Observation of an Anisotropic Wigner Crystal

We report a new correlated phase of two-dimensional charged carriers in high magnetic fields, manifested by an anisotropic insulating behavior at low temperatures. It appears in a large range of low Landau level fillings $1/3\lesssim \nu \lesssim 2/3$ in hole systems confined to wide GaAs quantum wells when the sample is tilted in magnetic field to an intermediate angle. The parallel field component ($B_{\parallel }$) leads to a crossing of the lowest two Landau levels, and an elongated hole wave function in the direction of $B_{\parallel }$. Under these conditions, the in-plane resistance exhibits an insulating behavior, with the resistance along $B_{\parallel }$ about 10 times smaller than the resistance perpendicular to $B_{\parallel }$. We interpret this anisotropic insulating phase as a two-component, striped Wigner crystal.

Figure 1

(a) Conceptual rendition of an anisotropic (striped) Wigner crystal. (b) The charge distribution (red) and potential (black), from calculating the Schroedinger and Poisson’s equations self-consistently at $B=0$. (c) Experimental geometry: $R_{xx}$ and $R_{yy}$ denote the longitudinal magnetoresistance measured along and perpendicular to the parallel magnetic field ($B_{\parallel }$), respectively. (d) Schematic diagram, showing the crossing of the lowest two Landau levels at $\theta \simeq 35°$ near $\nu =1$. (e) Magnetoresistance traces measured at tilt angle $\theta \simeq 35°$ for a 2DHS with density $p=1.28\times 10^{11}{\mathrm{cm}}^{-2}$ and confined to a 40-nm-wide GaAs QW. Note the factor of 50 change in the scale for $R_{xx}$ and $R_{yy}$ for $B>8\mathrm{T}$. We observe an anisotropic insulating phase in a large filling factor range, from $\sim 2/3$ to $\sim 1/3$; note also the competition with FQHSs at several fillings.

Figure 2

Magnetoresistance traces for the sample of Fig. 1, measured at $\theta =0°$ (a) and 50° (b). Both $R_{xx}$ and $R_{yy}$ are much smaller near $\nu =1/2$ than in Fig. 1 data.

Figure 3

(a) $R_{xx}$ and $R_{yy}$ measured at three temperatures in the 40-nm-wide QW near $\nu =1/2$ at $\theta \simeq 35°$. (b) $T$ dependence of $R_{xx}$ and $R_{yy}$ near $\nu =1/2$. To avoid the influence of the relatively sharp $\nu =1/2$ resistance minima seen in some of the traces, here we are plotting the background resistances by interpolating between the shoulders flanking the $\nu =1/2$ minima. Also plotted is the $T$ dependence of the $R_{xx}$ minimum for the $\nu =2/5$ FQHS.

Figure 4

(a) $R_{yy}$ vs $B_{\perp }$ traces measured for a 2DHS confined to a 50-nm-wide GaAs QW at density $p=0.95\times 10^{11}{\mathrm{cm}}^{-2}$ and at different $\theta$. The 2DHS exhibits an insulating behavior near $\nu =1/2$ at $\theta \simeq 37°$ and at $\theta =65°$, but not at $\theta =25°$ or $\theta =55°$. The inset shows the calculated charge distribution and potential at $B=0$. (b) $R_{xx}$ and $R_{yy}$ traces are shown at $\theta \simeq 35°$ and at a slightly larger density ($p=1.12\times 10^{11}{\mathrm{cm}}^{-2}$) for different temperatures. Similar to the data of Fig. 3, both $R_{xx}$ $R_{yy}$ exhibit insulating behavior and the system is anisotropic near $\nu =1/2$.