Seeing emergent phases in quantum Hall double layersa)
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(Color online) (a) Kinematics of inelastic light scattering. (b) Typical setup for inelastic light scattering experiments at low temperature and high magnetic field. The sample [a coupled GaAs double quantum well (DQW)] is placed in a magnetocryostat. A tunable single-mode titanium-sapphire laser is used as the source of the incident radiation. (c) Sequence of layers in a typical GaAs/AlGaAs modulation-doped DQW heterostructure grown for light scattering experiments. The conduction-band profile along the growth axis is also shown. The high-mobility 2D electron system (2DES) resides in the GaAs quantum wells. Buffer and substrate layers are made of GaAs. The distance between Si doping (crosses) and GaAs DQW is around 100 nm.
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(Color online) (a) Schematic representation of the backscattering geometry and of the double quantum well in the single-particle configuration at . Transitions in the spin-wave (SW) and spin-flip (SF) modes are indicated by curved vertical arrows. Short vertical arrows indicate the orientations of spin. “S” and “A” label the symmetric and antisymmetric levels separated by the tunneling gap . and indicate the wave vector and frequency of incident (scattered) light. , , and are the total magnetic field and its components perpendicular and parallel to the plane of the two–dimensional electron system (2DES). is the tilt angle. (b) Polarized (thick curve) and depolarized (thin curve) inelastic light scattering spectra at and normal incidence. SDE and CDE label the peak due to spin- and charge-density excitations, respectively. SPE is the single-particle excitation at . (c) Resonant inelastic light scattering spectrum showing SW and SF excitations at after conventional subtraction of the background due to the laser and main luminescence. Solid and dashed lines show the fit with two Lorentzian functions. After Ref. 15.
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(a) Resonant inelastic light scattering spectra showing spin-wave (SW) and spin-flip (SF) excitations as a function of tilt angle at . Values of the in-plane magnetic field are also shown. At only one peak identified as the SW is observed. (b) Angular dependence of the energy difference between the SW and SF peaks (dots). The dashed curve is the predicted angular dependence of the tunneling gap evaluated in Ref. 24. (c) Angular dependence of the emergent fraction of electrons in the excited state ( and are the average electron densities in the lowest and excited levels, respectively). After Ref. 15.
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