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Publication# Quantum size effects in ultrathin metallic islands

Résumé

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.

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Scanning tunneling spectroscopy

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I-Po Hong, François Patthey, Wolf-Dieter Schneider

The energy gap Delta of superconducting Pb islands grown on Si(111) was probed in situ between 5 and 60 monolayers by low-temperature scanning tunneling spectroscopy. Delta was found to decrease from its bulk value as a function of inverse island thickness. Corresponding T-c values, estimated using bulk gap-to-T-c 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 freestanding Pb films show that the electron-phonon coupling constant, determining T-c, decreases with diminishing film thickness.

2009This 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%.

I-Po Hong, François Patthey, Wolf-Dieter Schneider

Using low-temperature scanning tunneling spectroscopy at 5 and 50 K, we studied the linewidth of unoccupied quantum-well states in ultrathin Pb islands, grown on Si(111) on two different Pb/Si interfaces. A quantitative analysis of the differential conductance spectra allowed us to determine the electron-electron (e-e), electron-phonon (e-ph) and the interface and defect contributions to the lifetime. Layer-dependent ab initio calculations of the e-ph linewidth contribution 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.

2009