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2009 TWO-DIMENSIONAL ELECTRON GASEmergent fractional quantum Hall effect in a triple quantum wellFractional quantum Hall (FQH) effect in a two-dimensional(2D) electron gas is a consequence of the existence of incompressiblestates at certain fractional filling factors ν ofLandau levels. Bilayer and trilayer systems possess an extradegrees of freedom and this leads to the appearance ofnew FQH states which are not present in single layer systems.Such correlated states occur if the interlayer electronelectroninteraction, controlled by the ratio of layer separationto the magnetic length, is comparable to the intralayerinteraction. Correlated states have already been discoveredin bilayer systems. In trilayer systems (triple quantumwells, TQWs), correlated states should also exist in acertain interval of parameters determined by the interlayerseparation, electron density and the magnetic length. Experimentsin low-density TQWs have not revealed the statespredicted in [MacDonald, Surf. Sci. 229, 1 (1990)]. A furtheradvance in fractional quantum Hall physics is based onnew many-body ground states in multilayer electron systemswhich are different from already studied bilayer systems.In our experiments we use symmetrically doped GaAsTQWs with a 230 Å wide central well and equal 100 Åwide lateral wells coupled by tunneling. The total electronsheet density is n s = 9·10 11 cm −2 and the mobility is 4·10 5cm 2 /V s. Here we present results with a barrier thicknessof 20 Å. The estimated density in the central well is 30%smaller than in the side wells. Experiments have been carriedout in a diluation refrigerator at low temperatures downto T ≃ 50 mK.of the tunneling gap is expected. Now electron motion isconfined into a single layer and correlation of eletrons innearby layers can lead to new states. In fact, when the sampleis tilted to an angle Θ > 45 ◦ , three new minima occurin R xx and Hall resistance exhibits precursors of the correspondingquantized plateaus. In figure 42(b) we presentedthe situation where three new fractional states are developed.Within an accuracy of 2%, the plateau at B ⊥ ≃10.2 Tcorresponds to the filling factor ν=10/3. The same effectoccurs for filling factor ν=2 [Gusev et al., Phys. Rev. B 80,161302(R) (2009)].To summarize, the observation of the collapse of integerfilling factors ν=4 and ν=2 and the emergence of new FQHstates with increasing in-plane magnetic field can be attributedto new correlated states in a trilayer electron systembecause these states occur when the in-plane magneticfield suppresses tunneling and multilayer many-body correlationsbecome possible.In order to observe many-body correlations one have toincrease the localization of electrons by applying an inplanemagnetic field. This in-plane magnetic field adds anAharanov-Bohm phase to the tunneling amplitude whichcauses oscillations of the tunnel coupling between electronstates in the layers and a suppression of this coupling forlow Landau levels (LLs) [G.M. Gusev et al., Phys. Rev. B78, 155320 (2008)]. This effect, which is a single-particlephenomenon, can be seen in figure 42(a) in the plot of R xxin the tilt angle - perpendicular magnetic field plane for thesecond LL at filling factors ν=7, 9 and 10 which vanish andreappear with increasing tilt angle. In this sample, fractionalquantum Hall states also occur with filling factorsν=17/3, 16/3 and 8/3 up to 15 T.Now, we focus on integer filling factor ν=4 where a completesuppression of the resistance is observed at Θ ≃ 40 ◦whereas the state at ν=5 remains robust with increasingtilt angle. The corresponding parallel magnetic field correspondsto the situation where the exponential suppressionFigure 42: (a) Longitudinal magnetoresistance in the tilt angle–magentic field plane for a TQW with a barrier width of 2.0 nm.Minimum for ν=4 is suppressed and three new FQH states occur.(b) Longitudinal and Hall resistance at Θ = 0 ◦ (dashed line) andΘ = 49 ◦ (solid) for T =50 mK.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)33