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
-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.