Mise en page 1 - Laboratoire National des Champs Magnétiques ...

2009 TWO-DIMENSIONAL ELECTRON GASMagneto-intersubband oscillations in multilayer electron systemsTwo-dimensional (2D) electron systems with several occupiedsubbands exhibit magneto-intersubband (MIS) oscillationsdue to the modulation of intersubband scatteringprobability when Landau levels of different subbands arealigned. In contrast to Shubnikov de Haas (SdH) oscillations,the MIS oscillations are only weakly damped with increasingtemperature. Recently, MIS oscillations have beenobserved and investigated in double quantum well systemswhich consist of two quantum wells coupled by tunneling[Mamani et al., Phys. Rev. B 77, 205327 (2008)]. The finalstep is now a theory generalized to the multi-subband casewith N layers which is presented in this report, experimentallyverified in triple quantum wells (TQWs).We have studied symmetrically doped GaAs TQWs witha total electron sheet density n s = 9 × 10 11 cm −2 and mobilitiesof 5 × 10 5 cm 2 /V s. In a perpendicular magneticfield, Landau levels (LLs) pass sequentially the Fermi energyand the LL staircase associated with each subband issketched in figure 45(a) as well as a FFT analysis allowingus to extract the corresponding energy gaps. We havefound ∆ 12 = 4.0 meV, ∆ 13 = 5.4 meV and ∆ 23 = 1.4 meVfor a TQW with d b = 14 Å . The theory is generalized tothe multi-subband case [Wiedmann et al., to be publishedin Phys. Rev. B (2009)]. Here we present the MIS contributionto resistivity (second order quantum contribution).We use a simplified approximation that partial subband occupationsn j , transport scattering rates ν trj j ′ , and quantumlifetimes τ j are equal to each other (τ j = τ q ). Due to hightotal density and strong tunnel coupling, this approximationis reasonable for our system. In the regime of classicallystrong magnetic fields, we obtain the magnetoresistance forN=3 in the formρ d (B)ρ d (0) = 1 + 2 [3 d2 1 + 2 ( )3 cos 2π∆12ω c+ 2 ( )3 cos 2π∆13+ 2 ( )]ω c 3 cos 2π∆23, (5)ω cto electron-electron scattering which becomes essential forT >2.0 K. The result is in good agreement with experimentalobservations in single or bilayer systems, indicating thatthe sensitivity to electron-electron scattering is the fundamentalproperty of magnetoresistance oscillations originatingfrom second-order Dingle factor.Figure 45: Landau level staircase for a three-subband system andpicture of a TQW with three occupied subbands (1,2,3). (b) FFTspectra for the TQW with a barrier thickness of d b = 14 Å .where d = exp(−π/ω c τ q ) is the Dingle factor. This theoreticalmodel is in a good agreement with our observations andconfirms also the value of the energy gaps ∆ j j ′. The magnetoresistancein equation (5) is calculated assuming that thescattering potential is essential only in the side wells sincegrowth technology implies that most of the scatterers residein the outer barriers.In figure 46 we present temperature dependence of MISoscillations and the extracted averaged quantum lifetime.SdH oscillations are suppressed for T >4.2 K. The behaviorof τ q follows a T 2 -dependence and this is attributedFigure 46: (a) Temperature dependence of MIS oscillations and(b) extraction of averaged quantum lifetime as a function of temperaturefor samples with d b = 14 Å . For 4.2 K, SdH oscillationsare completely suppressed for B ≤0.6 T.S. Wiedmann, J.C. PortalN.C. Mamani, G.M. Gusev (Instituto de Física da Universidade de São Paulo, SP, Brazil), O.E. Raichev (Institute ofSemiconductor Physics, NAS of Ukraine, Kiev, Ukraine), A.K. Bakarov (Institute of Semiconductor Physics, Novosibirsk,Russia)35