Rhombohedral-stacked Multilayers Exhibit -Fold Degenerate Zero-Energy Edge States with Winding Number, Enabling High-Winding-Number Topological Phases

The pursuit of robust, high-performance electronic components drives ongoing research into topological insulators, materials that conduct electricity along their edges while remaining insulating within their volume. Feng Lu, Ao Zhou, and Shujie Cheng, from Xingzhi College and Zhejiang Normal University, alongside Gao Xianlong, now demonstrate a pathway to create topological insulators with unprecedented control over their conductive edge states. Their work investigates multilayered materials constructed with a specific rhombohedral stacking arrangement, revealing that these systems host edge states with a winding number directly proportional to the number of layers. This discovery establishes a layer-by-layer amplification mechanism for topological properties, offering a systematic approach to engineer materials with enhanced functionality and potential applications in advanced information processing.

With winding number W equal to N, the research provides a direct route to high-winding-number topological phases where the winding number scales linearly with the number of layers. Scientists demonstrate this layer-by-layer topological amplification mechanism using effective Hamiltonian theory and Zak phase calculations. They introduce Wigner entropy as a novel detection method for these edge states, showing that topological boundary states exhibit significantly enhanced Wigner entropy compared to bulk states. The results establish rhombohedral stacking as a systematic approach for engineering high-winding-number topological insulators with potential applications in quantum information processing.

Layered Graphene Reveals Complex Topological Phases

This research explores the fascinating world of topological phases of matter, focusing on the Su-Schrieffer-Heeger model and its extension to multilayer systems like graphene. Scientists investigate how to realize, control, and characterize these topological states, with a particular emphasis on achieving high winding numbers and understanding layer-dependent effects. The team also focuses on developing methods for measuring key topological invariants. The research highlights the potential of rhombohedral graphene multilayers to exhibit complex topological properties and quantum anomalous Hall effects.

Scientists emphasize the importance of directly measuring topological invariants, such as the Zak phase and Chern number, to definitively identify topological phases. They demonstrate the versatility of these concepts by exploring a wide range of physical platforms for realizing and studying topological states. A notable aspect of the work is the exploration of using the Wigner function as a tool for characterizing these states.

Topological Amplification via Layered Material Stacking

This research establishes a new understanding of topological properties in specifically stacked one-dimensional materials. Scientists demonstrate that rhombohedral stacking of layers in a Su-Schrieffer-Heeger network creates systems with predictably high-winding-number topological phases. Increasing the number of layers directly corresponds to an increase in the winding number, a key topological invariant, through a process of topological amplification. This linear scaling offers a systematic route to engineer materials with enhanced topological characteristics. The team further advanced detection methods by introducing Wigner entropy as a novel tool to distinguish between topological edge states and bulk states, revealing significantly enhanced entropy in the boundary states.

This provides a new perspective for characterizing these states, particularly in systems where traditional measurement techniques are difficult to apply. The findings extend observations of layer-dependent topological amplification, previously seen in two-dimensional graphene, to one-dimensional systems, confirming rhombohedral stacking as a versatile strategy for creating materials with tailored topological properties. Researchers acknowledge that the analysis relies on specific conditions, including weak interlayer coupling, and future work could explore the behaviour of these systems under varying conditions. The highly degenerate edge states discovered in this study may prove valuable for developing platforms for topological quantum computation and investigating the potential for fractional charge localization in systems with higher winding numbers.