X iv : c on d - m at / 9 50 70 63 v 1 1 7 Ju l 1 99 5 Charge Density Wave Behaviour of the Integer Quantum Hall Effect Edge States

We analyze the effect that the Coulomb interaction has on the edge excita-tions of an electron gas confined in a bar of thickness W , and in presence of a magnetic field corresponding to filling factor 1 Quantum Hall effect. We find that the long-range interaction between the edges leads the system to a ground state with a quasi-long range order, similar to a Charge Density Wave. The spectral density of states vanishes at zero frequency, and increases with frequency faster than any power law, being the conductance of a infinite long system zero. Edge states play a very important role in the understanding of the Quantum Hall Effect (QHE). [1] Some properties of the integer QHE can be understood from the one-electron picture of the edge states [2], but at the moment the edge structure in the fractional QHE regime is unclear. [3] Due to the one-dimensional (1D) character of the QHE edge states, it has been proposed that they behave as a Fermi liquid in the integer case and as a Luttinger liquid in the fractional case. [4,5] In these works, it is assumed short range electron-electron interaction and therefore it is also neglected the interaction between outgoing and ingoing edge states. However, in order to obtain high mobility electron samples, any metallic gate in the actual physical systems must be far away from the plane where the two-dimensional