Realizing non-abelian anyons in van der Waals materials

Introduction

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.

Background

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.

Objectives

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.

Research Plan

1. Spatial-Domain QH-Interferometry (Obj. 1)
   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, allowing the study of coherence and braiding of anyons.

2. Time-Domain Exchange Statistics (Obj. 2)
   We will study their exchange statistics in the time-domain via cross-correlation of current fluctuations of partitioned anyons.

3. Higher-Order Non-Abelian Anyons (Obj. 3)
   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, while low-disorder vdW-SC interfaces necessitate an in-situ stacking and integration of pre-patterned vdW-SC layers.

Conclusion

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.