Periodic Reporting for period 4 - ADMIRE (Atomic-scale Design of Majorana states and their Innovative Real-space Exploration)
Reporting period: 2023-07-01 to 2024-12-31
Fault-tolerant topological quantum computation has become one of the most exciting research directions in modern condensed matter physics. Making use of topologically protected quantum bits can solve the major problem of quantum computing, namely high error rates as a result of quantum decoherence effects. As a key operation of topological quantum computation, 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.
The ADMIRE project focussed on fundamental studies of the emergence of Majorana states in bottom-up fabricated magnet – superconductor hybrid systems. The experimental investigations concentrated on model-type systems which were prepared and thoroughly characterized with atomic level precision. Atomic-scale characterization at low energy-scales was performed by low-temperature spin-averaged and spin-polarized scanning tunnelling microscopy (STM) and spectroscopy (STS).
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, has 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 has been greatly facilitated by the atomic-scale design and control of the structure and chemical composition of the investigated magnet - superconductor hybrid systems.
The ADMIRE project focussed on fundamental studies of the emergence of Majorana states in bottom-up fabricated magnet – superconductor hybrid systems. The experimental investigations concentrated on model-type systems which were prepared and thoroughly characterized with atomic level precision. Atomic-scale characterization at low energy-scales was performed by low-temperature spin-averaged and spin-polarized scanning tunnelling microscopy (STM) and spectroscopy (STS).
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, has 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 has been greatly facilitated by the atomic-scale design and control of the structure and chemical composition of the investigated magnet - superconductor hybrid systems.
For the 1D systems, we were able to demonstrate the emergence of Majorana bound states in artificially fabricated atomic Fe and Mn chains on elemental superconducting substrates (Re, Nb). In particular, we have applied scanning tunneling microscopy (STM) based single-atom manipulation techniques to create perfect, disorder-free atomic spin chains on atomically clean elemental superconducting substrates and demonstrated the non-local nature of the Majorana bound states at both ends of such chains. Moreover, we have successfully applied Bogoliubov quasiparticle interference analysis of the 1D atomic chains, thereby revealing their low-energy in-gap band structure from which the topological nature of the hybrid magnet-superconductor system could be proven.
In Fe-chains on Re(0001) the observed zero-energy states are compatible with Majorana states. Also ab-initio based theory simulations supported this interpretation. However, excited bulk states overlap with these zero-energy states due to the limited energy resolution of the STS measurements at 300 mK. To observe isolated Majorana states inside a hard gap would require a reduction of temperature by a factor of 10, or the use of a superconducting substrate with a significantly higher transition temperature like niobium.
Indeed, Mn[1-10]-chains on Nb(110) feature clear zero-energy states for certain chain lengths. The experimental measurement of the low-energy states as a function of chain length revealed an oscillatory behavior, which can be understood by assuming hybridized Majorana states. Longer chains would be required to obtain non-interacting, isolated Majorana states. Importantly, the observed length dependent energy splitting oscillations can be regarded as a "smoking gun" for the existence of Majorana states since trivial states would not show such behaviour.
Mn[001]-chains on Nb(110) were shown to possess a gap within the Shiba bands which is reminiscent of a gapped Dirac Hamiltonian, thereby proving that the gap is of topological origin. The associated zero-energy states do not possess significant spectral weight at the chain ends. Instead, they feature a standing-wave pattern with spectral weight pushed to the sides of the chain. Extensive (ab-initio based) theoretical modeling reproduced such zero-energy states, and identified them as Majorana states characteristic for a multi-orbital magnet-superconductor hybrid system.
Based on the atomic-resolution spin mapping capabilities, we have also discovered novel types of complex non-collinear spin textures, e.g. a magnetic triple-q structure, in the framework of the project. If this triple-q structure is brought in contact with an elemental superconductor, topological superconductivity as well as Majorana modes can emerge. Moreover, we could demonstrate the emergence of chiral Majorana edge modes in 2D magnet - superconductor hybrid systems with atomically engineered interfacial layers.
In Fe-chains on Re(0001) the observed zero-energy states are compatible with Majorana states. Also ab-initio based theory simulations supported this interpretation. However, excited bulk states overlap with these zero-energy states due to the limited energy resolution of the STS measurements at 300 mK. To observe isolated Majorana states inside a hard gap would require a reduction of temperature by a factor of 10, or the use of a superconducting substrate with a significantly higher transition temperature like niobium.
Indeed, Mn[1-10]-chains on Nb(110) feature clear zero-energy states for certain chain lengths. The experimental measurement of the low-energy states as a function of chain length revealed an oscillatory behavior, which can be understood by assuming hybridized Majorana states. Longer chains would be required to obtain non-interacting, isolated Majorana states. Importantly, the observed length dependent energy splitting oscillations can be regarded as a "smoking gun" for the existence of Majorana states since trivial states would not show such behaviour.
Mn[001]-chains on Nb(110) were shown to possess a gap within the Shiba bands which is reminiscent of a gapped Dirac Hamiltonian, thereby proving that the gap is of topological origin. The associated zero-energy states do not possess significant spectral weight at the chain ends. Instead, they feature a standing-wave pattern with spectral weight pushed to the sides of the chain. Extensive (ab-initio based) theoretical modeling reproduced such zero-energy states, and identified them as Majorana states characteristic for a multi-orbital magnet-superconductor hybrid system.
Based on the atomic-resolution spin mapping capabilities, we have also discovered novel types of complex non-collinear spin textures, e.g. a magnetic triple-q structure, in the framework of the project. If this triple-q structure is brought in contact with an elemental superconductor, topological superconductivity as well as Majorana modes can emerge. Moreover, we could demonstrate the emergence of chiral Majorana edge modes in 2D magnet - superconductor hybrid systems with atomically engineered interfacial layers.
In the framework of this project, 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 end 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.
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.
We were able to demonstrate the emergence of Majorana bound states in artificially fabricated atomic Fe and Mn chains on elemental superconducting substrates (Re, Nb). In particular, we have applied scanning tunneling microscopy (STM) based single-atom manipulation techniques to create perfect, disorder-free atomic spin chains on atomically clean elemental superconducting substrates and demonstrated the non-local nature of the Majorana bound states at both ends of such chains. Moreover, we have successfully applied Bogoliubov quasiparticle interference analysis of the 1D atomic chains, thereby revealing their low-energy in-gap band structure from which the topological nature of the hybrid magnet-superconductor system could be proven.
Finally, we have developed concepts for the realization of Majorana qubits based on magnet – superconductor hybrid (MSH) systems as well as for the manipulation of Majorana bound states, i.e. their creation, annihilation, adiabatic motion, and braiding in artificially built model-type MSH structures.
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.
We were able to demonstrate the emergence of Majorana bound states in artificially fabricated atomic Fe and Mn chains on elemental superconducting substrates (Re, Nb). In particular, we have applied scanning tunneling microscopy (STM) based single-atom manipulation techniques to create perfect, disorder-free atomic spin chains on atomically clean elemental superconducting substrates and demonstrated the non-local nature of the Majorana bound states at both ends of such chains. Moreover, we have successfully applied Bogoliubov quasiparticle interference analysis of the 1D atomic chains, thereby revealing their low-energy in-gap band structure from which the topological nature of the hybrid magnet-superconductor system could be proven.
Finally, we have developed concepts for the realization of Majorana qubits based on magnet – superconductor hybrid (MSH) systems as well as for the manipulation of Majorana bound states, i.e. their creation, annihilation, adiabatic motion, and braiding in artificially built model-type MSH structures.