Non-Equilibrated to Fully Equilibrated Edge Heat Transport in Hole-Conjugate States of the Fractional Quantum Hall Effect

The edge structure of hole-conjugate states in the fractional quantum Hall effect has long been the subject of extensive theoretical and experimental works. Originally proposed to host a backwards-flowing mode, carrying fractional charge, along with a forwards-flowing integer charge mode [1], the edge at the seminal hole-conjugate filling factor nu=2/3 was later understood to undergo a reconstruction due to disorder [2]. This reconstruction leads to the appearance of a backwards-flowing neutral mode which only carries heat, while a single fractional charge mode flows forwards. This peculiar structure turns out to raise further questions, in particular whether these two charge and neutral edge modes could exchange energy along their propagation, a phenomenon referred to as thermal equilibration. While the first experiments seemed to indicate a partial equilibration [3], very recent experiments, in both GaAs/Ga(Al)As and graphene, showed on the contrary that no equilibration takes place up to large distances (200 µm). Here we present the results of a heat transport experiment in graphene at the fractional filling factor 8/3, where we show that upon introducing a small amount of disorder in the same sample, a transition from non-equilibrated to fully-equilibrated edge modes is observed. This clear observation of the full thermal equilibration at the edge of a hole-conjugate fractional quantum Hall state allows us to set constrains to the different regimes of edge reconstruction.<br/>[1] MacDonald, PRL <b>64,</b> 220 (1990)<br/>[2] Kane, Fisher, Polchinski, PRL <b>72,</b> 4129 (1994)<br/>[3] Banerjee <i>et al., </i>Nature <b>545, </b>75 (2017)<br/>[4] Srivastav <i>et al., </i>Phys. Rev. Lett. <b>126, </b>216803 (2021)<br/>[5] Melcer <i>et al., </i>arXiv:2106.12486 (2021)