Charge Density Wave in Two-Dimensional Electron Liquid in 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 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 .The nature of the ground state of an interacting twodimensional (2D) electron gas in magnetic field has attracted much attention. The studies have been focused mostly on the case of very strong magnetic fields where only the lowest Landau level (LL) is occupied, so that the filling factor ν = k 2 F l 2 does not exceed unity (here k F is the Fermi wave-vector of the 2D gas in zero magnetic field and l is the magnetic length, l 2 = /mω c ). The physics at the lowest LL turned out to be so rich that, perhaps, only at ν = 1 the ground state has a simple structure. Namely, it corresponds to one fully occupied spin subband of the lowest LL. The charge density in such a state is uniform. The case of a partial filling, ν < 1, is much more interesting. Using the Hartree-Fock (HF) approximation, Fukuyama et al. [1] found that a uniform uncorrelated spin-polarized electron liquid (UEL) is unstable against the formation of a charge density wave (CDW) at wave-vectors larger than 0.79 l −1 . The optimal CDW period was later found to coincide with that of the classical Wigner crystal (WC) [2].Subsequently, however, it turned out that non-HF trial states suggested by Laughlin [3] for ν = 1/3, 1/5 to explain the fractional quantum Hall effect are by a few percent lower in energy. The Laughlin states were further interpreted in terms of an integer number of fully occupied LLs of new quasiparticles, composite fermions [4]. This concept was then applied to even denominator fractions [5]. Thus, although the HF approximation gives a rather accurate estimate of the energy, it fails to describe important correlations at a partially filled lowest LL.Recently, the requirement of the complete spin polarization in the ground state was also reconsidered. It was found that a partially filled lowest LL may contain skyrmions [6].In this Letter we consider the case of weak magnetic fields or high LL numbers N . There is growing evidence from analytical and numerical calculations that fractional states, composite fermions and skyrmions are restricted to the lowest and the first excited LLs (N = 0, 1) only (see ). We will present an additional argument in favor of this conclusion. This point of view is also consistent with the experiment because none of those structures has been observed for N > 1.Before we proceed to the main subject of the paper, a partially filled upper LL, note that we can use the concept of LLs only if th...

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Spin and Charge Ordering in the Quantum Hall Regime

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