Emergent-gravity Hall effect from quantum geometry

TL;DR

This paper introduces a novel Hall effect driven by emergent gravitational fields from quantum geometry, unifying multiple mechanisms within a semiclassical framework and demonstrating potential for new gravitational phenomena in quantum transport.

Contribution

It proposes the concept of an emergent-gravity Hall effect, developing a unified theoretical framework and identifying conditions for observable Hall responses due to quantum geometric effects.

Findings

Identification of four mechanisms for emergent-gravity Hall effect

Development of a unified semiclassical theoretical framework

Model calculations demonstrating conditions for finite Hall response

Abstract

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.