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

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2004-04-02##### Author

Silva, Sanderson Francisco Fernandes Pereira da

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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 diﬀerent problems concerning the
eﬀects 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 eﬀects (the electron-electron interaction including exchange
and correlation eﬀects 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 ν = 1 for an electron
channel of eﬀective 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 ν = 1 is termodinamically unstable. This
scenario is analyzed within the generalized local density approximation (GLDA) developed
here for the QW, at high magnetic fields - ωc À Ω, where ωc and Ω 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 ν = 2 with an eﬀective
width W/2, at a critical magnetic field B(2)
cr . In this scenario, the collapse of the IQHR at ν = 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 eﬀect 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 ν = 1 (2) and 4, in
the range ¯hωc À kB T À ¯hvH
gn/2 0, for diﬀerent dissipation regimes, by extending the pioneering
work by Balev and Studart; here, ¯h is the constant of Planck constant (by 2π), 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 ν = 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
eﬀect of the gate and the air from a distance d of the wide electron channel is considered.