Tuning MgB2(0001) surface states through surface termination

Surface state localization and hybridization on B, Mg, and Li terminated MgB${}_{2}$(0001) surfaces are studied within density functional theory (DFT). For the B terminated surface we find a low energy B ${\ensuremath{\sigma}}_{1}$ surface state, a $s{p}_{z}$ surface state, and B ${\ensuremath{\sigma}}_{2}$ and ${\ensuremath{\sigma}}_{3}$ quantum well states, which are $90%$ localized in the topmost B layer. Our results demonstrate that by charging the B atomic layer, either by changing the surface termination or through electro-chemical doping, the B $\ensuremath{\sigma}$ surface states are shifted down in energy, filled, and delocalize through hybridization as they cross the bulk MgB${}_{2}$ bulk bands. On the other hand, the $s{p}_{z}$ surface state should be shifted up in energy, emptied, and gain an increasingly metallic $s$ character by adding a Mg, Mg${}^{+1}$, or Li terminating atomic layer. These results clearly show both the robust nature of MgB${}_{2}$(0001) surface states, and how their localization and energy range may be tuned by surface termination and charging, with implications for the superconducting and plasmonic behavior of MgB${}_{2}$.