Charge Density Wave Behaviour of the Integer Quantum Hall Effect Edge States

We analyze the effect that the Coulomb interaction has on the edge excitations 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.