Magnetic Fields Induce Topological Flat Bands of Majorana Fermions in Spin Liquids

The search for materials hosting exotic quantum states continues to drive innovation in condensed matter physics, and recent work focuses on uncovering novel properties in systems with fractionalized excitations. Kiyu Fukui from The University of Tokyo and Ritsumeikan University, along with Yukitoshi Motome and colleagues, demonstrate the existence of topological Majorana flat bands within a modified Kitaev model applied to a unique Bishamon-kikko lattice. This research reveals that applying a magnetic field to the system transforms initially flat Majorana bands into topologically non-trivial states, creating a variety of new phases not found in the original model, and offering a promising avenue for exploring materials with rich topological properties stemming from these unusual quantum excitations. The findings highlight a previously unknown mechanism for generating topological states through the hybridization of flat bands and unpaired Majorana fermions, potentially paving the way for the design of materials with enhanced quantum functionality.

The research investigates a theoretical model exhibiting quantum spin liquid behaviour, similar to systems found on honeycomb lattices, within the framework of perturbation theory. This model is easily extended while maintaining exact solvability, and its fundamental state features fractionalized excitations, including unpaired Majorana fermions, itinerant Majorana fermions, and Z2 fluxes. The study demonstrates that, without a magnetic field, these Majorana fermions occupy completely flat bands at zero energy, but the application of a magnetic field transforms them into topological flat bands possessing a nonzero Chern number, revealing a diverse range of behaviours dependent on interaction strength and field magnitude.

This compilation details research papers and preprints primarily focused on Kitaev materials, flat bands, topological superconductivity, and the effects of disorder and vacancies on these systems. The following breakdown categorizes key themes and observations within the research landscape. I. Kitaev Materials & Quantum Spin Liquids (QSLs) This constitutes the dominant theme, with many papers investigating real materials believed to host or approach Kitaev QSL phases. * Iridium-based Honeycomb Materials (α-RuCl3, Na2IrO3, Li2IrO3, etc.): A significant portion of the research focuses on these materials, exploring the impact of disorder, vacancies, doping (such as Ru doping in α-RuCl3, Cr doping in α-RuCl3, and Li/Na doping in IrO3), pressure effects, and the properties of OsxCl3, which features honeycomb nano-domains potentially hosting Kitaev physics.

Key Observations & Trends: There is a strong interplay between the research on Kitaev materials, flat bands, topology, and disorder, as researchers attempt to understand how these concepts connect and engineer materials with desired properties. Disorder and vacancies are increasingly viewed not just as detrimental effects, but as potential tuning parameters that can stabilize certain quantum phases or lead to novel behaviour. The role of quantum geometry and the quantum metric is gaining increasing attention as a key factor in understanding the properties of flat band systems and topological phases. A significant amount of research focuses on finding and characterizing Majorana fermions, which are believed to be crucial for realizing topological quantum computation. The list includes both theoretical studies and experimental investigations, highlighting the importance of combining these approaches to advance our understanding of these complex systems. This is a very comprehensive list, providing a good overview of the current state of research in these exciting fields, and it is clear that there is a lot of ongoing work aimed at understanding and harnessing the potential of Kitaev materials, flat bands, and topological phases for future technologies.