Ground state of a two-dimensional electron liquid in a weak magnetic field

We consider a clean two-dimensional electron liquid in a weak magnetic field where N≫1 lower Landau levels are completely filled, while the upper level is only partially filled. Due to a screening by the lower Landau levels, the repulsive interaction between any two electrons at the upper level as a function of the separation between the guiding centers of their cyclotron orbits abruptly drops at the distance of two cyclotron radii. Such a “box-like” component in the interaction potential makes the uniform distribution of the electron density at the upper Landau level unstable, and domains with filling factor equal to one and zero are formed. The shape of domains is studied both analytically and numerically. We show that when the filling factor of the upper Landau level is close to one-half, the domains have the form of parallel stripes alternating with a spatial period close to three cyclotron radii. Away from a small interval around half-filling, a “bubble” phase is more favorable. We investigate the implications of the proposed ground state for the one-particle density of states, which can be probed by tunneling experiments. For the stripe phase, the density of states is shown to have a pseudogap linearly dependent on the magnetic field in the limit of large N.