Intrinsic anomalous Hall effect across the magnetic phase transition of a spin-orbit-coupled Bose-Einstein condensate

TL;DR

This paper theoretically investigates the intrinsic anomalous Hall effect in a 2D spin-orbit coupled Bose gas, revealing phase-dependent Hall responses and their relation to system symmetries, chirality, and Berry curvature.

Contribution

It demonstrates the existence of phase-dependent ac and dc Hall responses in a spin-orbit-coupled Bose-Einstein condensate without magnetic fields, linking them to symmetries and topological properties.

Findings

Finite ac Hall responses in both phases due to inter-band transitions.

Finite dc Hall conductivity appears only in one phase.

Hall responses are linked to system's chirality and Berry curvature.

Abstract

We study theoretically the zero temperature intrinsic anomalous Hall effect in an experimentally realized 2D spin-orbit coupled Bose gas. For anisotropic atomic interactions and as the spin-orbit coupling strength increases, the system undergoes a ground state phase transition from states exhibiting a total in-plane magnetization to those with a perpendicular magnetization along the $z$ direction. We show that finite frequency, or ac, Hall responses exist in both phases in the absence of an artificial magnetic field, as a result of finite inter-band transitions. However, the characteristics of the anomalous Hall responses are drastically different in these two phases because of the different symmetries preserved by the corresponding ground states. In particular, we find a finite dc Hall conductivity in one phase but not the other. The underlying physical reasons for this are analyzed further by exploring relations of the dc Hall conductivity to the system's chirality and Berry curvatures of the Bloch bands. Finally, we discuss an experimental method of probing the anomalous Hall effect in trapped systems.