Energy gap and spin polarization in the 5/2 fractional quantum Hall effect

We consider the issue of the appropriate underlying wave function describing the enigmatic 5/2 fractional quantum Hall effect (FQHE), the only even denominator FQHE unambiguously observed in a single-layer two-dimensional electron system. Using experimental transport data and theoretical analysis, we argue that the possibility of the experimental 5/2 FQH state being not fully spin polarized cannot be ruled out. We also establish that the parallel field-induced destruction of the 5/2 FQHE arises primarily from the enhancement of effective disorder by the parallel field with the Zeeman energy playing an important quantitative role.

Figure 1

(Color) The activation energy gap the 5/2 FQH state measured by various groups (filled symbols) is shown versus the perpendicular field (Refs. 3, 14, 15, 22, 23, 24, 25, 26, 27, 28). Assuming $f_1=1$ (i.e., not including the finite width correction), the trend of these data points can be fit to Eq. (1) with the following parameters: $a_1=1421$, $T_D=1387$, $a_3=1$, and $g=0.44$ (solid black); $a_1=1000$, $T_D=1000$, $a_3=1$, and $g=0.30$ (dashed green); $a_1=1000$, $T_D=1200$, $a_3=1$, and $g=0.27$ (dotted blue); $a_1=800$, $T_D=1200$, and $a_3=0$ (dotted-dashed red). Including the finite-width correction for a typical 30 nm QW, new set of fit parameters $a_1=1600$, $T_D=1600$, and $g=0.44$ (dashed purple) are needed for a better fit but the qualitative curve shape remains the same. The inset shows the energy gaps for the spin-polarized 1/3 FQH state determined using transport measurements (Refs. 29, 30, 31, 32, 33, 34) and direct measurement of the chemical jump (Ref. 35). These data points are fit to Eq. (1) with the following parameters: $a_1=3.14$, $T_D=4.57$, and $a_3=0$ (solid red); $a_1=3.05$, $T_D=5.30$, and $a_3=0$ (solid blue); $a_1=2.56$, $T_D=6.88$, and $a_3=0$ (solid black).

Figure 2

(Color) Suppression of the activation energy gap in a tilted field for the (a) 1/3 (Ref. 39); (b) 2/5 (Ref. 39); (c) 5/2 (Refs. 14, 25); and (d) 7/2 (Ref. 14) FQH states, all measured in a 40 nm sample. The data for the 1/3 and 2/5 FQH states (Ref. 39) are shown for different cooldown with square and circle symbols. For the 5/2 state, data from Ref. 25 measured in the same wafer were added and are shown as filled circles. The gap suppression calculated from Eq. (1) is shown by the lines, using the following parameters: $g=0$, $T_D=230\text{mK}$ (solid red); $g=0$, $T_D=0\text{mK}$ (dashed blue); $g=0.44$, $T_D=230\text{mK}$ (dashed green); $g=0.44$, $T_D=0\text{mK}$ (dotted black). The disorder parameter, $\gamma \left(B_{\parallel }\right)$, was extracted from a second-order polynomial fit to the low-field (0–6 T) parallel field magnetoresistance (Ref. 38).