Experimental studies of the fractional quantum Hall effect in the first excited Landau level

Abstract

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.

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

“…Therefore, they may strongly overlap at these system sizes, thereby leading to a finite gap for finite-size systems [78]. Hence, the extrapolation to the thermodynamic limit might be a much more delicate procedure then previously appreciated and, in fact, could point to a potential reason for the long-noticed discrepancy between calculated energy gaps and experimentally measured gaps [2][3][4][5][6][7][8][9][10]12,[14][15][16][17][18][19][20][21][22][23].…”

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 .…”

Observation of a Fractional Quantum Hall State atν=1/4in a Wide GaAs Quantum Well

“…Fg, 73.43.Qt, 73.63.Hs Interest in the even-denominator fractional quantum Hall (FQH) state at ν = 5/2 in the first excited Landau level continues to remain high over twenty years after its discovery [1]. Generally believed to be due to the p−wave pairing of composite fermions [2,3,4,5], the quasi-particle excitations of this state are thought to obey nonabelian statistics and thus may be relevant to faulttolerant, topological quantum computing schemes [6,7].To date, observations of even-denominator FQH states have been rare beyond the ν = 5/2 state in single-layer systems [8]. In particular, experimental evidence for a FQH state at ν = 1/2, the lowest Landau level counterpart of the ν = 5/2 state, does not exist, although previous theoretical work has suggested that it may form in thick two-dimensional electrons systems (2DES) [9].…”