Fig. 3: Emergence of split-off bands due to the formation of V-V dimers in nonmagnetic monoclinic VO2.
From: Hidden magnetism and split off flat bands in the insulator metal transition in VO2
a–c Density of states from R-PBE exchange-correlation functional of nonmagnetic monoclinic VO2 with given degrees of bond alternation. The crystal structures with different DBA values are generated by linear interpolation of the relaxed (by R-PBE) rutile and monoclinic structures. The majority states are indicated in a–c. Blue area indicates the occupied states. The split-off flat-band states in c are indicated by bold red boundary, which have a band width of 0.43 eV and are separated from the other d states in the conduction band by 0.14 eV (Eg). \(\triangle {d}_{{\rm{||}}}\) in c indicates the splitting energy between the bonding and antibonding \({d}_{{\rm{||}}}\) bands mainly consisting of \({a}_{1g}\) states. d Band gaps of the monoclinic structures generated by linear interpolation of the R and M structures as a function of DBA from different types of exchange-correlation functionals29,30,31,51,55 without U.
