Linearly dispersive exciton band in freestanding hexagonal boron nitride

Excitons, as elementary excitations of bound electron-hole pairs, are crucial for understanding the optical properties of materials. Previous theory predicts a non-analytic, lightlike linear exciton dispersion for the spin-allowed longitudinal excitons due to the long-range exchange interaction in materials with C3 symmetry. However, observing a clear linear dispersion is challenging because the linearly dispersive regime in typical transition metal dichalcogenides (TMDs) is too small to be resolved by conventional techniques. In this work, we used momentum-resolved electron energy loss spectroscopy, along with \textit{ab initio} GW plus Bethe-Salpeter equation (GW-BSE) methods, to directly measure the exciton band structure of a freestanding monolayer of hexagonal boron nitride (hBN). We observe a clear massless, linear exciton dispersion with a direct K-K gap of 6.65 eV. These findings have implications for exciton-mediated superconductivity and realizing Bose-Einstein exciton condensation in two dimensions, and are valuable for the fundamental understanding of exciton dynamics in low-dimensional systems.