Estado polarônico de elétrons em canais quase unidimensionais na superfície de hélio líquido

Abstract

In this work, we have investigated the polaronic state formed in the system of surface electrons confined in a quasi-one-dimensional channel over liquid helium. The electrons bound to the surface by a holding electric field can be laterally confined by electrostatic or structural means and the lateral confinement can be modeled by a parabolic potencial. The polaron is a quasi-particle composed by the eleçtron coupled to the surface deformation (dimple) wich arises from the pressing field. The polaron properties are obtained from the solution of the coupled nonlinear system formed by the Schrõdinger equation and the equation for mechanical equilibrium of the surface deformation. We have employed two kinds of approximations to solve the system. The first one, named the harmonic approximation, consists in expanding the surface deformation in second order for dimensions smaller than a localization radius, and the other one is the variational method, in which a harmonic-oscillator like trial function is proposed. We have determined the surface deformation, the electron energy in the dimple, and the polaron energy as a function of the holding electric field. We have also studied the influence of a magnetic flield applied in the direction perpendicular to the surface. We established the field threshold for the existence ofbound states in the system. Our results for the ground-state energy are the same in both approximations. However, for the excited states, we show that the harmonic approximation is reliable only in certain conditions.