EFFECTS OF ELECTRON-ELECTRON INTERACTIONS ON THE GROUND-STATE OF QUANTUM HALL EDGE STATES

We study the effects of electron-electron interactions on the ground states of integral and fractional quantum Hall edge states. We introduce a realistic model of a mesa-etched sample edge and solve it within an electrostatic approximation. Applying the Hartree-Fock approximation to integral quantum Hall edge states, we show that, in the absence of Zeeman splitting, the outermost edge state undergoes a spontaneous transition between spin-unpolarized and spin-polarized ground states at a confining-potential-dependent critical value of the bulk filling nu(bulk)c. We apply these general results to our model of mesa-etched sample edges and obtain nu(bulk)c as a function of model parameters, with nu(bulk)c almost-equal-to 4. The relatively abrupt appearance, in the spin-polarized state, of a sizable (about a magnetic length) separation between edge states of opposite spin should make this transition accessible to a range of magneto-transport experiments. For a 2DEG in the fractional quantum Hall regime we use our electrostatic model to obtain the widths of the fractional quantum Hall strips separating the conducting edge states from each other and from the conducting bulk. This allows us to estimate the quasi-particle scattering rate and the corresponding equilibration length between the edge states and the bulk. We compare these estimates with measurements of non-local resistance.