Incognizant 1T/1H Charge-Density-Wave Phases in Monolayer NbTe₂

While experimental realization of multiple charge-density waves (CDWs) has been ascribed to monolayer 1T-NbTe₂, their atomic structures are still largely unclear, preventing a deep understanding of their novel electronic structures. Here, comparing first-principles-calculated orbital textures with reported STM measurements, we successfully identify multiple CDWs in monolayer NbTe₂. Surprisingly, we reveal that both 1T/1H phases could exist in monolayer NbTe₂, which was incognizant before. Particularly, we find that the experimentally observed 4 × 1 and 4 × 4 CDWs could be attributed to 1H stacking, while the observed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mn>19</mml:mn></mml:msqrt><mml:mo>×</mml:mo><mml:msqrt><mml:mn>19</mml:mn></mml:msqrt></mml:math> phase could possess 1T stacking. The existence of 1T/1H phases results in competition between CDW, spin-density wave (SDW), and ferromagnetism in 1H stacking under an external field and results in CDW-induced quantum phase transitions from a Kramers-Weyl fermion to a topological insulator in 1T stacking. Our study suggests NbTe₂ as an exotic platform to investigate the interplay between CDW, SDW, and topological phases, which are largely unexplored in current experiments.