  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.
