Resonant Rayleigh Scattering from Bilayer Quantum Hall Phases

We observe resonant Rayleigh scattering of light from quantum Hall bilayers at Landau level filling factor $\nu =1$. The effect arises below 1 Kelvin when electrons are in the incompressible quantum Hall phase with strong interlayer correlations. Marked changes in the Rayleigh scattering signal in response to application of an in-plane magnetic field indicate that the unexpected temperature dependence is linked to formation of a nonuniform electron fluid close to the phase transition towards the compressible state. These results demonstrate a new realm of study in which resonant Rayleigh scattering methods probe quantum phases of electrons in semiconductor heterostructures.

Figure 1

(a) Schematic view of the double quantum well at $\nu =1$. Transitions in the SW and SF modes are indicated. Short vertical arrows indicate the orientation of spins, symmetric (S) and antisymmetric (A) states are separated by the tunneling gap ${\Delta }_{\mathrm{SAS}}$. (b) Transitions that contribute to the interband magnetoexciton (Ex) responsible for the resonance in the Rayleigh scattering intensity. The red lines represent Landau levels. Valence (VB) and conduction bands (CB) are separated by the interband gap $E_g$. (c) Representative example of the resonant profile of the Rayleigh scattering intensity at $\nu =1$ and $T=60\mathrm{mK}$: each sharp peak is the elastically scattered light with wavelengths and line shapes that match the ones of the incoming laser light. The dotted line is the magnetoluminescence with off-resonant excitation. (d) Logarithmic scale color plot of the light scattering intensities for the case reported in (c). The horizontal scale is the incident laser wavelength and the vertical scale is the energy shift between the scattered and incident light. The resonant Rayleigh scattering occurs at zero energy shift. Also indicated are the SW and SF inelastic light scattering peaks and the incoherent emission due to luminescence.

Figure 2

(a) Evolution of the Rayleigh scattering peaks as a function of incident laser wavelength at two different temperatures for sample 2 and (b) resonant profile for the Rayleigh scattering at $T=60\mathrm{mK}$. (c) Phase diagram for the incompressible (shaded area) and compressible (white area) states of the bilayer at $\nu =1$ [8]. The blue and red dots refer to samples 1 and 2, respectively. The sequence of open circles marks the evolution of the position of sample 2 at different angles $\theta$ (values in degrees). (d) Temperature behavior of the resonant Rayleigh scattering at different angles for sample 2. The best fits to Eq. (1) reported in the text are shown as solid lines. Data at each angle are shifted vertically for clarity.

Figure 3

(a) and (b) show color plots of RRS at $T=60\mathrm{mK}$ at $\theta <{\theta }_c$ and $\theta >{\theta }_c$, respectively. The sharp resonant enhancement of RRS observed in (a) disappears above ${\theta }_c=35°$. (c) Evolution of the binding energy $E_b$ [defined in Eq. (1)] as a function of angle (bottom horizontal axis) and ${\Delta }_{\mathrm{SAS}}/E_C$ (top horizontal axis). Data are in sample 2 except for the points in the blue rectangle that refer to sample 1 at $\theta =30°$. (d),(e) same as in (c) but for the Rayleigh intensity (d) and resonance width (e) as obtained as in Fig. 2b.