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 MoS2. These formulas reliably predict topological transitions (e.g., Z2 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 MoS2, with potential extensions to other 2D materials and heterostructures, which may facilitate applications in quantum computing, spintronics, and optoelectronics through strain engineering.