Near-field heat transfer between multilayer hyperbolic metamaterials

We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the impact of the first single layer on the heat transfer. Furthermore, we compare the contribution of surface modes to that of hyperbolic modes. Finally, we also compare the exact results with predictions from effective medium theory.