated situation. The possibility to functionalize the STM tip with a YSR state opens more possibilities, and we show the tunneling between two YSR states as a first application, laying the basis for possible extension of the YSR-STM to more scenarios.

The aim of this thesis is to characterize the properties of a Josephson junction in a Scanning Tunneling Microscope (STM) at millikelvin temperatures and to implement Josephson STM (JSTM) as a versatile probe at the atomic scale. To this end we investigate the I(V) tunneling characteristics of the Josephson junction in our STM at a base temperature of 15 mK by means of current-biased and voltage-biased experiments. We find that in the tunneling regime, the Josephson junction is operated in the dynamical Coulomb blockade (DCB) regime in which the sequential tunneling of Cooper pairs dominates the tunneling current. Employing P(E)-theory allows us to model experimental I(V) characteristics from voltage-biased experiments and determine experimental values of the Josephson critical current in agreement to theory. Moreover, we observe a breakdown of P(E)-theory for experiments at large values of the tunneling conductance on the order of the quantum of conductance, which could indicate that the coherent tunneling of Cooper pairs strongly contributes to the tunneling current in this limit. We also observe that the Josephson junction in an STM at temperatures well below 100 mK is highly sensitive to its electromagnetic environment that results from its tiny junction capacitance of a few femtofarads. The combination of the experimental results with numerical simulations reveals that the immediate environment of the Josephson junction in an STM is frequency-dependent and, additionally, that a typical STM geometry shares the electromagnetic properties of a monopole antenna with the STM tip acting as the antenna. Comparing the I(V) curves of voltage-biased and current-biased experiments, we observe that the time evolution of the phase is strongly effected by dissipation due to quasiparticle excitations. From investigations on the retrapping current we show first that the temporal evolution of the junction phase in our STM satisfies a classical equation of motion. Second, we can determine two different channels for energy dissipation of the junction phase. For tunneling resistance values RN< 150 kOhm the junction dissipates via Andreev reflections whereas for larger values of RN