Chiral transport of pseudospinors induced by synthetic gravitational field in photonic Weyl metamaterials

Abstract

Weyl particles exhibit chiral transport property under external curved space-time geometry. This effect is called the chiral gravitational effect, which plays an important role in quantum field theory. However, the absence of real Weyl particles in nature hinders the observation of such interesting phenomena. In this paper, we show that chiral gravitational effect can be manifested in Weyl metamaterials with spatially controlled nonlocality. This inhomogeneous modulation results in a spatially dependent group velocity in the Weyl cone dispersion, which is equivalent to introducing a curved background space-time (or gravitational field) for Weyl pseudospinors according to the Clifford algebra. The Weyl equation describing the Weyl cone dispersions is reformulated into the covariant form that contains a nonAbelian gauge field by considering the parallel transport of pseudospinors. The synthetic gravitational field (i.e., space-time curvature) leads to the quantization of energy levels, including chiral zeroth order energy modes (or simply chiral zero modes) that determine the chiral transport property of pseudospinors. Inhomogeneous Weyl metamaterials can potentially become a platform for investigating the interaction between Weyl particles and gravitational fields in future table-top experiments. The theoretical model and the associated results may serve as a guidance for experimentalists to observe such chiral transport effects in photonic Weyl systems.