Spin Hall effect and Berry curvature of gravitons from quantum field theory

TL;DR

This paper derives the spin Hall effect of gravitons from quantum field theory, showing how Berry curvature causes helicity-dependent splitting in graviton energy flow in curved spacetime.

Contribution

It formulates the Wigner function for gravitons and reveals the Berry curvature-induced spin Hall effect specific to gravitons, extending photon spin Hall phenomena to gravity.

Findings

Spin Hall effect of gravitons demonstrated in curved spacetime.

Berry curvature causes opposite effects for right- and left-handed gravitons.

Splitting magnitude is twice that of photon spin Hall current.

Abstract

Based on quantum field theory of linearized gravity, we formulate the Wigner function for right- and left-handed gravitons. By applying the Wigner transformation to the second-order metric perturbations in the graviton energy-momentum tensor obtained from the Einstein-Hilbert action, we demonstrate the emergence of the spin Hall effect of gravitons in curved spacetime. This effect originates from the Berry curvature of gravitons, which has opposite signs for right- and left-handed helicities, and leads to a helicity-dependent splitting of the graviton energy Hall current. The magnitude of this splitting is found to be exactly twice that of the corresponding spin Hall current for photons.