Beyond surfaces: quantifying internal radiative heat transport in dense materials

While phonons and electrons are well-established heat carriers in solids, photons are typically associated only with radiative transfer between surfaces. Yet for over 70 years, theorists have speculated that thermal photons could also conduct heat within dense, opaque materials -- an idea that has remained unproven and unquantified. Here, we resolve this longstanding question by developing a first-principles framework that reveals and quantifies the internal radiative contribution to thermal conductivity in solids. By analyzing 15 crystalline materials, we uncover photon mean free paths (MFPs) ranging from $\sim$100$\mu$m to over 1cm, with some materials exhibiting surprisingly large radiative thermal conductivity ($\kappa_{\text{rad}}$). Contrary to common assumptions, we show that $\kappa_{\text{rad}}$ can scale steeply with temperature (from $T^{1}$ to $T^{4}$), even as MFPs decrease (from $T^{-0.3}$ to $T^{-3}$). We also discover a robust link between photon MFP and phonon linewidths, revealing an unexpected interplay between radiative and phononic heat transport. Crucially, we establish a general formalism to calculate $\kappa_{\text{rad}}$ across arbitrary sample thicknesses and surface emissivities -- bridging ballistic and diffusive regimes. Our findings overturn long-held assumptions, uncover a missing channel of heat conduction, and provide a powerful new tool for thermal management in extreme environments.