Strain engineering of topological transitions in 2D materials: a multi-band approach

This study presents a comprehensive multi-band analytical and numerical framework to investigate strain-induced topological phase transitions and electronic structure changes in two-dimensional (2D) materials. We derive accurate formulas for strain-dependent band gaps and critical strain thresholds, elucidating the role of strain in band inversion, Berry curvature, and electronic properties in phosphorene and MoS 2 . These formulas reliably predict topological transitions (e.g., Z 2 index or Chern number) and nonlinear band gap reductions, validated by tight-binding simulations, first-principles calculations, and experimental data. The framework is demonstrated for phosphorene and MoS 2 , with potential extensions to other 2D materials and heterostructures, which may facilitate applications in quantum computing, spintronics, and optoelectronics through strain engineering.