Yuval Ronen Lab

In the fractional quantum Hall effect, quasiparticles are collective excitations that have a fractional charge and show fractional statistics as they interchange positions. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, fractional statistics is most notable through quantum interference. Here we study fractional statistics in a bilayer graphene FabryPérot interferometer. We tune the interferometer from the Coulomb-dominated regime to the AharonovBohm regime, both for integer and fractional quantum Hall states. Focusing on the fractional quantum Hall state with a filling factor ν = 1/3, we follow the evolution of the AharonovBohm interference of quasiparticles while varying the magnetic flux through an interference loop and the charge density within the loop independently. When their combined variation is such that the Landau filling remains 1/3, the charge density in the loop varies continuously. We then observe pristine AharonovBohm oscillations with a period of three flux quanta, as expected for quasiparticles of one-third of the electron charge. Yet, when the combined variation leads to discrete events of quasiparticle addition or removal, phase jumps emerge and alter the phase evolution. Notably, across all cases with discrete and continuous charge variation, the average phase consistently increases by 2π with each addition of one electron to the loop, as expected for quasiparticles, obeying fractional statistics.

Bilayer graphene has emerged as a key platform for studying non-Abelian fractional quantum Hall (FQH) states. Its multiple half-filled plateaus with large energy gaps combined with its tunability offer an opportunity to distill the principles that determine their topological order. Here, we report four additional plateaus at ν=12 for different spin and valley, revealing a systematic pattern of non-Abelian states according to their Levin--Halperin daughter states. Whenever a pair of N=1 Landau levels cross, anti-Pfaffian and Pfaffian develop at half filling of the lower and higher levels, respectively. In the N=0 levels, where half-filled plateaus are absent, we instead observe four unexpected incompressible quarter-filled states along with daughters. The mutual exclusion of half- and quarter-filled states indicates a robust competition between the interactions favoring either paired states of two-flux or four-flux composite fermions. Finally, we observe several FQH states that require strong interactions between composite fermions. Our combined findings herald a new generation of quantum Hall physics in graphene-based heterostructures.

Electronic interferometers using the chiral, one-dimensional (1D) edge channels of the quantum Hall effect (QHE) can demonstrate a wealth of fundamental phenomena. The recent observation of phase jumps in a single edge channel Fabry-Pérot (FP) interferometer revealed anyonic quasiparticle exchange statistics in the fractional QHE. When multiple edge channels are involved, FP interferometers have exhibited anomalous Aharonov-Bohm (AB) interference frequency doubling, suggesting interference of 2e quasiparticles. Here, we use a highly tunable graphene-based QHE FP interferometer to observe the connection between integer QHE interference phase jumps and AB frequency doubling, unveiling the intricate nature of inter edge state coupling in a multichannel QHE interferometer. By tuning the electron density continuously from the QHE filling factor {\nu}7, we observe periodic interference phase jumps leading to AB frequency doubling. Our observations clearly demonstrate that in our samples the combination of repulsive Coulomb interaction between the spin-split, copropagating edge channels and charge quantization explains the frequency-doubled regime without electron pairing, via a near-perfect anti-correlation between the two edge channels. Our results show that interferometers are sensitive probes of microscopic interactions between edge states, which can cause strong correlations between chiral 1D channels even in the integer QHE regime.