Javad Ghorbani - Department of Physics, Qom Branch, Islamic Azad University, Qom, Iran.
Mehdi Ghaffarian - Department of Physics, University of Qom, Qom, Iran.
Hasan Tashakori - Department of Physics, Qom Branch, Islamic Azad University, Qom, Iran.
Alireza Baradaran - Department of Physics, University of Qom, Qom, Iran.

This research explores how two-dimensional honeycomb materials can be used in advanced electronics, focusing on zigzag honeycomb nanoribbons. These nanoribbons can create zero-energy band gaps, enabling helical spin current edge states. The study investigates the quantum spin Hall state, showcasing the adaptability of the Kane-Mele model in various honeycomb lattices. In addition to the theoretical discussions, this study presents a detailed Hamiltonian, performs band structure computations, and introduces a novel spin-filtering technique for zigzag nanoribbons. This method enhances our understanding of edge-localized quantum states and can revolutionize spintronics. By revealing the quantum states in honeycomb nanoribbons, this study contributes to the advancement of electronics and offers a promising path for highly efficient spin-based technologies.

Haldane Model, Kane-Mele Model, Pseudo-Graphene, Quantum Spin Hall Effect, Topological Insulator, Two-Dimensional Honeycomb Materials, Zigzag Nanoribbon