Atomic collapse in gapped graphene: Lattice and valley effects

We study the atomic collapse phenomenon in $K$ and ${K}^{\ensuremath{'}}$ valleys of gapped graphene. Bound states induced by Coulomb impurity in the gap turn into atomic collapse resonances as the charge increases beyond the supercritical charge ${Z}_{c}$. ${Z}_{c}$ increases sublinearly with the band gap $\mathrm{\ensuremath{\Delta}}$. The atomic collapse resonances result in peaks in the local density of states (LDOS) at the same energies in $K$ and ${K}^{\ensuremath{'}}$ valleys, but the strong (weak) LDOS peaks in the $K$ valley are weak (strong) LDOS peaks in the ${K}^{\ensuremath{'}}$ valley reminiscent of pseudospin polarization phenomenon. From a spatial LDOS analysis of the atomic collapse resonance states, we assign specific atomic orbitals to the atomic collapse resonances. Remarkably, the two $p$ atomic orbital atomic collapse states are no longer degenerate and split into two, having lobes in different directions in the graphene plane.