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.