Hamiltonian Theory of Disorder at $\nu =1/3$

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Figure 1

A comparison of experimental gaps at $\frac{1}{3}$ of Dethlefsen et al. [7] as a function of total perpendicular field and the predictions of our approach. For sample $A$, ${\alpha }_{mn}=5\times {10}^{-4}$ and vary ${\alpha }_{00}$, while for sample $B$ we use ${\alpha }_{00\uparrow }=1.65\times {10}^{-3}$, ${\alpha }_{00\downarrow }=2.2\times {10}^{-3}$, ${\alpha }_{mn}=5.25\times {10}^{-4}$.

Figure 2

A comparison of the light-scattering data of Groshaus et al. [21] to theoretical results for the $n=0\uparrow \Rightarrow n=1$, $\uparrow$ and $n=1$, $\uparrow \Rightarrow n=0$, $\downarrow$ CF-LL gaps. The theoretical results are for ${\alpha }_{00\uparrow }=1.2\times {10}^{-3}$, ${\alpha }_{00\downarrow }=1.1\times {10}^{-3}$, and other ${\alpha }_{mn}=6.5\times {10}^{-4}$.