Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $\nu =1/3$

Resonant inelastic light scattering experiments at $\nu =1/3$ reveal a novel splitting of the long-wavelength modes in the low energy spectrum of quasiparticle excitations in the charge degree of freedom. We find a single peak at small wave vectors that splits into two distinct modes at larger wave vectors. The evidence of well-defined dispersive behavior at small wave vectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long-wavelength modes of the electron liquid.

Figure 1

Inelastic light scattering spectra of low-lying long-wavelength charge modes at $\nu =1/3$ at various angles $\theta$ in (a) sample A and (b) sample B. The spectra are also labeled by the equivalent wave vector $k=(2{\omega }_L/c)\sin \theta$ in units of $1/l_0$. The gray arrows highlight the splitting of the single peak at small wave vectors into two peaks at larger wave vectors. The light gray lines show the background. The upper inset in panel (a) shows the inelastic light scattering geometry.

Figure 2

Spectra from Figs. 1a, 1b with backgrounds subtracted. The gray lines show fits with two Lorentzian line shapes.

Figure 3

(a) Energy difference between the two modes from samples A (red or gray) and B (black) as a function of $k{l}_0$ based on fits of spectra. The black bar at $k{l}_0=0.052$ represents the uncertainty in the mode separation based on the linewidth of the observed single peak. (b) Energy vs $k{l}_0$ for each individual mode. Open and solid triangles represent energies obtained by fits with two modes from samples A (red or gray) and B (black). Error bars do not include the uncertainty in determining the zero offset ($\lesssim 5\times {10}^{-4}{e}^2/ϵl_0$) for each spectrum. The dashed lines are guides for the eye for possible dispersions of the two modes.

Figure 4

(a) Spectrum at $\nu =1/3$ with $\theta =30°$. The arrows label assigned modes. A number of modes $\Delta (q_R)$, ${\Delta }_R^{\prime }$, and ${\Delta }_R^{\prime \prime }$ are seen in the range of the roton energy. Also indicated is the position of $2\Delta (q_R)$ and $E_B$. (b) Schematics for the quadrupolelike ${\Delta }_{2R}(q)$ dispersion [15, 17] and the $\Delta (q)$ excitation [3, 4, 18], which becomes dipolelike at $q_R$.