Stripe and Bubble Phases in Quantum Hall Systems

Abstract

We present a brief survey of the charge density wave phases of a twodimensional electron liquid in moderate to weak magnetic fields where several higher Landau levels are occupied. The review follows the chronological development of this new and emerging field: from the ideas that led to the original theoretical prediction of the novel ground states, to their dramatic experimental discovery, to the currently pursued directions and open questions.

Spin and Charge Ordering in the Quantum Hall Regime

“…For these density modulated phases, the homogeneous electron system in the topmost Landau level breaks up into alternating regions of high and low electron density. Two types of density modulated phases are believed to exist [3]: the bubble phase having a twofold periodicity and the stripe phase, which consists in the simplest case of parallel stripes with a strictly one-dimensional (1D) periodicity ( Fig. 2.16).…”

“…In both cases, the system alternates between regions where the topmost Landau level branch is completely filled and locations where it is totally empty. The reason for the formation of density modulated phases is rooted in the competition between the repulsive direct Coulomb interaction on the one hand and the attractive exchange interaction on the other hand [3,5]. Whenever the 2DES deviates from a homogeneous distribution, this comes at the cost of direct Coulomb energy.…”

“…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 . The optimal number of electrons per bubble can be well approximated by 3˜ [3,98]. Thus, when increasing˜starting from˜= 0, at first only a single electron occupies a bubble site.…”

“…Similar physics is at play at the formation of stripe and bubble phases in magnetic and organic films [4]. In the quantum Hall regime, these phases emerge from the competition between the repulsive direct Coulomb interaction and the attractive exchange interaction [3,5]. Their dominance over the fractional quantum Hall effect stems from subtle differences in the relative strength of these interactions, primarily caused by changes in the shape and extent of the wavefunction in higher Landau levels.…”

“…No fractional quantum Hall states form here, instead density modulated phases are prevalent at partial fillings. They arise by the spontaneous ordering of electrons in spatial patterns with either one-dimensional stripe order (stripe phase) or a two-dimensional crystalline order (bubble phase) [3]. Such phases constitute an evident signature of systems with strong competition between attractive and repulsive interactions acting on different length scales.…”