Even-denominator states of the fractional quantum Hall effect (e.g. ??=5/2) are expected to host excitations that have non-abelian anyonic statistics, making them promising candidates for the realization of topological quantum computing [1]. While the demonstration of these non-abelian statistics has long been an extremely challenging endeavor, recent experiments in GaAs semiconductor heterostructures have shown that the edge thermal conductance of the ??=??/?? state is quantized in half-integer values of the thermal conductance quantum [2,3]. This half-integer quantization is known to be an universal signature of non-abelian statistics, including of Majorana fermions [4]. However, many of the suspected candidates for the ground state of ??=5/2 have complex edge structures exhibiting counterpropagating neutral modes, which can modify the edge thermal conductance and give them non-integer values similar to that of a non-abelian edge. A very recent experiment [3] has circumvented the issue by finding a way to separate the contributions of the different channels at the edge, confirming the existence of a non-abelian channel with half-integer quantized electrical and thermal conductance. The next obvious interrogation is whether this result is truly universal: does it hold for different material, and different even-denominator states?

In this project, we propose to address these questions by performing heat transport measurements in fractional quantum Hall states in bilayer graphene. Bernal-stacked bilayer graphene (BLG) has recently shown to host a large variety of robust even-denominator fractional quantum Hall states [5-8], both hole- and electron-type. This provides an excellent test-bed on which to probe the thermal conductance, as these fractions are expected to be described by different (possibly non-abelian) ground states; furthermore, the ability to apply electric displacement fields allows a further degree of control over the even-denominator states, which can be investigated in terms of heat transport.

This experimental project relies on ultra-low temperature, high magnetic field thermal transport [9] based on high sensitivity-sensitivity electrical measurements. We are looking for highly motivated candidates whoe are interested in all aspects of the project, both experimental (sample fabrication, low noise measurements, cryogenics) and theoretical.

[1] Nayak, et al., RMP 80, 1083 (2008) [2] Banerjee, et al., Nature 559, 205 (2018)
[3] Dutta, et al., Science 377, 1198 (2022) [4] Kasahara, et al., Nature 559, 227 (2018)
[5] Ki, et al., Nano Letters 14, 2135 (2014) [6] Li, et al., Science 358, 648 (2017)
[7] Zibrov, et al., Nature 549, 360 (2017) [8] Huang, et al., PRX 12, 031019 (2022)
[9] Le Breton, …, & Parmentier, PRL 129, 116803 (2022)