Topological bands by design
Linear magnetic chains on the surface of an elemental superconductor can host topologically non-trivial bands in their bulk and, as a result, the exotic Majorana modes on their ends. However, it is very challenging to specifically tailor these bands and to design a topologically non-trivial phase “on demand”. Scientists from the University of Hamburg have now demonstrated a way to do this using a bottom-up strategy: by positioning single magnetic atoms with the tip of a scanning tunneling microscope, they were able to track the band formation in a magnetic chain during its growth process. Exploiting the anisotropic nature of the atoms’ electronic structure, they chose the optimal crystallographic direction on the surface to realize a topologically non-trivial band structure. Consequently, signatures of the precursors of Majorana modes were found, which are expected to converge into unpaired Majorana modes for long chains. The study has been published in the journal Nature Nanotechnology.
Emergent Majorana modes (MMs) in condensed matter systems are of great interest to fundamental science because of their fascinating and exotic properties. But beyond that, Majorana-based devices are also expected to be among the leading candidates for next-generation qubits. MMs are predicted to appear at the boundaries of topologically non-trivial superconductors, for instance at the ends of one-dimensional magnetic chains in contact with a regular elemental superconductor. However, while several experimental works claim the observation of MMs, no fully conclusive proof of their existence has been given yet. In particular, it would be important to find signatures of MMs together with a topologically non-trivial band structure in the bulk of the sample.
Now, a team of physicists in the research group of Prof. Roland Wiesendanger at the University of Hamburg has presented a platform where topological bulk bands can be tailored almost at will. They have investigated single Manganese atoms adsorbed on an atomically clean superconducting Niobium surface. The magnetic moment of the adatoms locally induces electronic states within the gap of the superconductor, the so-called Yu-Shiba-Rusinov (YSR) states. When moving multiple adatoms close to each other, their individual YSR states couple and eventually form bands. Interestingly, the YSR states are spatially anisotropic. Therefore, their coupling - and consequently the band formation in one-dimensional chains - depend on the crystallographic direction connecting the adatoms. In this way, the team has found the optimal geometric structure for magnetic chains to develop a topologically non-trivial band structure.
If the bulk of a chain is non-trivial, the bulk-boundary correspondence of topological matter predicts the presence of MMs at the ends of the magnetic chains. Indeed, the team has found spectroscopic signatures of end states which are consistent with the precursors of MMs, which are only limited by the finite length of the experimentally realized chains. For this reason, they show characteristic energy oscillations versus the chain length. Importantly, these energy oscillations are always synchronized on both chain ends, which rules out an interpretation of the end states by local disorder.
“These results will allow us to deepen our understanding of how topologically superconducting phases emerge in condensed matter systems – and they clearly set the stage for the next steps towards strongly protected Majorana states”, says Lucas Schneider, first author of the study and postdoc in the research group.
Figure: Artist’s view of single Mn atoms with anisotropic YSR states (orange) and a linear assembly of coupled atoms. The interaction between the atoms leads to the emergence of topologically non-trivial bands and the precursors of Majorana end modes (blue). Image: UHH/MIN/Schneider.
Lucas Schneider, Philip Beck, Jannis Neuhaus-Steinmetz, Levente Rózsa, Thore Posske, Jens Wiebe and Roland Wiesendanger,
Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains
Nature Nanotechnology (2022).
Prof. Dr. Prof. h.c. Dr. h.c. Roland Wiesendanger
Department of Physics
University of Hamburg
Phone: 040 / 42838-5244