Finite-temperature behavior in the second Landau level of the two-dimensional electron gas

Reports of weak local minima in the magnetoresistance at $\nu =2+3/5, 2+3/7, 2+4/9, 2+5/9, 2+5/7$, and $2+5/8$ in the second Landau level of the electron gas in GaAs/AlGaAs left open the possibility of fractional quantum Hall states at these filling factors. In a high-quality sample we found that the magnetoresistance exhibits peculiar features near these filling factors of interest. These features, however, cannot be associated with fractional quantum Hall states; instead, they originate from magnetoresistive fingerprints of the electronic bubble phases. We found only two exceptions: at $\nu =2+2/7$ and $2+5/7$ there is evidence for incipient fractional quantum Hall states at intermediate temperatures. As the temperature is lowered, these fractional quantum Hall states collapse due to a phase competition with bubble phases.

Figure 1

Waterfall plot of the magnetoresistance in lower spin branch of the second Landau level ($2<\nu <3$). Filling factors of the five most prominent FQHSs are shown. The shaded areas mark the bubble phases present. Near 5.4 T there are two different bubble phases present. Arrows indicate precursors of the bubble phases, i.e. transport features at the highest temperature that can still be associated with the bubbles. Numbers on the side show the measured temperatures in mK.

Figure 2

A magnified view of the magnetoresistance at $2<\nu <3$ as measured at $T=59$ and 6.9 mK. The various filling factors of interest are marked by vertical lines. The shaded areas are bubble phases.

Figure 3

Details of the $T$ dependence of the magnetoresistance at filling factors less than $2+1/2$. Vertical arrows mark the precursors of the bubble phases $R2c$ and $R2d$.

Figure 4

Details of the $T$ dependence of the magnetoresistance at filling factors larger than $2+1/2$. Vertical arrows mark the precursors of the bubble phase $R2b$.

Figure 5

(a) Temperature dependence of the magnetoresistance in the vicinity of $\nu =2+2/7$. (b) The Hall resistance for the same range of filling factors and (c) a magnified view of the Hall resistance. Shading marks the bubble phases $R2a$ and $R2\tilde{a}$ at 6.9 mK. These bubble phases are separated by a deep minimum in $R_{xy}$ seen at $T=29$ and 32 mK, as shown in (b). Quantization of the Hall resistance at $\nu =2+1/3$ and at $2+2/7$ is marked by horizontal dotted lines.