Emergent-gravity Hall effect from quantum geometry

We theoretically propose a Hall effect driven by effective gravitational fields arising from quantum geometry. We develop four mechanisms for this ''emergent-gravity Hall effect" : real-space gravity, momentum-space gravity, gravitional anomalous velocity, and gravitational Lorentz force which are described by the Christoffel symbols in real, momentum, and time spaces. We construct a unified theoretical framework to systematically investigate the effects of emergent gravity in these spaces on transport phenomena based on the semiclassical theory. We demonstrate these effects by model calculations and clarify the conditions under which a finite Hall response can arise. Our findings open a new avenue for exploring gravitational effects in quantum systems.