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From Bulk to Edge: Realization and Characterization of Fractionalized Quantum Matter

Periodic Reporting for period 1 - sharpEDGE (From Bulk to Edge: Realization and Characterization of Fractionalized Quantum Matter)

Reporting period: 2017-10-01 to 2019-09-30

Quantum effects, topology and strong interactions can act together to produce a vast array of exotic phases of matter at low temperature. Their interplay is essential to describe the phenomena occurring in physical systems as varied as semiconductor heterostructures, superconducting quantum circuits, magnetic insulators or ultracold atomic gases. Powerful concepts have arisen from the study of this trio, describing collective phenomena with no equivalent in single-particle systems. For example, anyons are particles which behave like a fraction of an electron; they do not exist as fundamental particles, but emerge as collective excitations in the fractional quantum Hall effect. The first objective of this project was to determine how to realize a device made by coupling the edges of a fractional quantum Hall system with a superconductor, a set-up which is currently envisioned to realize a qubit for quantum computation intrinsically immune to decoherence. The second objective of this project was to design experimental protocols to detect strongly interacting phases in systems (such as cold atoms, or some solid state systems) where these protocols are not available. For all tasks of this project, a major challenge is to relate microscopic properties with the concepts of condensed matter theory, due to the many-body origin of the studied phenomena. To address this challenge, numerical methods are necessary and were the cornerstone of the methodology of this project.
The work performed in this project resulted in 4 scientific articles published in renowned peer-reviewed journals: 3 high impact articles in Phys. Rev. Lett. (one of which received the Editor's suggestion award), 1 in npj Quantum Materials. All papers resulting from the project are available in a form identical to the published version on the preprint server www.arxiv.org as a form of green open access, following European Union guidelines for Open Science. The results can be summarized as follows:

-Proximity coupling fractional quantum Hall (FQH) edges with superconductors
Non-abelian anyons are associated with a degeneracy that cannot be lifted by any local perturbation and hold the key to quantum computation intrinsically immune to decoherence. These have been predicted in heterostructures of FQH states whose edge is proximity coupled to a superconductor. We devised a numerical set-up allowing the quantitative study of such heterostructure. Its originality is that it retains the 2D bulk degrees of freedom, allowing us to determine appropriate lengths and superconducting order parameter to realize this device experimentally. C. Repellin, A.M. Cook, T. Neupert, N. Regnault, Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures, npj Quantum Materials 3 (1), 1-8 (2018).

-Realizing FQH states without a magnetic field is a long standing goal, because the large magnetic field is an important drawback for technological applications, such as the device described above (superconductors cannot exist in large magnetic fields)
We used analytical and numerical evidence to establish the conditions of emergence of ferromagnetism and quantized anomalous Hall effect in the narrow bands of several moire materials. Besides providing a theoretical understanding of recent experiments in twisted bilayer graphene (TBG), our work predicted the emergence of ferromagnetism in other moire systems. This work paves the way to the realization of the FQH effect without a magnetic field. C. Repellin, Z. Dong, Y.H. Zhang, T. Senthil, Ferromagnetism in narrow bands of moiré superlattices, Phys. Rev. Lett. 124 (18), 187601 (2020).

-Detection of topology through circular dichroism
We demonstrated that a clear signature of topological order can be obtained using circular dichroism. We showed how measuring the excitation rates of an atomic cloud upon circular driving can reveal the fractional nature of its Hall conductance, a signature of topological order in FQH states. C. Repellin, N. Goldman, Detecting fractional Chern insulators through circular dichroism, Phys. Rev. Lett. 122 (16), 166801 (2019).
We proposed that circular dichroism could also be used to detect higher order topology in 3D axion insulators. Our proposal has the benefit of distinguishing different types of higher order insulators. We clarified the real space distribution of topological properties of these materials, previously unaccounted for, and their connection to circular dichroism and local surface probes. O. Pozo, C. Repellin, A.G. Grushin, Quantization in chiral higher order topological insulators: Circular dichroism and local chern marker, Phys. Rev. Lett. 123 (24), 247401 (2019).
Our work focuses on fundamental science and is an important contribution to the domain of many-body topological systems. The understanding of the physics of such systems is necessary to allow the design and realization of decoherence-free devices, with potential impact across quantum technologies. Scientifically, our work specified the conditions of emergence of exotic quantum phases in realistic experimental set-ups, in cold atom experiments as well as graphene moire superlattices. Cold atom gases have emerged as highly tunable quantum simulators; realizing strongly correlated topological order in these system is an important goal of ongoing research. In this project, we have provided realistic protocols which permit the detection of topological order in cold atoms. In 2D solid state materials, this project has provided the first unbiased numerical study of the magic angle graphene moire superlattices. Using these new theoretical tools, we have explained existing experiments.
Circular dichroism of a fractional Chern Insulators