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Project Topic
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Bosonic and fermionic statistics are at the heart of our understanding for a plethora of physical phenomena, such as electric conductivity in materials or neutron stars. For a long time, the potential existence of anyons, i.e., particles that have exchange statistics beyond this paradigm, would be a major breakthrough of modern Physics. Topologically ordered phases and its most celebrated experimental implementation, the Fractional Quantum Hall (FQH) effect, may host these exotic quasiparticles, including non-Abelian anyons, where the exchange is described by matrices rather than phase factors (like + 𝜋 for bosons and - 𝜋 for fermions). Beyond its impact on fundamental Physics, non-Abelian anyons could pave the way to topological quantum computing, implementing a hardware error code protection by design. After three decades of efforts to provide experimental evidence of anyons, the situation has recently experienced a major step forward. Two independent experiments have obtained a clear signature of fractional statistics, the simplest anyonic statistics, in GaAs/AlGaAs devices in the FQH regime. Moreover, advances in moiré superlattices and Van der Waals heterostructures, including twisted bilayer graphene at magic angles, are on the verge of realizing fractional Chern insulators, i.e. putative non-Abelian systems even without magnetic field. The proposal relies on a well-balanced consortium providing a broad theoretical and experimental international expertise to address the next major steps: the experimental detection, engineering, and manipulation of non-Abelian anyons in GaAs/AlGaAs devices and the theoretical and technological transfer to graphene platforms. The experimental component of the consortium will bring a synergetic alliance of the key ingredients for the proposal success: development of GaAs/AlGaAs devices, thermal measurement, interferometry, and engineering graphene heterostructure. The consortium will benefit from its strong theoretical and numerical backbone for system design and data analysis. The search for direct experimental proof of non-Abelian anyons and their controllability for braiding will be pursued through three interlinked work packages. We will develop thermal probing for non-Abelian anyons in GaAs/AlGaAs heterostructure where we will study bulk-edge correspondence and several edge-equilibration processes in higher Landau levels. We will address the anyonic statistics in graphene via interferometry measurement. Here we will probe the edge-dynamics in relation to the bulk and with the physical atomically sharp edges, an important unsolved issue that will impact future studies of non-Abelian states in Dirac materials. And for the long-term goal of designing the non-Abelian anyon platform, we will work on tunnel coupled FQH states in bilayer two-dimensional materials. In this system, the non-Abelian phase transition can be tuned via interlayer edge-edge tunneling, which can be detected through current-current correlation measurement.
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