Characterizing Neutral Modes of Fractional States in the Second Landau Level

Fractionally charged quasiparticles, which obey non-Abelian statistics, were predicted to exist in the $\nu =8/3$, $\nu =5/2$, and $\nu =7/3$ fractional quantum Hall states (in the second Landau level). Here we present measurements of charge and neutral modes in these states. For both $\nu =7/3$ and $\nu =8/3$ states, we found a quasiparticle charge $e=1/3$ and an upstream neutral mode only in $\nu =8/3$—excluding the possibility of non-Abelian Read-Rezayi states and supporting Laughlin-like states. The absence of an upstream neutral mode in the $\nu =7/3$ state also proves that edge reconstruction was not present in the $\nu =7/3$ state, suggesting its absence also in $\nu =5/2$ state, and thus may provide further support for the non-Abelian anti-Pfaffian nature of the $\nu =5/2$ state.

Figure 1

Hall effect data. (a) Fully developed fractional quantum Hall states are observed in $\nu =7/3$, $5/2$, and $8/3$ states. (b) Schematic description of the gated Hall bar. The chiral charge mode flows counterclockwise. Current driven into “charge sources” $C1$ and $C2$ flows towards the QPC; it is being partitioned and thus generating shot noise proportional to the tunneling charge, which is measured in probe $M$. The upstream neutral mode, if present, flows clockwise, presented by the red and blue trajectories that emerge from the “neutral source” $N$. The charge current (blue) flows into the ground $G1$. The upstream neutral mode (red) flows towards the QPC and generates charge mode fluctuations (dashed blue), which can be measured in $M$.

Figure 2

Excess noise and conductance in $\nu =8/3$ due to the arrival of a neutral mode at the QPC at $T=10\mathrm{mK}$. (a) Excess noise as a function of the current in the upper $2/3$ channel, $I_N^{8/3–2}$, injected from $N$ (charge current flows into $G1$ and the upstream neutral mode arrives at the QPC), for three different transmission probabilities of the QPC (obtained in three different gate voltages on the QPC). Excess noise proves the existence of an upstream neutral mode. (b) Excess noise at $I_{8/3–2}=1.25\mathrm{nA}$ as a function of the transmission probability of the QPC. The dashed line is proportional to $t_{8/3–2}$ ($1-t_{8/3–2}$). (c) Differential transmission probability (measured by current in $C1$ and measurement at $M$) as a function of the current $I_N^{8/3–2}$ at $N$. Strong dependence of the transmission probability is observed at lower transmissions.

Figure 3

Transmission probability and shot noise in $\nu =8/3$ as a function of the impinging current (injected from $C1$), with (red) and without (blue) an additional upstream neutral mode (injected from $N$). Measured shot noise is in dots; solid lines are the expected shot noise for specific charges and temperatures, as indicated. (a),(b) For a transmission probability independent of the impinging current, charge equals $e/3$ with and without the additional neutral current. (c),(d) For a transmission probability dependent on the impinging current, the presence of a neutral mode linearizes the transport as well as lowers the charge to almost $e/3$. In both cases the addition of the neutral mode raises the temperature to 25 mK.

Figure 4

Comparison between the excess noise, as a function of the injected current from contact $N$, in $\nu =7/3$, $5/2$, and $8/3$. Excess noise in $\nu =8/3$ and $5/2$ states proves the existence of an upstream neutral mode, oppositely to the case of $\nu =7/3$. Excess noise in the $\nu =8/3$ state was measured only for the positive injected current range and was mirror imaged.