Evidence of interlayer correlation in spin excitations of quantum Hall bilayers with negligible tunneling

Manifestations of interlayer excitonic coherence in a quantum Hall bilayer with negligible tunneling occur in low-lying spin excitations measured by inelastic light scattering. The observation of quasiparticle spin-flip excitations with energies below the Zeeman gap identifies a composite-fermion metal as the high-temperature phase of the quantum Hall coherent state. Spin-flip intensities enable the determination of a critical temperature for this transformation that is in general agreement with those obtained from charge transport experiments.

Figure 1

(Color online) (A) Particle-hole transformation in bilayers at total filling factor ${\nu }_T=1$ allows us to describe the population of one of the two layers in terms of holes. The resulting ground state consists of a condensate of interlayer excitons and a conventional quantum Hall fluid formed by the excess charge that fully occupy the spin-up Landau level and supports a well-defined SW mode across the Zeeman gap. (B) Schematic of CF levels and spin excitations of the bilayer CF metal. $E_F$ is the CF Fermi energy. In the CF phase, a spin-flip $\left({\text{SF}}_{\text{CF}}\right)$ continuum of excitations across the Fermi level extends from the Zeeman gap down to an energy value $E_{gap}^{\text{CF}}$ determined by the relative position of the Fermi level within the spin-up and -down CF states. The drawing shown in the figure refers to the case of a spin-polarized CF metallic state.

Figure 2

(Color online) Left panels: representative spin excitation spectra (upper black lines) at $T=50\text{mK}$ and two values of filling factors ${\nu }_T=1$ and ${\nu }_T=1.25$ after on-resonant excitation with incoming laser energies $E_L=1526.7$ and 1526.2 meV, respectively. The luminescence backgrounds obtained with an off-resonant excitation at $E_L=1527.7\text{meV}$ are also shown and fitted with a Gaussian function (red/gray lines). A Lorentzian fit to the SW superimposed to the luminescence background (green/light gray lines) highlights the impact of the continuum of spin-flip excitations ${\text{SF}}_{\text{CF}}$ (shaded in blue/dark gray). Right panel: evolution of the integrated intensity of ${\text{SF}}_{\text{CF}}$ as a function of filling factor at $T=50\text{mK}$ normalized to the intensity of the SW peak.

Figure 3

(Color online) Representative spin excitation spectra at ${\nu }_T=1$ and two different temperatures. Red/gray and green/light gray lines are as in Fig. 2. The blue/dark gray shaded region represents the contribution of the continuum of composite-fermion spin-flip excitations ${\text{SF}}_{\text{CF}}$.

Figure 4

(Color online) Evolution of the composite-fermion spin-flip intensity normalized to the spin-wave intensity at ${\nu }_T=1$ as a function of temperature. Red/gray and black points refer to two sets of measurements on different positions on the sample.