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Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 2003, 90, 013001]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original 2D two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove the GP within a two-state problem. Using the stabilization graph technique we have shown that the GP is crucial for emergence of BSCs.

Topological Origins of Bound States in the Continuum for Systems with Conical Intersections