Collective Modes and the Periodicity of Quantum Hall Stripes

We investigate the quantum Hall stripe phase at filling factor $9/2$ at the microscopic level by probing the dispersion of its collective modes with the help of surface acoustic waves with wavelengths down to 60 nm. The dispersion is strongly anisotropic. It is highly dispersive and exhibits a roton minimum for wave vectors aligned along the easy transport direction. In the perpendicular direction, however, the dispersion is featureless, although not flat as predicted by theory. Oscillatory behavior in the absorption intensity of the collective mode with a wave vector perpendicular to the stripes is attributed to a commensurability effect. It allows us to extract the periodicity of the quantum Hall stripes.

Figure 1

(a) The device geometry consisting of a cross-shaped mesa with legs oriented along the main crystal directions. SAW transducers are located at the end of each leg. (b) Chip carrier containing high frequency coaxial connectors and terminated coplanar waveguides. The chip with cross-shaped mesa is mounted in the central cavity. (c) Experimental setup highlighting the three electromagnetic waves incident on the sample.

Figure 2

(a)–(b) Absorption strength versus excitation frequency recorded at filling factor $9/2$ for an electron density of $2.63\times {10}^{11}/{\mathrm{cm}}^2$ and $k_{\mathrm{SAW}}=3.97\times {10}^7$ (top curve) or $1.98\times {10}^7/\mathrm{m}$ (bottom curve). In (a) the SAW propagates along the [110] direction, while in (b) along the $[1\overline{1}0]$ direction. (c) Resonance frequency as a function of $k_{\mathrm{SAW}}$ for both propagation directions. The data points were recorded at the same density on samples with different SAW transducers.

Figure 3

(a) Filling factor dependence of the frequency of the collective excitations of the quantum Hall stripe phase at filling $\nu =9/2$ at an electron density of $2.63\times {10}^{11}/{\mathrm{cm}}^2$ for $k_{\mathrm{SAW}}=3.97\times {10}^7/\mathrm{m}$ along either the [110] or $[1\overline{1}0]$ propagation direction. (b) Temperature dependence of the resonance frequency at $\nu =9/2$ for the same values of the density and $k_{\mathrm{SAW}}$.

Figure 4

(a) Microwave absorption strength at filling $\nu =9/2$ for density $2.04\times {10}^{11}$ (bottom green curve) and $2.95\times {10}^{11}/{\mathrm{cm}}^2$ when the SAW with $k_{\mathrm{SAW}}=5.29\times {10}^7/\mathrm{m}$ propagates along the $[1\overline{1}0]$ direction. (b) The same as in (a) except that the SAW is launched along the [110] direction. (c) Ratio of the absorption intensity of the resonances for surface acoustic waves propagating along the $[1\overline{1}0]$ and [110] directions as a function of $p_{\mathrm{SAW}}/R_c$. This ratio oscillates and exhibits maxima when $p_{\mathrm{SAW}}$ equals a multiple of $3.6R_c$.