An even-denominator rational quantum number has been observed in the Hall resistance of a twodimensional electron system. At partial filling of the second Landau level v=2+ y = y and at temperatures below 100 mK, a fractional Hall plateau develops at p xy =(h/e 2 )/y defined to better than 0.5%. Equivalent even-denominator quantization is absent in the lowest Landau level under comparable conditions.

Magnetotransport experiments on high mobility two-dimensional electron gases in GaAs͞AlGaAs heterostructures have revealed striking anomalies near half filling of several spin-resolved, yet highly excited, Landau levels. These anomalies include strong anisotropies and nonlinearities of the longitudinal resistivity r xx which commence only below about 150 mK. These phenomena are not seen in the ground state or first excited Landau level but begin abruptly in the third level. Although their origin remains unclear, we speculate that they reflect the spontaneous development of a generic anisotropic many-electron state. [S0031-9007(98) A magnetic field applied perpendicular to the plane of a two-dimensional electron gas (2DEG) resolves the energy spectrum into discrete Landau levels (LLs). As the field increases, the Fermi level drops down through the Landau ladder in a series of steps until, at high field, it resides in the lowest (N 0) level. In this situation the kinetic energy of the electrons is quenched and electron-electron interactions dominate the physics with the fractional quantized Hall effect (FQHE) as the most spectacular consequence [1]. After more than 15 years of study, much is known about electron correlations in this lowest LL case. The same cannot be said when the Fermi level is in a higher Landau level. In the second LL (N 1), the FQHE is virtually absent; only fragile and poorly understood states at Landau filling fractions n 7͞3, 5͞2, and 8͞3 are seen in the best samples. In the third and higher LLs (N $ 2) still less is known, although there have been interesting suggestions of charge density waves in the clean limit [2,3]. At very high N, and therefore very low magnetic field, the Landau level splitting becomes insignificant and the 2DEG assumes the character of a weakly disordered Fermi liquid.In this paper we report the observation of several dramatic anomalies in the low temperature magnetotransport of clean 2DEGs when the Fermi level lies near the middle of a spin-resolved highly excited Landau level. These effects, which commence only below about 150 mK, abruptly begin and are strongest in the third (N 2) LL, but persist up to about N 6. Including strong anisotropies and intriguing nonlinearities of the resistivity, these effects suggest a considerably more interesting tableau at high N than independent electrons moving in a disordered Landau band.The samples used in this study are GaAs͞AlGaAs heterojunctions grown by molecular beam epitaxy (MBE). Data from six samples (A through F) will be discussed. Samples A, B, and C were taken from one MBE wafer, D and E from a second, and F from a third. Each wafer was rotated during growth to ensure high homogeneity of the electron density n s . These densities (in units of 10 11 cm 22 ) are close to n s 2.67 for samples A, B, and C; n s 2.27 for samples D and E; and n s 1.52 for sample F. The low temperature mobility of each is m $ 9 3 10 6 cm 2 ͞V s. Each sample was cleaved (along ͗110͘ directions) into a 5 3 5 mm square from its parent ͗001͘ wa...

'These authors contributed equally to this work'An ordered state of electrons in solids in which excitons condense was proposed many years ago as a theoretical possibility but has, until recently, never been observed. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron-electron bilayers as in electron-hole bilayers. In current quantum Hall exciton condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer counterflow conductivity.In many-particle quantum physics bosons are special. Unlike the ubiquitous electrons and their fermionic cousins, any number of bosons can crowd into the same microscopic state. Indeed, in 1924 Einstein predicted that at low temperatures essentially all of the bosons in a macroscopic system would spontaneously "condense" into the same low energy quantum state.In quantum mechanics, an individual particle is represented by a wave that has both amplitude and phase. The most remarkable consequence of Bose-Einstein condensation (BEC) of a vast number of particles is that macroscopic properties become dependent on a single wavefunction, promoting quantum physics to classical length and time scales. A BEC is a highly ordered state in which the wavefunction phase is

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classical nematics generally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr(3)Ru(2)O(7) in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr(3)Ru(2)O(7) experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors

The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling n T 1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed. PACS numbers: 71.10.Pm, 73.40.Hm, 73.40.Gk When two parallel two-dimensional electron systems (2DES) are sufficiently close together, interlayer Coulomb interactions can produce collective states which have no counterpart in the individual 2D systems [1][2][3]. One of the simplest, yet most interesting, examples occurs when the total electron density, N T , equals the degeneracy, eB͞h, of a single spin-resolved Landau level produced by a magnetic field B. In the balanced case (i.e., with layer densities N 1 N 2 N T ͞2), the Landau level filling factor of each layer viewed separately is n hN T ͞2eB 1͞2. If the separation d between the layers is large, they behave independently and are well described as gapless composite fermion liquids. No quantized Hall effect (QHE) is seen. On the other hand, as d is reduced, the system undergoes a quantum phase transition [4-6] to an incompressible state best described by the total filling factor n T 1͞2 1 1͞2 1. A quantized Hall plateau now appears at r xy h͞e 2 . Both Coulomb interactions and interlayer tunneling contribute to the strength of this QHE but there is strong evidence from experiment [3,7] and theory [1,8] that the incompressibility survives in the limit of zero tunneling. This remarkable collective state exhibits a broken symmetry [9][10][11][12], spontaneous interlayer phase coherence, and may be viewed as a kind of easy-plane ferromagnet. The magnetization of this ferromagnet exists in a pseudospin space; electrons in one layer are pseudospin up, while those in the other layer are pseudospin down. Numerous interesting properties are anticipated, including linearly dispersing Goldstone collective modes (i.e., pseudospin waves), a finite temperature Kosterlitz-Thouless transition, dissipationless transport for currents directed oppositely in the two layers, and bizarre topological defects in the pseudospin field [9][10][11][12][13]. To date, most experimental results on this system have derived from electrical transport measurements [3,4,7,14,15] although recently an optical study has been reported [16].In this paper we report on a new study of the double layer n T 1 ferromagnetic quantum Hall state, and its transition at large layer separation to a compressible phase, using the method of tunneling spectroscopy. Earlier experiments have shown that there is a strong suppression of the equilibrium tunneling between two widely separated parallel 2DESs at high magnetic field [17,18]. This suppression is a ...