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TWO-DIMENSIONAL ELECTRON GAS 2009Reentrant fractional quantum Hall states in a triple quantum wellTriple quantum wells (TQWs) consist of three quantumwells separated by thin barriers and can be considered asthree parallel two-dimensional (2D) electron layers coupledby tunneling. The corresponding Landau level (LL)fan diagram for TQWs consists of spin-split LLs separatedby energy gaps which are described by the expressionω c (N + 1/2) ± ∆ Z /2 + E j , where ω c is the cyclotron energy,∆ Z the Zeeman energy, and E j ( j = 1,2,3) the energiesof quantization in the TQW potential. Within thetight-binding model [Hanna et al., Phys. Rev. B 53, 15981(1996)] these energies as well as the corresponding singleelectronwave functions can be estimated. An in-plane magneticfield adds an Aharonov-Bohm phase to the tunnelingamplitude which causes oscillations of the tunnel couplingbetween electron states in the layers and suppresses the tunnelcoupling for low LLs. Here, we investigate fractionalquantum Hall (FQH) around total filling factor ν=5/2.An interesting behavior is observed in the region betweenfilling factors 2 and 5/2, see figure 44. Several new plateausoccur which are absent for B ‖ =0 T. The exact origin of theemergent and reentrant plateaus at fractional filling factorsis still not clear. We believe that this phenomenon involvescorrelation of electron states in several (three) partially populatedsubbands. Further studies are needed to understandthe nature of FQH effect in TQWs.We have studied symmetrically doped GaAs TQWs with a230 Å wide central well and equal 100 Å wide lateral wells.The total electron sheet density is n s = 9 × 10 11 cm −2 andthe mobility is 4 × 10 5 cm 2 /V s. The estimated density inthe central well is 30% smaller than in the side wells. Allmeasurements have been carried out in a resistive magnetat a temperature of T ≃ 100 mK up to 34 T.Figure 43 presents our main observation: the FQH stateν =7/3 first disappears with increasing tilt angle, is then replacedby an emergent ν = 12/5 state and exhibits a reentrancefor Θ = 55 ◦ with a very wide plateau. We explainthis behavior by the influence of perpendicular and parallelmagnetic fields. The perpendicular field leads to a consecutivedepopulation of the subbands whereas the parallelcomponent is responsible for a decrease of the subbandgaps due to suppression of tunnel coupling. If tunnel couplingis present, we have always gaps between subbands.When tunnel coupling is cut off by the in-plane field, thedepopulation of the upper subband is accompanied by a decreaseof the separation between the upper and the lowersubbands, as a result of modification of the TQW potentialprofile owing to electron redistribution, until subbands startto overlap. The overlap effect is essential for total fillingfactors ν < 5/2. We estimate that the depletion of the uppersubband down to partial filling factor ν 3 = 1/3 correspondsto a strong overlap whereas the depletion to ν 3 = 2/5 correspondsto a weak overlap. This gives rise to a suppressionof ν = 7/3 and the emergence of a more favourable plateauat ν = 12/5 but the reentrance of ν = 7/3 with increasing tiltangle cannot be attributed within this model, and is possiblyrelated to enhancement of electron-electron correlations bythe parallel magnetic field [Gusev et al., Phys. Rev. B 80,161302(R) (2009)].Figure 43: Longitudinal and Hall resistance for Θ = 0 ◦ (dashed),Θ = 46.3 ◦ (red/gray) and Θ = 55 ◦ (blue/dark grey) present reentranceof the FQH state ν=7/3 and the appearance of the emergentFQH state ν=12/5.Figure 44: Hall resistance R xy as a function of B ⊥ at 100 mKfor different tilt angles. Plateau ν=7/3 fist dissappears and is replacedby ν= 12/5 with increasing tilt angle. For Θ = 49.5 ◦ , ν=7/3exhibits reentrant behavior. Several new FQH states occur.S. Wiedmann, J.C. PortalG.M. Gusev (Instituto de Física da Universidade de São Paulo, SP, Brazil), O.E. Raichev (Institute of SemiconductorPhysics, NAS of Ukraine, Kiev, Ukraine), A.K. Bakarov (Institute of Semiconductor Physics, Novosibirsk, Russia)34