Upstream Neutral Modes in the Fractional Quantum Hall Effect Regime: Heat Waves or Coherent Dipoles

Counterpropagating (upstream) chiral neutral edge modes, which were predicted to be present in hole-conjugate states, were observed recently in a variety of fractional quantum Hall states ($\nu =2/3$, $\nu =3/5$, $\nu =8/3$, and $\nu =5/2$), by measuring the charge noise that resulted after partitioning the neutral mode by a constriction (denoted, as $N\to C$). Particularly noticeable was the observation of such modes in the $\nu =5/2$ fractional state—as it sheds light on the non-Abelian nature of the state’s wave function. Yet, the nature of these unique, upstream, chargeless modes and the microscopic process in which they generate shot noise, are not understood. Here, we study the ubiquitous $\nu =2/3$ state and report of two main observations: First, the nature of the neutral modes was tested by “colliding” two modes, emanating from two opposing sources, in a narrow constriction. The resultant charge noise was consistent with local heating of the partitioned quasiparticles. Second, partitioning of a downstream charge mode by a constriction gave birth to a dual process, namely, the appearance of an upstream neutral mode ($C\to N$). In other words, splitting “hole conjugated” type quasiparticles will lead to an energy loss and decoherence, with energy carried away by neutral modes.

Figure 1

Collision measurements—setup and results. Schematics of the measurements setup is presented in (a) and (b). Ohmic contacts in green (medium gray), 2DEG in light gray, and QPC constriction in black. The chiral neutral (charge) mode in red [medium-dark gray] (blue [dark gray]), flowing in opposite directions. Distance from $N1$ and $N2$ to the center of QPC opening $8\mu \mathrm{m}$. Distance from $C1$ and $C2$ to center of QPC opening $150\mu \mathrm{m}$. (a) $N\to C$ setup. Neutral mode injected (upstream) from source $N1$ toward the QPC, where it generates excess noise $S_{\mathrm{single}}$, which flows (downstream) towards voltage probe $N2$. (b) Collision setup. Neutral mode injected (upstream) simultaneously from contacts $N1$ and $N2$, flowing toward the QPC, where they generate excess noise $S_{\mathrm{collision}}$, which is measured in voltage probe $N2$. (c) and (d) Excess noise generated when a single neutral mode (red, $S_{\mathrm{single}}$) or two (black, $S_{\mathrm{collision}}$) neutral modes reach the QPC, for two different transmission probabilities $t$. $S_{\mathrm{single}}$ does not depend on the injecting contact ($N1$ or $N2$). (e) and (f) Scaling $S_{\mathrm{collision}}$; $S_{\mathrm{collision}}/S_{\mathrm{single}}=1.6$.

Figure 2

Collision experiment—results and model. (a) Dependence of excess noise at injection current 2 nA on transmission probability $t$ of the QPC—one (red triangles) or two (black squares) upstream neutral mode(s) reach the QPC. The noise follows the $t(1-t)$ trend (represented by a dashed line), with $S_{\mathrm{collision}}/S_{\mathrm{single}}=1.6$ for all $t$. Empty/full shapes represent measurements performed on different samples. (b) Schematics of the model calculation in the text. The charge mode propagates from $C1$ or $C2$ toward the voltage probe and partitioned by the QPC. The measured noise signal is made of the emitted noise from the contacts and the noise generated at the QPC. (c) Noise generated by partitioning the charge mode. Without an excited neutral mode (blue [dark gray]), the noise agrees with the tunneling of $2e/3$ quasiparticles at low temperature. When a constant neutral mode is introduced to the opposite edge (red [medium gray], $I_n=2\mathrm{nA}$), it elevates its temperature to $T_n$, and a reduction in the tunneling quasiparticles charge (to $e/3$) is observed. A temperature increase to $T_n\sim 50\mathrm{mK}$ is estimated from the dependence of the noise near $I_c=0$. In contrast, the increase in background noise leads to $T_n\sim 250\mathrm{mK}$.

Figure 3

Detection of the neutral mode by an Ohmic contact. (a) Schematics of the measurement setup. Injecting current from contact $N3$, gives birth to a neutral mode flowing upstream, reaching the voltage probe $N2$ ($25\mu \mathrm{m}$ away), where it generates excess noise. (b) Noise at voltage probe $N2$ as a function of injected current at $N3$ for $\nu =2/3$ (black). No noise is observed at $\nu =1$ (red). (c) Similar results at the first excited Landau level, measured on a different sample. Noise signal is observed at $\nu =5/2$ but not at $\nu =7/3$.

Figure 4

$N\to C$ and $C\to N$ processes. (a) and (b) Schematics of the measurement setup for $N\to C$ and $\mathrm{C}\to \mathrm{N}$, respectively. In the $C\to N$ process, current (blue [dark gray]) is injected from source $C1$, flowing downstream and reaching the QPC, where it is partitioned. The neutral mode (red [medium gray]), generated at the QPC, flows upstream and reaches the voltage probe $M1$ ($8\mu \mathrm{m}$ apart). The distance from the center of the QPC to $C1$ is $150\mu \mathrm{m}$. (c) and (d) Noise measured at the voltage probe as a function of the injected current for different transmission probabilities $t$ of the QPC. Noise in the $N\to C$ process is presented in (c), and noise in the $C\to N$ process is presented in (d). Data points are connected by a guide to the eye. (e) and (f) Noise measured at the voltage probe for different transmission probabilities $t$ for 1 nA injection current. In the two plots the data follows the $t(1-t)$ trend—given by a dashed line. Empty and full circles represent data points from different samples.