Graphene Strips Support Majorana Modes with Tunable Polarization and Wavefunctions for Fault-tolerant Quantum Computation

The pursuit of stable Majorana modes holds immense promise for realising fault-tolerant quantum computation, and researchers are increasingly exploring novel material platforms to host these exotic states of matter. Shubhanshu Karoliya from the Indian Institute of Technology Mandi, Sumanta Tewari from Clemson University, and Gargee Sharma from the Indian Institute of Technology Delhi, have undertaken a detailed theoretical investigation into graphene strips as potential hosts for Majorana modes. Their work systematically examines how the geometry of these strips, combined with external factors like spin-orbit coupling and magnetic fields, influences the stability and characteristics of these modes, even in the presence of material imperfections. By uniting detailed analysis of Majorana polarisation with spatial wavefunction mapping and disorder effects, the team establishes clear design principles for building robust, graphene-based superconducting devices capable of supporting these crucial quantum building blocks.

Polarization Controls Majorana Zero Mode Wavefunctions

Topologically protected Majorana zero modes (MZMs) are intensely studied as potential building blocks for fault-tolerant quantum computation. This research investigates how MZMs emerge in proximitized graphene strips, focusing on the interplay between polarization, wavefunctions, disorder, and Andreev states. The team employs a theoretical framework combining tight-binding modelling with the Bogoliubov, de Gennes equation to analyse the electronic structure of graphene strips in proximity to an s-wave superconductor, exploring how the polarization of the induced superconducting order parameter affects the spatial distribution and energy characteristics of the MZMs. The study demonstrates that MZMs exhibit spatially extended wavefunctions localized at the edges of the graphene strip, and their robustness is significantly influenced by the degree of disorder present in the system. The research elucidates the formation of Andreev bound states at the interface between the graphene strip and the superconductor, and how these states couple to the MZMs, impacting their stability and coherence. The findings reveal that a critical level of disorder can localize and eventually suppress the MZMs, highlighting the importance of material quality and precise control over the system’s parameters.

Graphene Ribbons Host Robust Majorana Zero Modes

This research presents a comprehensive theoretical investigation into the potential of graphene nanoribbons to host Majorana zero modes, crucial for developing fault-tolerant quantum computers. Scientists systematically explored various ribbon geometries, including armchair, zigzag, and nearly square, subjected to superconductivity, spin-orbit coupling, magnetic fields, and disorder. Through detailed analysis of the electronic structure, the team identified conditions under which stable Majorana modes emerge and distinguished them from other similar states. Importantly, the study demonstrates that armchair ribbons with short zigzag edges offer the most robust platform for supporting these modes, even in the presence of imperfections. Researchers employed a tight-binding model and exact diagonalization techniques to simulate the behavior of electrons in these nanostructures, allowing them to map out the conditions necessary for realizing Majorana modes. Future work could explore the impact of stronger disorder or different types of impurities, as well as investigate the feasibility of creating and manipulating Majorana modes in fabricated devices.

Graphene Hosts Majorana Fermions and Superconductivity

This collection of research papers and topics focuses on Majorana fermions, topological superconductivity, and related areas, with a strong emphasis on graphene-based systems. The central theme is the search for and understanding of Majorana fermions, particles that are their own antiparticles, predicted to emerge as quasiparticles in topological superconductors. The papers cover the theoretical basis for their existence, how to identify them, and the materials systems where they might be found. Several papers discuss topological invariants, mathematical tools crucial for characterizing topological phases of matter and confirming the presence of topological protection, essential for robust Majorana fermions.

Majorana polarization is a key diagnostic tool for identifying Majorana bound states, and the papers detail how to calculate and interpret it, distinguishing between trivial and topological zero-energy modes. A significant concern is the impact of disorder on Majorana fermions, which can destroy topological protection and obscure the signatures of Majorana modes. Several papers address how to mitigate or account for disorder effects. Hybrid structures combining semiconductors with superconductors are a primary focus, as the proximity effect between them can induce superconductivity and potentially create Majorana modes.

Graphene nanoribbons and carbon nanotubes receive particularly strong emphasis as potential platforms for Majorana fermions. The unique electronic properties of graphene, combined with proximity effects or other mechanisms, could lead to topological superconductivity. Researchers are particularly interested in the edge states in graphene nanoribbons, which can be tuned by the ribbon width and edge shape, and in combining graphene with superconductors or magnetic materials. Strain engineering is also explored as a method to modify the electronic properties of graphene and induce topological phases.

The field faces a reproducibility crisis, as consistently observing and verifying Majorana fermions in experiments proves difficult. This underscores the need for more robust theoretical understanding, better materials control, and more reliable experimental signatures. Developing strategies to protect Majorana modes from disorder is crucial for realizing practical applications. The ultimate goal is to use Majorana fermions as qubits for topological quantum computation, requiring the ability to braid, or exchange, Majorana modes to perform quantum gates. Researchers are exploring alternative materials and heterostructures beyond traditional semiconductor nanowire/graphene approaches, and developing more sophisticated theoretical models and computational techniques to understand the behavior of Majorana fermions in complex systems.

The application of topological invariants to finite systems, more realistic for experimental setups, is also being investigated. In summary, this collection of papers represents a comprehensive overview of the field of Majorana fermions and topological superconductivity, with a strong emphasis on the potential of graphene-based systems. The field faces significant challenges, but ongoing research efforts are paving the way for potential breakthroughs in quantum computing and materials science.