Isolated highly localized bands in $\mathrm{YbI_2}$ monolayer caused by $4f$ orbitals

The novel electronic structures can induce unique physical properties in two-dimensional (2D) materials. In this work, we report isolated highly localized bands in $\mathrm{YbI_2}$ monolayer by the first-principle calculations within generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). It is found that $\mathrm{YbI_2}$ monolayer is an indirect-gap semiconductor using both GGA and GGA+SOC. The calculations reveal that Yb-$4f$ orbitals constitute isolated highly localized bands below the Fermi level at the absence of SOC, and the bands are split into the $j = 7/2$ and $j = 5/2$ states with SOC. The isolated highly localized bands can lead to very large Seebeck coefficient and very low electrical conductivity in p-type doping by producing very large effective mass of the carrier. It is proved that isolated highly localized bands have very strong stability again strain, which is very important for practical application. When the onsite Coulomb interaction is added to the Yb-$4f$ orbitals, isolated highly localized bands persist, and only their relative positions in the gap change. These findings open a new window to search for novel electronic structures in 2D materials.