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

Periodic Reporting for period 2 - sharpEDGE (From Bulk to Edge: Realization and Characterization of Fractionalized Quantum Matter)

Reporting period: 2019-10-01 to 2020-09-30

Quantum effects, topology and strong interactions act together to produce a vast array of exotic phases of matter at low temperature in physical systems as varied as 2D materials, superconducting quantum circuits 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 (FQH) 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 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. This action resulted in important advances on both fronts: we showed numerical evidence for the emergence of a topological qutrit in a FQH-superconductor device, and predicted that FQH states could emerge in the absence of a magnetic field in realistic 2D moire materials. We also provided practical protocols to detect strongly correlated quantum phases using methods available in cold atomic gases.
The work performed in this project resulted in 6 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, 1 in Phys. Rev. Research, and 1 in Phys. Rev. A. 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. Additionally to the publications, the results were disseminated in 30 scientific events (international conferences or seminars). 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 (2018)

-Realizing FQH states without a magnetic field is a long standing goal in the field, because the large magnetic field is an important drawback in view of technological applications, such as the device described above. 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. C. Repellin, Z. Dong, Y.H. Zhang, T. Senthil, Ferromagnetism in narrow bands of moiré superlattices, Phys. Rev. Lett. (2020).
The nearly flat band with Chern number 1 in TBG makes it a promising candidate to realize a FQH state with no magnetic field. We numerically showed that these states may indeed be realized in TBG at temperatures accessible to experiments. Further, we showed the existence of an unexpected spin order. C Repellin, T Senthil, Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition, Phys. Rev. Research (2020)

-Detection of topology through circular dichroism
We demonstrated that a clear signature of topological order can be obtained through circular dichroism. More specifically, 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. (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. O. Pozo, C. Repellin, A.G. Grushin, Quantization in chiral higher order topological insulators: Circular dichroism and local chern marker, Phys. Rev. Lett. (2019)

-Detecting FQH states of few bosons in cold atoms
Ultracold atom experiments are currently designed to realize FQH states with very few atoms. This raises the question of whether such small systems would display the features of FQH states, such as their quantized Hall response. We addressed this question positively by demonstrating the existence of emergent plateaus in the Hall drift of few atoms, initially prepared in a FQH state. Our method is based on monitoring the center-of-mass drift of the small atomic cloud upon release in a larger system, while applying a weak static force. On this plateau, the Hall conductivity approaches the quantized value expected for this FQH state. These results indicate that FQH states can be detected in ultracold atoms, using available detection tools, hence offering a practical guideline for ongoing experiments. C. Repellin, J. Leonard, N. Goldman, Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles, Phys. Rev. A 2020.
Our work focuses on fundamental science and is an important contribution to the domain of many-body topological systems. The action uncovered the conditions of emergence of exotic quantum phases in realistic experimental set-ups realistic for cold atoms and solid state materials. 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. We have provided the protocols which permit the detection of these exotic phases in cold atoms, a necessary step in view of their experimental realization and detection. In solid state materials, this project has provided the first unbiased numerical study of strong correlations in the new 2D material magic angle bilayer graphene. We have explained existing experiments and predicted the emergence of a more exotic topological phase at lower temperature. Overall, the results of the action show that new topologically ordered phases may be realized in experiments, and we have shown in which experimental conditions this could be achieved, motivating further experiments. Beyond their fundamental importance, many-body topological systems are key to engineer quantum bits immune to decoherence for error-free quantum computation. Our results contribute to this quest, and may thus have a profound societal impact in the long term, through their impact on quantum technologies.
Circular dichroism of a fractional Chern Insulators