Optimal materials for maximum near-field radiative heat transfer

We consider the space of all causal bulk materials, 2D materials, and metamaterials for maximum near-field radiative heat transfer (RHT). Causality constrains the bandwidth over which plasmonic response can occur, explaining two key traits in ideal materials: small background permittivities (minimal high-energy transitions in 2D materials), and Drude-like free-carrier response, which together optimally yield 10X enhancements beyond the theoretical state-of-the-art. We identify transparent conducting oxides, III-Nitrides, and graphene as materials that should offer nearly ideal near-field RHT rates, if doped to exhibit plasmonic resonances at what we term "near-field Wien frequencies." Deep-subwavelength patterning can provide marginal further gains, at the expense of extremely small feature sizes. Optimal materials have moderate loss rates and plasmonic response at 19 {\mu}m for 300K temperature, suggesting a new opportunity for plasmonics at mid- to far-infrared wavelengths, with low carrier concentrations and no requirement to minimize loss.