Electron Correlation in the Second Landau Level: A Competition Between Many Nearly Degenerate Quantum Phases

Abstract

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...

Spin and Charge Ordering in the Quantum Hall Regime

“…2.19 shows four reentrant states per spin branch, interposed by different FQHS. They appear at partial filling˜= 0.29, 0.43, 0.57, and 0.70, in agreement with previous publications [116][117][118]. That raises the question whether the reentrant states in the second Landau level are of equal nature as the bubble phases in higher levels.…”

Flatland Electrons in High Magnetic Fields

“…There is, however, no clear picture yet as to what determines the direction of the stripes in a purely perpendicular field [42,53,54]. Figure 14 provides yet another example of magnetotransport data [43] at T = 9 mK of an extremely high-quality GaAs 2DES with a mobility of 3.1 × 10 7 cm 2 /Vs. Here data are shown in the filling factor range 2 < ν < 3.…”

“…The physics of 2D carrier systems in the second and higher LLs is particularly delicate [42,43]. The electron wavefunction in these excited levels has a larger extent and also possesses one or more nodes.…”

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

“…This FQHS was discovered 1 and studied in depth in high quality two-dimensional electron gases (2DEGs) confined to GaAs/AlGaAs heterostructures . Other even denominator FQHSs in the GaAs/AlGaAs system develop at ν = 7/2 6,16,40,41 and ν = 2 + 3/8 [42][43][44] and possibly related FQHSs have been observed at even denominators in ZnO/MgZnO 45 and in bilayer graphene [46][47][48][49] . Since its discovery it was clear that, owing to the even denominator of the filling factor, the ν = 5/2 FQHS is not part of the sequence prescribed by the free composite fermion theory 50,51 .…”