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The novel electronic structures can induce unique physical properties intwo-dimensional (2D) materials. In this work, we report isolated highlylocalized bands in $\mathrm{YbI_2}$ monolayer by the first-principlecalculations within generalized gradient approximation (GGA) plus spin-orbitcoupling (SOC). It is found that $\mathrm{YbI_2}$ monolayer is an indirect-gapsemiconductor using both GGA and GGA+SOC. The calculations reveal that Yb-$4f$orbitals constitute isolated highly localized bands below the Fermi level atthe 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 largeSeebeck coefficient and very low electrical conductivity in p-type doping byproducing very large effective mass of the carrier. It is proved that isolatedhighly localized bands have very strong stability again strain, which is veryimportant for practical application. When the onsite Coulomb interaction isadded to the Yb-$4f$ orbitals, isolated highly localized bands persist, andonly their relative positions in the gap change. These findings open a newwindow to search for novel electronic structures in 2D materials.

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