Dynamic electron localization initiated by particle-bath coupling

We consider the quantum evolution and relaxation of an electron or hole which is coupled to a set of bath modes. In most applications the bath modes would be the vibronic coordinates but the model considered applies to any type of dynamic boson environment. The method is developed specifically for the problem of dynamic polaron formation in small nonperiodic systems. It can describe a broad group of experimental situations, including in particular electron localization in organics and polymeric materials and devices. The immediate bath is allowed to dissipate energy to a secondary bath. The bath obeys classical dynamics which puts some restriction on the range of validity of this approach. Using the density matrix formalism on a tight binding model consisting of a linear chain coupled to vibronic coordinates, we demonstrate in real time how the interaction with a dissipative bath makes the initial quantum distribution reach a steady-state population. This calculation is based on the Ehrenfest dynamics approximation. As an example we consider coupling at a single impurity site and find that for given parameters (bath coupling, site energy, and relaxation rate), the particle becomes dynamically localized in space on a particular time scale. This localized particle can be called a polaron. We define a population formation time in the same way as done in the experimental measurement. This formation time is studied as a function of the coupling strength, bandwidth, and energy dissipation rate. Energy dissipation plays a crucial role in the spatial localization process. The formation time shortens as the electron-vibration coupling increases, and as the intersite tunneling increases, but lengthens with impurity trap depth. Polaron formation is suppressed for sufficiently wide electronic bands. DOI: 10.1103/PhysRevB.87.094302