Strain-Induced Charge Density Waves with Emergent Topological States in Monolayer NbSe₂

Emergence of topological states in strongly correlated systems, particularly two-dimensional (2D) transition-metal dichalcogenides, offers a platform for manipulating electronic properties in quantum materials. However, a comprehensive understanding of the intricate interplay between correlations and topology remains elusive. Here we employ first-principles modeling to reveal two distinct 2 × 2 charge density wave (CDW) phases in monolayer 1H-NbSe₂, which become energetically favorable over the conventional 3 × 3 CDWs under modest biaxial tensile strain of about 1%. These strain-induced CDW phases coexist with numerous topological states characterized by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> topology, high mirror Chern numbers, topological nodal lines, and higher-order topological states, which we have verified rigorously by computing the topological indices and the presence of robust edge states and localized corner states. Remarkably, these topological properties emerge because of the CDW rather than a pre-existing topology in the pristine phase. These results elucidate the interplay between correlations, topology, and geometry in 2D materials and indicate that strain-induced correlation effects can be used to engineer topological states in materials with initially trivial topology. Our findings may be applied in electronics, spintronics, and other advanced quantum devices that require robust and tunable topological states.