Majorana fermions in chains of magnetic atoms on a superconductor

Abstract: We propose an easy-to-build easy-to-detect scheme for realizing Majorana fermions at the ends of a chain of magnetic atoms on the surface of a superconductor. Model calculations show that such chains can be easily tuned between trivial and topological ground state. In the latter, spatial resolved spectroscopy can be used to probe the Majorana fermion end states. Decoupled Majorana bound states can form even in short magnetic chains consisting of only tens of atoms. We propose scanning tunneling microscopy as the ideal technique to fabricate such systems and probe their topological properties.

• The paper demonstrates that tuning parameters in atomic chains can produce localized Majorana bound states even in chains of around 50 atoms.
• The study employs a two-dimensional tight-binding model and Pfaffian index computation to reveal topological transitions and robust Majorana modes.
• The findings propose STM-based spatial spectroscopy as a practical method to distinguish genuine Majorana signals from disorder-induced anomalies.

Majorana Fermions in Chains of Magnetic Atoms on a Superconductor

This paper addresses the theoretical realization of Majorana fermions (MFs) in a particularly promising experimental setup: chains of magnetic atoms deposited on a superconductor. The authors propose a straightforward system, built using scanning tunneling microscopy (STM), where such chains are capable of transitioning between trivial and topological ground states. The key insight is the possibility of generating Majorana bound states, even in ostensibly short chains composed of tens of atoms. This scheme invokes the potential for localized MF detection and suggests a promising path for fabricating robust, real-world topological quantum computers.

A significant contribution of this study is the construction of a model that demonstrates the formation of decoupled Majorana bound states at the ends of the atomic chains. By tuning parameters within their model, the authors show that Majorana states emerge and are preserved even when chains of only ~50 atoms are considered. The authors argue for STM-based spatially resolved spectroscopy as an ideal means to probe these systems, emphasizing its capability to discern Majorana end states from spurious zerobias anomalies caused by disorder.

The primary theoretical approach involves a two-dimensional tight-binding model Hamiltonian for a superconductor, incorporating a one-dimensional array of magnetic atoms interfacing with superconducting sites. Using both open and periodic boundary conditions, the presence of Majorana modes is evaluated by computing the Pfaffian index—a key indicator of topological state transition. The authors emphasize the role of specific geometric configurations and site-specific magnetic interactions in supporting topological modes. Importantly, they note that parameters such as the magnetic moments, internal Zeeman energy, and the orientations of spins within the atomic chain significantly influence the architectural spacing of Majorana modes.

Numerical analyses depict the impact of quantum tunneling and confirm that emergent Majorana modes can be effectively contained within limited spatial boundaries, characterized by short localization lengths. This contradicts previous systems, like semiconductor nanowires, which tend to exhibit longer coherence lengths.

Critically, the paper advances the discussion of more intricate atomic structures, such as zig-zag chains. The formulation of these chains can induce spiral spin arrangements that propagate the conditions necessary for MFs. The authors' findings indicate the generation and stabilization of such topological phases, contingent upon the system's specific construction and inherent physical properties.

The authors underscore the importance of optimizing experimental conditions to realize these theoretical predictions. The proposals invite magnetic atom manipulation and single-impurity state characterization as foundational methods to explore the generation of MFs experimentally. The study reveals the potential for using self-assembled chains and then scrutinizing coupled chain structures to elucidate the Z2 character of MF modes in complex systems.

In summary, this research provides a solid theoretical framework for the realization of Majorana fermions within atomic chains on superconductors. The study deftly illustrates the conditions under which topological superconductivity can be observed and proposes feasible methodologies for experimental realization. Moving forward, these insights could lead to profound advances in both the theoretical understanding and practical applications of topological quantum computations.