# Paired composite superfluid phases

Many of the phenomena in condensed matter physics are based on correlations between electrons where strong interactions among electrons lead to new entities and new states of matter. One of the most celebrated examples is the fractional quantum Hall (FQH) effect which is the result of the highly correlated motion of electrons in two-dimensions exposed to a strong out-of-plane magnetic field, moreover, exhibit topological order. Its driving force is the reduction of Coulomb interaction between the like-charged electrons.

The even-denominator FQH states are of fundamental interest and biggest mysteries in quantum Hall physics, where immensely valuable non-Abelian anyons that are thought to be used in future topological quantum computers, reside. These states can host charge neutral Majorana excitations as well that dictates their topological order and offer great challenges in their detection via conventional conductance measurements. Here, we use monolayer or bilayer graphene as the two-dimensional electron gas. We aim to perform noise thermometry based thermal conductance measurements that are sensitive to both charged and neutral excitations, to probe the nature of these states and their hidden topological order. We also target the same by creating an interface of the even-denominator FQH states with the other states, with the interface harboring an isolated edge channel.

**Figure 1.** Longitudinal R_{xx} (red) and transverse R_{xy} (blue) resistances as a function of ν at T = 16 mK, B = 18 T for D = −80 mV/nm (N = 0) (top) and D = −160 mV/nm (N = 1) (bottom). Panels in the top right corners indicate the valley isospin and orbital. The shaded purple (center) and green (sides) regions correspond to FQH states composed of 2CFs and 4CFs. The insets show zoom-ins to R_{xy} plateaus at ν = 1/2 (bottom) and ν = 3/4 (top). We attribute these plateaus to pairing of 2CFs and 4CFs, respectively. In (top), R_{xx} data below ν = 1/3 were divided by 5 to accommodate large R_{xx} values.

## Publications

[1] Kumar R., Haug A., Kim J., Yutushui M., Khudiakov K., Bhardwaj V., Ilin A., Watanabe K., Taniguchi T., Mross D. F. & Ronen Y. (2024). Quarter-and half-filled quantum Hall states and their competing interactions in bilayer graphene. *arXiv preprint arXiv:2405.19405*.