At a very low temperature of 9mK, electrons in the 2nd Landau level of an extremely high mobility two-dimensional electron system exhibit a very complex electronic behavior. With varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed ν = 2 + 2/5 state separated from the even-denominator ν = 2 + 1/2 state by an insulating phase and a ν = 2 + 2/7 and ν = 2 + 1/5 state surrounded by such phases. A developing plateau at ν = 2 + 3/8 points to the existence of other even-denominator states.Low-temperature electron correlation in the lowest Landau level (LL) of a two-dimensional electron system (2DES) separates largely into two regions. At very low filling factor, ν ≤ 1/5, an insulating phase exists, which has now quite convincingly been determined to be a pinned electron solid [1,2,3]. At higher filling factor 1 > ν >∼ 1/5 the multiple sequences of fractional quantum Hall effect (FQHE) liquids [4,5, 6,7] dominate, which show the characteristic vanishing magneto resistance, R xx , and quantized Hall resistance, R xy , at many odd-denominator rational fractional fillings ν = p/q [8].Altogether about fifty such FQHE states have been observed in this region. Their multiple sequences can largely be described within the composite fermion (CF) model [9,10, 11,12], with the exact origin of some higher order states still being argued. The electrical behavior between FQHE states carries no particularly strong transport signature, being thought of as arising largely from the conduction of excited quasiparticles of the neighboring FQHE states, with CF liquids occurring at some even-denominator fractions.At high LL's a very different pattern seems to emerge. There charge density wave (CDW) or liquid crystal like states dominate, often referred to as electronic stripe and bubble phases [13,14,15]. Characteristically these states are pinned to the lattice, immobilizing the electrons of this LL, which leads to transport properties identical to those of the neighboring integer quantum Hall effect (IQHE) states. FQHE states are absent in these high LL's, except for the recent observation of two FQHE features in the third LL, at elevated temperatures [16]. Of course, high LL fillings typically occur at lower magnetic fields and hence at poorer resolution of potential FQHE features. However, very general theoretical arguments [17,18] based on an increasing extent of the wavefunction with increasing LL index, hence the increasing importance of exchange and the diminishing applicability of point-like interactions, clearly support this trend.It is in the 2nd LL where electron liquids and electron solids collide. The larger extent of the wavefunction as compared to the lowest LL and its additional zero allows for a much broader range of electron correlations to be favorable, leading to an ever changing competition between multiple electronic phases as the filling factor is varied and as the temperature is low...

We present a spectrum of experimental data on the fractional quantum Hall effect (FQHE) states in the first excited Landau level, obtained in an ultrahigh mobility twodimensional electron system (2DES) and at very low temperatures and report the following results: For the even-denominator FQHE states, the sample dependence of the ν=5/2 state clearly shows that disorder plays an important role in determining the energy gap at ν=5/2. For the developing ν=19/8 FQHE state the temperature dependence of the R xx minimum implies an energy gap of ~5mK.The energy gaps of the odd-denominator FQHE states at ν=7/3 and 8/3 also increase with decreasing disorder, similar to the gap at 5/2 state. Unexpectedly and contrary to earlier data on lower mobility samples, in this ultra-high quality specimen, the ν=13/5 state is missing, while its particle-hole conjugate state, the ν=12/5 state, is a fully developed FQHE state. We speculate that this disappearance might indicate a spin polarization of the ν=13/5 state.Finally, the temperature dependence is studied for the two-reentrant integer quantum Hall states around ν=5/2 and is found to show a very narrow temperature range for the transition from quantized to classical value.

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