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...

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 .

We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau-level filling factors N ϭ 1 3 and 1 5. The charge-density-wave period has been optimized and was found to be Ӎ3.3R c , where R c is the cyclotron radius. We conclude that the optimal charge density wave is lower in energy than the Laughlin liquid for the Landau-level numbers Nу2 at N ϭ 1 3 and for Nу3 at N ϭ 1 5. This implies that the

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. Two forms of electron-electron interaction potential are studied: the pure Coulomb interaction and the exponential interaction corresponding to the screening by a pair of close metallic gates. The electrons are assumed to reside in a parabolic external confining potential. Due to the crystalline symmetry the center of the confinement can be situated at distinct positions with respect to the crystal. With the increasing number of electrons N the center periodically hops from one such a location to another providing the lowest total energy. These events occur with the period ∼ N 1/2 . At these moments in the case of the pure Coulomb interaction the charging energy of the island has a negative correction ≈ 15%. For the case of the exponential interaction at the moments of switching the capacitance becomes negative and ∼ N 1/4 new electrons enter the island simultaneously. The configurations of disclinations and dislocations in the island are also studied.

A classical model for dc transport of two dimensional electrons in a perpendicular magnetic field and under strong irradiation is considered. We demonstrate that, near the cyclotron resonance condition, and for linear polarization of the ac field, a strong change of the diagonal component, σ d , of the dc conductivity occurs in the presence of a weak nonparabolicity of the electron spectrum. Small change in the electron effective mass due to irradiation can lead to negative σ d , while the Hall component of the dc conductivity remains practically unchanged. Within the model considered, the sign of σ d depends on the relative orientation of the dc and ac fields, the sign of the detuning of the ac frequency from the cyclotron resonance, and the sign of nonparabolic term in the energy spectrum.1. Introduction. Recently reported observation [1,2] of a zero-resistance state, that emerges upon microwave irradiation of a high-mobility 2D electron gas in a weak magnetic field, was immediately followed by a number of theoretical papers [3][4][5][6], in which the origin of this state was discussed. The only microscopic calculation to date [4] indicates that, for strong enough radiation intensity, the diagonal component, σ d , of the dc conductivity tensor changes sign from the dark value σ d > 0 to σ d < 0 within certain frequency intervals of the ac field, away from the cyclotron frequency and its harmonics. Negative local value of σ d results in the instability of the homogeneous current distribution. In Ref.[5] the scenario of how the instability might develop into the zero-resistance state was proposed.In this situation it seems important to trace the emergence of negative σ d in an ac-driven system from the simplest possible model. Such a model is considered in the present paper. Obviously, σ d is sensitive to the illumination only if the Kohn theorem is violated. It is commonly assumed that the reason for this violation is a random impurity potential. Here we consider a model, in which the Kohn theorem is violated due to an intrinsic reason, namely, due to a weak nonparabolicity of the electron spectrum. More specifically, we adopt the following form of the dispersion relation for the conduction band electrons