The layer Hall effect and the layer-locked hidden Berry curvature (IMAGE)
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Schematics of the layer Hall effect (a) and layer-locked hidden Berry curvature (b) in a two-layer antiferromagnetic insulator. In the layer Hall effect, electrons are spontaneously deflected to opposite sides at different layers (the red and blue arrowed curves) due to the layer-locked hidden Berry curvature. (c)-(d) When a perpendicular electric field (the cyan arrow) is applied, the system shows layer-locked anomalous Hall effects tunable by the electric-field direction. The yellow arrows specify the antiferromagnetic configurations. The green arrows denote the in-plane electric field Ey for the Hall measurement.
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