O papel da interação elétron-elétron no regime Hall quântico interio.

Abstract

Experimental and theoretical studies of the aspects of particle-like and collective behavior of electrons in the proximity of the edges of two-dimensional (2DES) and quasi-one-dimensional (Q1DES) systems, named quantum wires (QWs), in semiconductor heterostructures reveal the important role of the electron-electron interaction on the edge states in the integer quantum Hall regime (IQHR). In this thesis we treat two essentially di&#64256;erent problems concerning the e&#64256;ects of the electron-electron interaction in low-dimensional electron system in the IQHR. The first problem is related to the suppression of the spin-splitting of the lowest Landau level (LL) (n = 0) due to many-body e&#64256;ects (the electron-electron interaction including exchange and correlation e&#64256;ects of the edge states) in QWs in the IQHR, where the electron behavior is particle-like. Two scenarios are discussed for the collapse of the IQHR at &#957; = 1 for an electron channel of e&#64256;ective width W modelling the QW. In the first scenario we assume that there is no electron redistribution in the region limited by W at a critical magnetic field B(1) cr , for which the Fermi level (FL) coincides with the bottom of the highest empty LL, at the threshold of the spin-splitting. For B < B(1) cr the IQHR at &#957; = 1 is termodinamically unstable. This scenario is analyzed within the generalized local density approximation (GLDA) developed here for the QW, at high magnetic fields - &#969;c À &#8486;, where &#969;c and &#8486; are the ciclotronic and lateral confinement (which we assume as parabolic one) frequencies, respectively. In the second scenario, we consider the possibility of a transition for the IQHR at &#957; = 2 with an e&#64256;ective width W/2, at a critical magnetic field B(2) cr . In this scenario, the collapse of the IQHR at &#957; = 1 is studied within the Hartree-Fock approximation (HFA), when the bare factor g0 is neglected (this is a good approximation for QWs based on GaAs). We show that the contribution for the total energy coming from the direct interaction (Hartree term) has a strong e&#64256;ect on B(2) cr due to the high electron redistribution inside the narrow channel that defines the QW at B(2) cr . In both scenarios, the enhanced spin-splitting by exchange is suppressed at the critical magnetic field. From our results, we conclude that only the first scenario explains all the experimental findings obtained by Wróbel et al. and Pallecchi et al.. In the second problem, where the collective aspects of the electron system are dominant, we study the influence of the temperature on the dispersion relation and the spatial structure of the edge magnetoplasmons (EMPs) in wide electron channels in the RHQI at &#957; = 1 (2) and 4, in the range ¯h&#969;c À kB T À ¯hvH gn/2 0, for di&#64256;erent dissipation regimes, by extending the pioneering work by Balev and Studart; here, ¯h is the constant of Planck constant (by 2&#960;), kB is the constant of Boltzmann, vH gn is the group velocity (in Hartree approximation) of the edge states of n-th LL, and 0 is the magnetic lenght. A new mode called the edge helicon is found which is the only one that survive for very strong dissipation regime. For a sake of completeness, the general picture of the other modes is presented in the weak dissipation regime. EMPs in the IQHR for &#957; = 4 are also evaluated for weak dissipation and we find strong renormalization of the pure EMPs when the Coulomb interaction is considered appropriately. In all studied cases the important e&#64256;ect of the gate and the air from a distance d of the wide electron channel is considered.