Modulational instability and charge localization in the Holstein-SSH model of DNA with mass impurities

This research investigates the stability of localized charge modes in a Holstein-SSH DNA model incorporating a mass impurity. By deriving a semidiscrete nonlinear Schrödinger equation through Hamiltonian formalism and the adiabatic approximation, we analyze the modulational instability to assess the impact of impurity parameters on mode stability. Analytical results reveal that impurity mass significantly influences charge localization, especially near the Brillouin zone edges, with low coupling parameters favoring localized modes and higher values promoting charge delocalization. Numerical simulations confirm that the impurity's mass and sign critically affect energy and charge localization, with negative masses acting as potential wells and positive masses inducing dispersive effects. These findings highlight the crucial role of mass impurities in modulating charge transport in DNA, offering insights for designing biomolecular and nanotechnological systems with controlled electronic properties.