Importance of interactions for the band structure of the topological Dirac semimetal Na3Bi

We experimentally measure the band dispersions of topological Dirac semimetal ${\mathrm{Na}}_{3}\mathrm{Bi}$ using Fourier-transform scanning tunneling spectroscopy to image quasiparticle interference on the (001) surface of molecular-beam epitaxy-grown ${\mathrm{Na}}_{3}\mathrm{Bi}$ thin films. We find that the velocities for the lowest-lying conduction and valence bands are $1.6\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{4pt}{0ex}}\mathrm{m}{\mathrm{s}}^{\ensuremath{-}1}$ and $4.2\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{4pt}{0ex}}\mathrm{m}{\mathrm{s}}^{\ensuremath{-}1}$ respectively, significantly higher than previous theoretical predictions. We compare the experimental band dispersions to the theoretical band structures calculated using an increasing hierarchy of approximations of self-energy corrections due to interactions: generalized gradient approximation (GGA), meta-GGA, Heyd-Scuseria-Ernzerhof exchange-correlation functional (HSE06), and $GW$ methods. We find that density functional theory methods generally underestimate the electron velocities. However, we find significantly improved agreement with an increasingly sophisticated description of the exchange and interaction potential, culminating in reasonable agreement with experiments obtained by the $GW$ method. The results indicate that exchange-correlation effects are important in determining the electronic structure of this ${\mathrm{Na}}_{3}\mathrm{Bi}$, and are likely the origin of the high velocity. The electron velocity is consistent with recent experiments on ultrathin ${\mathrm{Na}}_{3}\mathrm{Bi}$ and also may explain the ultrahigh carrier mobility observed in heavily electron-doped ${\mathrm{Na}}_{3}\mathrm{Bi}$.