Browsing by Author "Ojanen, Teemu, Dr., Aalto University, Department of Applied Physics, Finland"

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  • Engineering low-dimensional topological superconductivity in magnetic heterostructures
    (2018) Pöyhönen, Kim
     School of Science | Doctoral dissertation (article-based)
    Topological matter, which derives its properties from the overall topology of the bulk material, has in the past few decades emerged as one of the most important topics in condensed-matter physics. As a consequence of the non-local character of these systems, their exotic properties -- such as conducting edges on bulk insulators, or fractally-charged quasiparticles -- are remarkably robust to perturbations, potentially enabling a multitude of applications. Topological superconductors, in particular, have attracted significant interest, as they are predicted to support zero-energy Majorana bound states, quasiparticles that arise as equal superpositions of electrons and holes. A characteristic feature of Majorana bound states are their non-Abelian exchange statistics, which could see future use in, for example, topological quantum computers. It is known that embedded point-like magnetic impurities in a superconducting substrate support slowly-decaying subgap bound states known as Yu-Shiba-Rusinov states. The bands created when these Yu-Shiba-Rusinov states hybridise have symmetry properties which make them especially suitable as a platform for topological superconductivity in both one and two dimensions. The main contribution of this dissertation lies in studying this type of system in mean-field BCS approach, using both analytical and numerical methods with focus on topological properties. The overarching goal is to contribute to the ongoing search for systems in which topological superconductivity can be realised and experimentally observed.  In Publications I-III we study the topological properties of systems based on one-dimensional chains of magnetic impurities, focusing on analytically solving for the topological phase transitions and spectral properties of the systems. In Publication I the focus is on coupled chains with nearest-neighbour hopping, while in Publications II-III, we move on to consider systems with infinite hopping, developing a general framework for approaching Yu-Shiba-Rusinov-based topological superconductors. In Publications V-VI we consider generalisations of the basic Yu-Shiba-Rusinov lattice; in the former, by making use of non-pointlike nanomagnets, and in the latter, by abandoning lattice structure altogether and showing that topologically nontrivial phases can arise even in amorphous systems with sufficiently dense impurities. In Publication IV, we instead examine a magnetic skyrmion coupled to an intrinsic two-dimensional topological superconductor. We find that the character of the bound states depends on the type of skyrmion and the form of the superconducting pairing terms, allowing the bound-state properties to act as a probe of the underlying system.
  • Majorana and Weyl Modes in Designer Materials
    (2018) Westström, Alex
     School of Science | Doctoral dissertation (article-based)
    Topology has recently become one of the main themes of research in condensed-matter physics. Not only does the theory of topological materials predict novel phenomena in already well-established areas of physics, it also suggests intriguing applications in future technology. Topological phases exist in both gapped and gapless systems. In gapped topological systems, the bulk is insulating, but the boundary hosts zero-energy modes. Gapless topological phases, on the other hand, exhibit non-trivial phenomena within the bulk itself. This thesis consists of two parts: in the first part, the focus is on topological superconductors, which are gapped systems where the boundary modes are Majorana zero modes -- condensed-matter analogues of the Majorana fermion. Majorana zero modes are neither fermions nor bosons but obey an exotic form of exchange statistics envisaged to be employable in future quantum-computer architectures. This alone has makes finding implementations of topological superconductivity one of the central objectives for researchers in the field. The second part involves Weyl semimetals, which are three-dimensional gapless topological systems. Much like the Majorana zero modes in topological superconductors, the low-energy modes in Weyl semimetals have a high-energy counterpart, namely the Weyl fermion. The connection between Weyl semimetals and Weyl fermions brings high-energy physics into a low-temperature setting, making relativistic phenomena accessible in table-top experiments. Moreover, the novel transport properties emerging from these effects, combined with non-trivial topology, make Weyl semimetals a prospective building block in future electronics. In Publications I-III, we study one-dimensional chains of magnetic atoms deposited on a conventional superconductor. This setup has previously been studied in a low-energy limit for dilute chains. In Publication I and II, we extend the theory to also incorporate parameter regimes beyond this limit. In Publication III, we study the consequences of two kinds of disorder in these systems: vacancies and disordered coupling between the magnetic atoms and the superconductor. In Publication IV, we apply the machinery developed in Publications I-III to study chains of scalar impurities on top of an intrinsic two-dimensional topological superconductor. In Publication V, we introduce Weyl metamaterials as a platform in which to realize effective curved spaces and gauge fields. A Weyl semimetal owes its existence to the breaking of at least time-reversal or inversion symmetry. By making the symmetry-breaking fields inhomogeneous, the Weyl-like excitations experience an effective curved space and gauge field. We develop a mathematical framework which provides a direct route between the symmetry-breaking fields, and the curved space and gauge field. We also present an example of a geometry with lens-like trajectories.
  • Topological superconductivity in magnetic adatom lattices
    (2016) Röntynen, Joel
     School of Science | Doctoral dissertation (article-based)
    Topological matter has emerged as one of the most prominent research fronts in condensed matter physics over the past three decades. The discovery of the role of topology in materials has shaped our fundamental understanding of how the constituents of matter organize themselves to produce various phases. Topology in these systems manifests as boundary states and exotic quasiparticles, whose intriguing properties are anticipated to facilitate various technological applications. In this thesis I have contributed to the search for topological superconductivity, which is expected to support localized, particle-like excitations called Majorana bound states. Majorana bound states break the dichotomy of bosons and fermions by obeying non-Abelian exchange statistics. Hence a Majorana bound state would be a manifestation of a fundamentally new type of physics. Furthermore, Majorana braiding is envisioned to be utilized in topologically protected quantum computing, which could revolutionize the future of computing. The experimental discovery of Majorana bound states is an outstanding goal in condensed matter physics at the moment. The systems investigated in this thesis consists of magnetic adsorbed atoms (adatoms) deposited on top of a conventional superconductor. In publications I and II we investigated the appearance of Majorana bound states in adatom chains. The main result in publication I is that coupled chains are more likely to exhibit Majorana bound states than uncoupled chains. In publication II we showed that a supercurrent can be used to control the topological phase, which could be helpful for the manipulation of Majorana bound states. In publications III and IV we showed that two-dimensional adatom structures support a generalization of px+ipy superconductivity, making it an interesting addition to the list of materials with unconventional superconductivity. The complex, mosaic-like structure of the topological phase diagram is remarkably rich due to long-range electron hopping. The number of propagating Majorana modes at the boundary is given by a topological invariant called a Chern number. We predicted that for typical experimentally available materials this number can be much larger than unity. The abundance of various topological phases with a large number of protected edge states makes the studied system potentially one of the richest topological materials discovered so far. Since two-dimensional structures in such systems are next in line to be studied experimentally, magnetic adatom structures provide a promising platform for realizing exotic phases of matter of fundamental interest.