Transition from a fractional quantum Hall liquid to an electron solid at Landau level filling $\nu =\frac{1}{3}$ in tilted magnetic fields

We have observed in a low density two-dimensional hole system (2DHS) of extremely high quality (with hole density $p=1.6\times {10}^{10}{\mathrm{cm}}^{-2}$ and mobility $\mu =0.8\times {10}^6{\mathrm{cm}}^2∕\mathrm{V}\mathrm{s}$) that, as the 2DHS is continuously tilted with respect to the direction of the magnetic field, the $\nu =\frac{1}{3}$ fractional quantum Hall effect (FQHE) state is weakened and at the temperature of $\sim 30\mathrm{mK}$ its magnetoresistivity rises from $\sim 0.4\mathrm{k}\mathrm{\Omega }∕\mathrm{◻}$ in the normal orientation to $\sim 180\mathrm{k}\mathrm{\Omega }∕\mathrm{◻}$ at tilt angle $\theta \sim 80\mathrm{°}$. We attribute this phenomenon to the transition from the FQHE liquid state to the pinned Wigner solid state, and argue that its origin is the strong coupling of subband Landau levels under the tilted magnetic fields.

Figure 1

Overview of ${\rho }_{\mathit{xx}}$ at $\theta =0\mathrm{°}$. The 2DHS density is $p\sim 1.6\times {10}^{10}{\mathrm{cm}}^{-2}$ and $T\sim 30\mathrm{m}\mathrm{K}$. Major IQHE and FQHE states are indicated by the arrows.

Figure 2

Tilted $B$ field dependence of ${\rho }_{\mathit{xx}}$ at seven angles at $\theta =0\mathrm{°}$, 33°, 49°, 61°, 71°, 77°, and 80° (from bottom to top). All the traces were taken at $T\sim 60\mathrm{m}\mathrm{K}$, except the one at $\theta =80\mathrm{°}$, which was taken at $T\sim 47\mathrm{m}\mathrm{K}$. The $x$ axis is the perpendicular $B$ field, $B_{\mathit{perp}}=B\times \cos \left(\theta \right)$. The right $y$ axis is in units of $h∕e^2$, for the same traces. The inset shows schematically the evolution from a FQHE liquid phase (e.g., at $\nu =\frac{1}{3}$) to the WS phase as $r_s$ is increased. This phase diagram is adopted from Ref. 5.

Figure 3

${\rho }_{\mathit{xx}}$ minimum at $\nu =\frac{1}{3}$ vs $B_{\mathit{ip}}$, plotted on a semi-log scale. The straight line is a linear fit to all data points, except the one at $\theta =80\mathrm{°}$.

Figure 4

Temperature dependence of ${\rho }_{\mathit{xx}}$ minimum at $\nu =\frac{1}{3}$ at different tilt angles: (a) ${\rho }_{\mathit{xx}}$ vs $T$; (b) ${\rho }_{\mathit{xx}}$ vs $1∕T$ for the same data.

Figure 5

Temperature dependence of ${\rho }_{\mathit{xx}}$ minimum at $\nu =\frac{2}{3}$ at different tilt angles: (a) ${\rho }_{\mathit{xx}}$ vs $T$; (b) ${\rho }_{xx}$ vs $1∕T$. The same symbol represents the same tilt angle as in Figs. 4a, 4b.

Figure 6

${\rho }_{\mathit{xx}}$ in parallel $B$ field, $\theta \sim 90\mathrm{°}$.