Intrinsic Gap of the $\nu =5/2$ Fractional Quantum Hall State

The fractional quantum Hall effect is observed at low magnetic field where the cyclotron energy is smaller than the Coulomb interaction energy. The $\nu =\frac{5}{2}$ excitation gap at 2.63 T is measured to be $262\pm 15\mathrm{mK}$, similar to values obtained in samples with twice the electronic density. Examining the role of disorder on the $\frac{5}{2}$ state, we find that a large discrepancy remains between theory and experiment for the intrinsic gap extrapolated from the infinite mobility limit. The observation of a $\frac{5}{2}$ state in the low-field regime suggests that inclusion of nonperturbative Landau level mixing may be necessary to fully understand the energetics of half-filled fractional quantum Hall liquids.

Figure 1

(a) Hall resistance and (b) corresponding magnetoresistance in the second Landau level of our low-density, high mobility 2DEG ($T\sim 20\mathrm{mK}$).

Figure 2

(a) Arrhenius plot showing activated temperature behavior at $\nu =\frac{5}{2}$. (b) Quasigap measurement for $\nu =\frac{7}{2}$ (see text). (c) Energy gaps for all FQH states observed in the second Landau level, plotted in Coulomb energy units. Open circles are our data. Solid squares and circles, respectively, refer to the “high mobility” and “low mobility” samples in Ref. [17].

Figure 3

(a) Experimental (open symbols) and theoretical (solid square and circle) $\nu =\frac{5}{2}$ gap energy values found in literature. Solid triangles represent our data (the two data points result from two different mobilities measured on separate cooldowns). Inset: Intrinsic gap and disorder at $\frac{5}{2}$ deduced from particle-hole conjugate pairs (see text). (b) Same plot as in (a) but for $\nu =\frac{1}{3}$ gap values reported in the literature.