Electronic structure of YbB$_{6}$: Is it a Topological Insulator or not?

To resolve the controversial issue of the topological nature of the electronic structure of YbB$_{6}$, we have made a combined study using density functional theory (DFT) and angle resolved photoemission spectroscopy (ARPES). Accurate determination of the low energy band topology in DFT requires the use of modified Becke-Johnson exchange potential incorporating the spin-orbit coupling and the on-site Coulomb interaction $U$ of Yb $4f$ electrons as large as 7 eV. We have double-checked the DFT result with the more precise GW band calculation. ARPES is done with the non-polar (110) surface termination to avoid band bending and quantum well confinement that have confused ARPES spectra taken on the polar (001) surface termination. Thereby we show definitively that YbB$_{6}$ has a topologically trivial B 2$p$-Yb 5$d$ semiconductor band gap, and hence is a non-Kondo non-topological insulator (TI). In agreement with theory, ARPES shows pure divalency for Yb and a $p$-$d$ band gap of 0.3 eV, which clearly rules out both of the previous scenarios of $f$-$d$ band inversion Kondo TI and $p$-$d$ band inversion non-Kondo TI. We have also examined the pressure-dependent electronic structure of YbB$_{6}$, and found that the high pressure phase is not a Kondo TI but a \emph{p}-\emph{d} overlap semimetal.