Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where N ≫ 1 lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factors equal to 1 and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a gap linearly dependent on the magnetic field in the limit of large N.