Contrasting Behavior of the $\frac{5}{2}$ and $\frac{7}{3}$ Fractional Quantum Hall Effect in a Tilted Field

Using a tilted-field geometry, the effect of an in-plane magnetic field on the even denominator $\nu =\frac{5}{2}$ fractional quantum Hall state is studied. The energy gap of the $\nu =\frac{5}{2}$ state is found to collapse linearly with the in-plane magnetic field above $\sim 0.5\mathrm{T}$. In contrast, a strong enhancement of the gap is observed for the $\nu =\frac{7}{3}$ state. The radically distinct tilted-field behavior between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wave function for the $\frac{5}{2}$ fractional quantum Hall effect.

Figure 1

Magnetoresistance under tilt in the second Landau level around (a) $\nu =\frac{5}{2}$ and (b) $\nu =\frac{7}{2}$ plotted versus perpendicular field ($T\sim 20\mathrm{mK}$). Inset: enlargement showing the trend of the $\nu =\frac{8}{3}$, $\frac{5}{2}$, and $\frac{7}{3}$ FQHE minima.

Figure 2

(a)–(c) Activation gaps under tilt (corresponding Arrhenius plots are shown inset). Two data sets are shown in (a) with the open symbols corresponding to a slightly smaller density and mobility than the solid symbols. Open symbol in (b) was taken from an already destroyed gap. In (a), (b), linear fits (dashed lines) are used to estimate the $g$-factor (see text); solid curves are a guide to the eye. In (c), solid line is a linear fit to the low B-field data; dashed line is for a single-particle Zeeman interaction. (d) Schematic of a 2DEG in a tilted-field.

Figure 3

Normalized gap values vs parallel field (datasets are vertically offset for clarity). All data are replotted from Fig. 2 except the solid circles which is replotted from Ref. 14. Inset: Experimental gap versus $B_{||}$ at $\nu =\frac{5}{2}$ (open squares) compared with the theoretical interaction for single spin flips (dashed lines, see text).