Layer Nernst and thermal Hall effects in two-dimensional antiferromagnets

In two-dimensional layered antiferromagnets, an out-of-plane electric field (\ensuremath{\mathcal{E}}) breaks the band spin degeneracy, inducing opposite spin polarizations in different layers due to spin-layer coupling. When an in-plane longitudinal temperature gradient ($\ensuremath{\nabla}$T) is applied, charge and heat currents in the top (J${}_{t}$ and J${}_{t}^{Q}$) and bottom (J${}_{b}$ and J${}_{b}^{Q}$) layers flow transversely in opposite directions with different magnitudes. This gives rise to net transverse charge and heat currents, referred to as the layer Nernst and layer thermal Hall effects, respectively.