Signatures of spin in theν=1∕3fractional quantum Hall effect

Abstract

The activation gap ⌬ of the fractional quantum Hall state at constant filling =1/3 is measured in a wide range of perpendicular magnetic field B. Despite the full spin polarization of the incompressible ground state, we observe a sharp crossover between a low-field linear dependence of ⌬ on B and a Coulomblike square root behavior at large B. From the global gap reduction we get information about the mobility edges in the fractional quantum Hall regime. DOI: 10.1103/PhysRevB.74.165325 PACS number͑s͒: 73.43.Fj, 71.10.Pm, 72.25.Dc In recent years the increased mobility of two-dimensional electron systems ͑2DES͒ has allowed for the experimental investigation of the fractional quantum Hall effect ͑FQHE͒ 1,2 at relatively small magnetic fields. In this regime the interplay between interactions and the electronic spin yields interesting properties of either the ground state or the excitation spectrum of the system. Quantum phase transitions between differently spin-polarized ground states have been predicted and experimentally observed for several FQH states while varying the perpendicular magnetic field B. 3-12In parallel, the theoretical understanding of the FQHE has been considerably deepened by the introduction of composite fermions ͑CF͒, 13 quasiparticles made of one electron and two magnetic flux quanta. The correlated many-electron problem in high magnetic fields can be interpreted in terms of weakly interacting CF in a smaller effective field, offering a unified theory of the compressible and incompressible electronic FQH states. The former are mapped onto CF Fermi liquids, 14 while the latter are viewed as the integer QHE of CF.One of the main experimental signatures associated to the incompressible FQH states is a thermally activated longitudinal resistivity, xx ϰ exp͓−⌬ /2T͔, with the associated finite activation gap ⌬. An accurate determination of ⌬ is therefore crucial in order to test the predictions of the CF theory on the spectrum of incompressible FQH states and to extract the quasiparticle effective parameters. Early measurements of ⌬ vs B revealed the importance of disorder and finite thickness of the 2DES in reducing the gap with respect to the numerically calculated one. 15 However, the limited experimental range of variation of electron densities and mobilities allowed only a few data points for each incompressible state. Detailed measurements of the activation gaps in the low-B regime were recently performed for filling factors =2/3 and 2 / 5 on high mobility samples. 16 The linearly vanishing gap close to their spin-polarization quantum phase transition highlighted the importance of the quasiparticle Zeeman energy in the spectrum at relatively small magnetic fields.In this paper we present a detailed analysis of the activation gap for the paradigmatic FQH state at fixed filling factor =1/3 in a very wide range of purely perpendicular magnetic field. We clearly observe a sharp crossover between two regimes: a linear B dependence for small magnetic fields and a ͱ B dependence for higher field...

Direct Measurements of Fractional Quantum Hall Effect Gaps

“…The fractional gap is predicted to be determined by the Coulomb interaction in the form e 2 /εl B (where ε is the dielectric constant and l B = ( c/eB) 1/2 is the magnetic length), which leads to a square-root dependence of the gap on magnetic field, B. Observation of such a behavior would confirm the predicted gap origin.Attempts to experimentally estimate the fractional gap value yielded similar results, at least, in high magnetic fields [6,7,8,9,10]. Still, the expected dependence of the gap on magnetic field has not been either confirmed or rejected.…”

“…The problems with experimental verification are as follows. Standard measurements of activation energy at the longitudinal resistance minima allow one to determine the mobility gap [6,7] which may be different from the gap in the spectrum. The data for the gap obtained by thermodynamic measurements depended strongly on temperature [8]; for this reason, the magnetic field dependence of the gap may be distorted.…”

Measurement of theν=1/3Fractional Quantum Hall Energy Gap in Suspended Graphene

“…As an alternative scenario, however, the activation energy gap could be linear in B, if the nature of charged quasiparticle excitations of this FQH state are associated with spin-flips in skyrmion-like excitations of a spin-polarized FQH ground state [20]. Given the field range and error bars of the data points, we cannot rule out either scenario at present.…”

“…The predicted gap is then in the range ∆ 1/3 =26-50 K at B =14 T, in reasonable agreement with the gap measured in our experiment. For comparison, the observed disorder reduced ∆ 1/3 in graphene is at least 3 times larger than that of the 2DEGs in the best quality GaAs heterojunctions in a similar field range [20]. We further remark that ∆ 1/3 obtained in this experiment is much larger than the gaps obtained for FQH states associated to ν > 1 considering those gaps are obtained at B =35 T [16].…”

Energy gap and spin polarization in the 5/2 fractional quantum Hall effect

“…Including the finite width correction for a typical 30 nm QW, new set of fit parameters a1 = 1600, TD = 1600 and g = 0.44 (dashed purple) are needed for a better fit, but the qualitative curve shape remains the same. The inset shows the energy gaps for the spin-polarized 1/3 FQH state determined using transport measurements [29][30][31][32][33][34] and direct measurement of the chemical jump 35 . These data points are fit to Eq.…”