Nearly-free-electron system of monolayer Na on the surface of single-crystal HfSe$_2$

The electronic structure of a single Na monolayer on the surface of single-crystal HfSe$_2$ is investigated using angle-resolved photoemission spectroscopy. We find that this system exhibits an almost perfect "nearly-free-electron" behavior with an extracted effective mass of $\sim\!1m_e$, in contrast to heavier masses found previously for alkali metal monolayers on other substrates. Our density-functional-theory calculations indicate that this is due to the large lattice constant, causing both exchange and correlation interactions to be suppressed, and to the weak hybridization between the overlayer and the substrate. This is therefore an ideal model system for understanding the properties of two-dimensional materials.