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Atomic-scale Design of Majorana states and their Innovative Real-space Exploration

Periodic Reporting for period 1 - ADMIRE (Atomic-scale Design of Majorana states and their Innovative Real-space Exploration)

Reporting period: 2019-01-01 to 2020-06-30

Fault-tolerant topological quantum computation has become one of the most exciting research directions in modern condensed matter physics. As a key operation the braiding of non-Abelian anyons has been proposed theoretically. Such exotic quasiparticles can be realized as zero-energy Majorana bound states at the ends of one-dimensional magnetic nanowires in proximity to s-wave superconductors in the presence of high spin-orbit coupling. In contrast to previous attempts to realize such systems experimentally, based on the growth of semiconducting nanowires or the self-assembly of ferromagnetic nanowires on s-wave superconductors, we design Majorana bound states in artificially constructed single-atom chains with non-collinear spin-textures or 2D arrays of magnetic adatoms on elemental superconducting substrates using scanning tunnelling microscope (STM)-based atom manipulation techniques. We study at the atomic level the formation of Shiba bands as a result of hybridization of individual Shiba impurity states as well as the emergence of zero-energy Majorana bound states as a function of chain structure, length, and composition. Moreover, we construct model-type platforms, such as T-junctions, rings, and more complex network structures with atomic-scale precision as a basis for demonstrating the manipulation and braiding of Majorana bound states. We make use of sophisticated experimental techniques, such as spin-resolved scanning tunnelling spectroscopy (STS) at micro-eV energy resolution, Josephson tunnelling spectroscopy, and multi-probe STS under well-defined ultra-high vacuum conditions, in order to directly probe the nature of the magnetic state of the atomic wires, the spin-polarization of the emergent Majorana states, as well as the spatial nature of the superconducting order parameter in real space.
The unambiguous detection and identification of Majorana states in systems being controlled at the atomic level will push novel concepts of fault-tolerant topological quantum computation - one of the biggest goals for advancing computation for future needs of our society.
The ADMIRE project started very successfully based on the already available infrastructure at Hamburg University for performing the planned research as well as due to the successful recruitment of excellent Ph.D. students and postdocs right at the beginning of the project. This is reflected by 5 publications as well as 7 submitted manuscripts for publication within the first 1,5 years of the project. Two more publications resulting from this start-up phase are currently being prepared.
Among the 5 major goals I-V of our project as described above, we achieved 2 of them in the first reporting period, namely:
II) the detailed investigations of the existence of Majorana bound states in dependence of the atomic chain structure (atomic spacing, elemental species, etc.) and choice of superconducting substrate,
III) in-depth studies of the role of magnetic order (collinear ferromagnetic vs. non-collinear spin spiral) for the formation of Majorana bound states.
ad II) We investigated the emergence or absence of Majorana bound states in artificially built atomic chains of transition metals (Cr, Mn, Fe, and Co) on various elemental superconducting substrates (Re, Ta, La, and Nb). By employing STM-based single-atom manipulation techniques, we were able to tune the structure of the chains (linear vs. zig-zag), the interatomic spacings within the chains, as well as the chemical composition of the chains (pure vs. hybrid chains). Moreover, we have varied the crystallographic direction of the atomic chains with respect to the crystalline lattices of the superconducting substrates. The latter were studied with different crystal structure and surface orientations.
ad III) By tuning the structure and chemical composition of the atomic chains as well as the chemical nature of the superconducting substrate, we were able to tailor the magnetic ground state of the atomic chains, being either collinear (ferromagnetic or antiferromagnetic) or non-collinear (spin spiral states). In the latter case, it was possible to tune the magnetic period of the spin spirals by an appropriate choice of magnetic adatoms and superconducting substrates.
The experiments and theoretical studies within the first reporting period closely followed the original workplan, thereby contributing to 5 of the total of 6 tasks of the original workplan.
Our experimental approach toward the unambiguous detection and manipulation of Majorana states, based on the direct combination of single-atom manipulation techniques for constructing well-defined 1D and 2D model-type magnet-superconductor hybrid systems with atomic-resolution spin-sensitive imaging and spectroscopy techniques, is worldwide unique and has already led to fundamentally new insight into the conditions for the emergence of Majorana states, taking details of the atomic, electronic, and spin structure of these hybrid systems into account. The direct comparison between theoretical predictions, experimental results and numerical simulations is greatly facilitated by the atomic-scale design and control of the structure and chemical composition of the investigated magnet - superconductor hybrid systems.
Already within the first reporting period, we could demonstrate the emergence of Majorana bound states in artificially fabricated atomic Fe chains on elemental superconducting substrates as well as the emergence of chiral Majorana edge modes in 2D magnet - superconductor hybrid systems with atomically engineered interfacial layers.
Moreover, we have developed a novel atomic-resolution spin-sensitive imaging techniques based on the 100% spin-polarized Shiba states of magnetic impurities at the front ent of sharp superconducting probe tips, allowing high-contrast mapping of artificially built atomic-scale magnets as well as 1D and 2D arrays of magnetic adatoms on surfaces.
Based on the atomic-resolution spin mapping capabilities, we discovered a novel type of complex non-collinear spin texture, namely a magnetic triple-Q structure, in the framework of the ADMIRE project. If this triple-Q structure is brought in contact with an elemental superconductor, topological superconductivity as well as Majorana modes can emerge, as we have predicted recently in collaboration with our international partners in Chicago and Melbourne.
Another major achievement within the first reporting period was the demonstration of magnetic skyrmions in Pd/Fe/Ir triple-layers grown on superconducting Re(0001). Magnetic skyrmions interacting with superconductors are theoretically predicted to host Majorana states as well. We will test these predictions experimentally within the second reporting period.
Our ultimate goal by the end of the project is the demonstration of the manipulation of Majorana bound states, i.e. their creation, annihilation, adiabatic motion and braiding in artificially built model-type structures. We have now numerous types of 1D and 2D platforms available after the first reporting period so that we can go for the next steps toward the realization of Majorana state manipulations.
Majorana bound states in artificially built magnetic atom chains on an elemental superconductor
Chiral Majorana edge modes of a 2D magnet-superconductor hybrid system