Abstract
Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor—also known as Shiba chains—up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.
Highlights
Realizing isolated Majorana modes (MMs) as zero-energy excitations in solid-state systems has been an immense quest in the past two decades, being motivated by their possible use for fault-tolerant topological quantum computing[1–3]
MMs on both ends of the chain may still interact, thereby splitting in energy away from zero in an oscillatory fashion as a function of the chain length, one of the key signatures of the so-called precursors of MMs (PMMs) in short chains . 19–21 Coulomb blockade spectroscopy in InAs nanowires coupled to Al has provided evidence for an oscillatory splitting of near-zero-energy states as a function of the Zeeman field, which decreased for longer devices[20]
We use scanning tunnelling microscopy (STM) and scanning tunnelling spectroscopy (STS) with a superconducting tip to probe the local density of states (LDOS) at subgap energies (Methods)
Summary
For certain chain lengths, such as N = 12, 21, 32 and 42, the energy of the end state can be tuned to zero within the experimental peak width, which corresponds to ΔE = 50 μeV In contrast to this observation, the hybridizing α-YSR states evolve into a comparably narrow band (Fig. 3g), which is irrelevant for the topological properties of the system (Extended Data Fig. 1b and Supplementary Note 1). The topological gap for the system at hand is calculated to be 50 μeV (Supplementary Note 7), which is considerably smaller than the observed energy splitting of the PMMs Ehyb and the finite-size gap ΔFS in our experimentally realized chains (Fig. 3, Supplementary Note 3 and Supplementary Fig. 1e) For systems with this sequence of orders of magnitude of the different parameters, the p-wave pairing Δp manifests as an emergent apparent avoided crossing of the lowest- and second-lowest-energy states at positions exemplarily indicated by the arrows, which is just too small to be detected within our experimental energy resolution The interactions of the observed fine-tuned zero-energy PMMs with the continuum of 1D modes are strongly suppressed by the presence of a relatively large finite-size gap ΔFS
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
