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Magnetic systems underlie the physics of quantum mechanics when reaching the limit of few or even single atoms. This behavior limits the minimum size of magnetic bits in data storage devices as spontaneous switching of the magnetization leads to the loss of information. On the other hand, exactly these quantum mechanic properties allow to use such systems in quantum computers. Proposals to realize qubits involve the spin states of single atoms as well as topologically protected Majorana zero modes, that emerge in coupled systems of magnetic atoms in proximity to a superconductor. In order to implement and control the proposed applications, a detailed understanding of atomic spins and their interaction with the environment is required.
In this thesis, two different systems of magnetic adatoms coupled to metallic and superconducting surfaces are studied by means of scanning tunneling microscopy (STM) and spectroscopy: Co atoms on the clean Cu(111) were among the first systems exhibiting signatures of the Kondo effect in an individual atom. Yet, a recent theoretical work proposed an alternative interpretation of these early experimental results, involving a newly described many-body state. Spin-averaged and -polarized experiments in high magnetic fields presented in this thesis confirm effects beyond the Kondo effect that determine the physics in these Co atoms and suggest a potentially even richer phenomenology than proposed by theory.
The second studied system are single and coupled Fe atoms on the superconducting Nb(110) surface. Magnetic impurities on superconducting surfaces locally induce Yu-Shiba-Rusinov (YSR) states inside the superconducting gap due to their pair breaking potential. Coupled systems of such impurities exhibit YSR bands and, if the bands cross the Fermi level such that the band structure is inverted, host Majorana zero modes. Using the example of Fe atoms on Nb(110), the YSR states’ dependence on the adatom–substrate interaction as well as the interatomic YSR state coupling is investigated. In the presence of oxygen on the Nb surface, the adatom–substrate interaction is shown to be heavily modified and the YSR states are found to undergo a quantum phase transition, which can be directly linked to a modified Kondo screening.
STM tips functionalized with CO molecules allow to resolve self-assembled one-dimensional chains of Fe atoms on the clean Nb(110) surface to study the YSR states’ coupling. Mapping out the states’ wave functions reveals their symmetry, which is shown to alter as a function of the states’ energy and number of atoms in the chain. These experimental results are reproduced in a simple tight-binding model, demonstrating a straightforward possibility to describe also more complex YSR systems toward engineered, potentially topologically non-trivial states.
Relativistic effects crucially influence the fundamental properties of many quantum materials. In the accelerated reference frame of an electron, the electric field of the nuclei is transformed into a magnetic field that couples to the electron spin. The resulting interaction between an electron spin and its orbital angular momentum, known as spin-orbit coupling (SOC), is hence fundamental to the physics of many condensed matter phenomena. It is particularly important quantitatively in low-dimensional quantum systems, where its coexistence with inversion symmetry breaking can lead to a splitting of spin degeneracy and spin momentum locking. Using the paradigm of Landau Fermi liquid theory, the physics of SOC can be adequately incorporated in an effective single particle picture. In a weak coupling approach, electronic correlation effects beyond single particle propagator renormalization can trigger Fermi surface instabilities such as itinerant magnetism, electron nematic phases, superconductivity, or other symmetry broken states of matter.
In this thesis, we use a weak coupling-based approach to study the effect of SOC on Fermi surface instabilities and, in particular, superconductivity. This encompasses a weak coupling renormalization group formulation of unconventional superconductivity as well as the random phase approximation. We propose a unified formulation for both of these two-particle Green’s function approaches based on the notion of a generalized susceptibility.
In the half-Heusler semimetal and superconductor LuPtBi, both SOC and electronic correlation
effects are prominent, and thus indispensable for any concise theoretical description. The metallic and weakly dispersive surface states of this material feature spin momentum locked Fermi surfaces, which we propose as a possible domain for the onset of unconventional surface superconductivity. Using our framework for the analysis of Fermi surface instability and combining it with ab-initio density functional theory calculations, we analyse the surface band structure of LuPtBi, and particularly its propensity towards Cooper pair formation. We study how the presence of strong SOC modifies the classification of two-electron wave functions as well as the screening of electron-electron interactions. Assuming an electronic mechanism, we identify a chiral superconducting condensate featuring Majorana edge modes to be energetically favoured over a wide range of model parameters.