In this paper, we propose a new type of bulk-boundary correspondence as a generic approach to theoretically and experimentally detect fragile topological states. When the fragile phase can be written as a difference of a trivial atomic insulator and the so-called obstructed atomic insulator, the gap between the fragile phase and other bands must close under a specific novel twist of the boundary condition of the system. We explicitly work out all the twisted boundary conditions (TBC) that can detect all the 2D fragile phases implied by symmetry eigenvalues in all wallpaper groups. We develop the concept of real space invariants -local good quantum numbers in real space -which fully characterize the eigenvalue fragile phases. We show that the number of unavoidable level crossings under the twisted boundary condition is completely determined by the real space invariants. Possible realizations of the TBC of the fragile band in metamaterial systems are discussed. arXiv:1910.06869v1 [cond-mat.mes-hall]
Osteopontin (OPN) was first identified in 1986. The prefix osteo‐ means bone; however, OPN is expressed in other tissues, including liver. The suffix ‐pontin means bridge and denotes the role of OPN as a link protein within the extracellular matrix. While OPN has well‐established physiological roles, multiple “omics” analyses suggest that it is also involved in chronic liver disease. In this review, we provide a summary of the OPN gene and protein structure and regulation. We outline the current knowledge on how OPN is involved in hepatic steatosis in the context of alcoholic liver disease and non‐alcoholic fatty liver disease. We describe the mechanisms whereby OPN participates in inflammation and liver fibrosis and discuss current research on its role in hepatocellular carcinoma and cholangiopathies. To conclude, we highlight important points to consider when doing research on OPN and provide direction for making progress on how OPN contributes to chronic liver disease.
Flat-bands in magic angle twisted bilayer graphene (MATBG) have recently emerged as a rich platform to explore strong correlations, superconductivity and magnetism. However, the phases of MATBG in magnetic field, and what they reveal about the zero-field phase diagram remain relatively unchartered. Here we use magnetotransport and Hall measurements to reveal a rich sequence of wedge-like regions of quantized Hall conductance with Chern numbers C = ±1, ±2, ±3, ±4 which nucleate from integer fillings of the moiré unit cell 𝜈 = ±3, ±2, ±1, 0 correspondingly. We interpret these phases as spin and valley polarized Chern insulators, equivalent to quantum Hall ferromagnets. The exact sequence and correspondence of Chern numbers and filling factors suggest that these states are driven directly by electronic interactions which specifically break time-reversal symmetry in the system. We further study quantum magneto-oscillation in the yet unexplored higher energy dispersive bands with a Rashba-like dispersion. Analysis of Landau level crossings enables a parameter-free comparison to a newly derived "magic series" of level crossings in magnetic field and provides constraints on the parameters w0 and w1 of the Bistritzer-MacDonald MATBG Hamiltonian. Overall, our data provides direct insights into the complex nature of symmetry breaking in MATBG and allows for quantitative tests of the proposed microscopic scenarios for its electronic phases.
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