DFT+\textit{U} invstigation of doped-PbPdO$_2$ spin gapless semiconductors

Spin gapless semiconductors (SGSs), with a zero gap in one spin channel and a finite gap in the other, have attracted considerable attention due to its potential in spintronics. Ever since PbPdO$_2$ was predicted a gapless semiconductor by local density approximation (LDA) calculations and confirmed by experiments afterward, it is anticipated to be a backbone material for SGS. Using density functional theory + self-consistent Hubbard \textit{U} (DFT+\textit{U}$_{sc}$) calculations, we investigate doped PbPdO$_2$ with different kinds of transition-metal dopants, including V, Cr, Mn, Fe, Co, and Ni, at different dopant concentration. We show that doped PbPdO$_2$ can be a SGS with a proper choice of dopant and dopant concentration. Furthermore, different dopant and dopant concentration can lead to different types of SGS.