The description of the interactions between the electron and its environment, which is an example of a highly correlated system, is one of the great challenges of quantum physics. In this work, we studied the characteristics of the polaron and bipolaron in nanostructures under the combined effect of potentials, constant electromagnetic fields and laser field. Due to the range of electron-phonon coupling constants, many variational methods are used, including Lee Low Pines (LLP), Pekar and modified Lee Low Pines. These methods are used in three coupling regimes, depending on whether the coupling is weak, strong or intermediate. The evaluation of the effect of the potential on their dynamics and coherence was done in 1D, 2D and 3D structures. We show that quantum confinement has a predominant role on polaronic effects because, due to the presence of potential control parameters, an improvement of polaronic effects is observed. From here, it follows that the loss of system properties can be avoided by taking these potentials into account. We find the delta potential is interesting because it has both good optical and thermodynamic properties.
In addition to the potentials, the effect of the electromagnetic field on polarons and bipolarons in nanostructures reveals that the presence of these two fields is ideal under certain conditions for the modulation of polaronic states. These two fields have opposite effects and can be used to control the coherence of polaronic and bipolaronic systems. The laser has proven to be a possible way to improve the polaronic and bipolaronic effects in nanostructures. We found that the shape of the laser influences the transition energy and decoherence time, as well as the mobility and stability of the studied particles. We note that polaronic effects are very sensitive to the presence of the laser. The magnetopolaron and the magnetobipolaron are also highlighted in this thesis and it emerges that these quasiparticles are indeed those that govern the transport properties in small dimensional structures.
The polaron and bipolaron can indeed form in graphene. Graphene is a current material with special properties such as high flexibility, good fineness and high conductivity. It is shown that the laser can be used to modulate the band gap in graphene. We have observed that the high laser frequency enhances the polaron-polaron interaction and promotes the formation of bipolarons in these structures. Compared to the polaron, the effects of laser frequency and laser intensity are opposite. We found that the laser reduces the lifetime of the polaron in the ground state and increases it in the excited state. The excited polaron survives the effects of the laser more than the excited bipolaron. However, the polaron and the ground-state bipolaron have approximately the same sensitivity to the laser. The polaron and bipolaron in graphene become massless under the some values of laser frequency. We have shown that the energies and optical
absorption of polaronic and bipolaronic systems depend strongly on the laser parameters and the characteristics in the graphene. The thermodynamic properties of our system are strongly dependent on the laser field.