The discovery of Berry curvature (BC) has spurred a tremendous surge of research into various quantum phenomena such as the anomalous transport of electrons and the topological phases of matter. In two-dimensional crystalline systems, the conventional definition of the BC lacks the in-plane components and thus it cannot explain the transverse transport along the plane-normal direction. Here, we modify the BC to provide in-plane components in two dimensions, giving rise to the vertical Hall effects that describe out-of-plane transports in response to in-plane perturbations and their Onsager reciprocity. Our first-principles calculations show that a large in-plane BC can appear even in an atomic-thick $\mathrm{Gd}{\mathrm{Ag}}_2$ monolayer, and a hexagonal $\mathrm{Bi}{\mathrm{Ag}}_2$ monolayer can host a large BC dipole known to vanish in the conventional BC. The quantum transports driven by the hitherto-hidden BC will become more significant in recently emerging two-dimensional platforms, including van der Waals heterostructures.

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• Anomalous Hall effect
• Electronic structure
• Geometric & topological phases
• 2-dimensional systems
• Density functional theory