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

Abstract

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 factor equal to one and zero. The domains alternate with a spatial period of the 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 pseudogap linearly dependent on the magnetic field in the limit of large N .

Fractional quantum Hall effect in a tilted magnetic field

“…Upon closer examination, we find that the momenta of the quasidegenerate states are of the form (k x , 0), indicating linear order along x-direction. This is known to be one of the signatures of the stripe phase [42][43][44][45][46] .…”

Spin and Charge Ordering in the Quantum Hall Regime

“…That raises the question whether the reentrant states in the second Landau level are of equal nature as the bubble phases in higher levels. Initially, theories did not consider the second Landau level for bubble phase formation at all [93,94]. This deficiency was remedied more recently [5,119].…”

“…If the modulation period is similar to the width of the wavefunction (∼ ), the density modulation and therefore also the increase in Coulomb energy will be small in comparison to the step-like change of the filling factor. The gain in exchange energy, however, is rather determined by the modulation of the filling factor [93]. In total, the 2DES can minimize its energy by modulating the electron density at certain filling factors of the topmost occupied Landau level branch [92][93][94].…”

“…The gain in exchange energy, however, is rather determined by the modulation of the filling factor [93]. In total, the 2DES can minimize its energy by modulating the electron density at certain filling factors of the topmost occupied Landau level branch [92][93][94]. The average filling factor determines the phase symmetry, i.e.…”

“…They predict that the electron bubbles arrange in a triangular lattice with a period of roughly 3 · , where = √ 2 /( ) is the cyclotron radius [92,93]. The number of electrons varies according to the partial filling˜with the restriction that the maximum number of electrons per bubble is limited to in the th Landau level (for > 1) [92,98] 1 .…”