Realizing non-abelian anyons in van der Waals materials

Demonstrating non-abelian exchange statistics holds the promise of leading science to new terrains where we can manipulate exotic quasiparticles.

Unlike fermions, bosons, and abelian anyons, the many-body wavefunction of indistinguishable non-abelian anyons is entirely altered when swapping their positions.

With the theoretical groundwork for uncovering exotic exchange properties, pioneering experiments provided preliminary evidence of the lowest-order non-abelian anyons, indicating the topological superconductivity phase.

Yet, due to technological limitations inherent to current state-of-the-art platforms, new observations of non-abelian statistics or preliminary signatures of higher-order non-abelian anyons must be offered.In this proposal, I aim to directly observe the exchange statistics of non-abelian anyons, overcoming present technological challenges by incorporating proven intricate designs to innovative van der Waals (vdW) heterostructures.We will study spatial-domain and time-domain braiding of non-abelian anyons in the fractional quantum Hall effect (FQHE) regime, realized in high-mobility graphene-based heterostructures.

We will perform spatial-domain QH-interferometry (Obj. 1), allowing the study of coherence and braiding of anyons; and study their exchange statistics in the time-domain via cross-correlation of current-fluctuations of partitioned anyons (Obj. 2).

Higher-order non-abelian anyons will be sought after via fractional Andreev Reflection (AR) in FQHE-superconductor (SC) hybrids.

Employing shot noise measurements will allow identifying the AR charge quanta (Obj. 3), while low-disorder vdW-SC interfaces necessitate an in-situ stacking and integration of pre-patterned vdW-SC layers.This research will identify phases hosting non-abelian anyons and thus lay the groundwork for their detection and manipulation.

This contribution, being fundamental in its core, may also offer a practical option for fault-tolerant topological quantum computation.