Nodal Line Spin-Gapless Semimetals and High-Quality Candidate Materials

Spin-gapless semimetals (SGSMs), which generate 100% spin polarization, are viewed as promising semi-half-metals in spintronics with high speed and low consumption. We propose and characterize a new ${\mathbb{Z}}_2$ class of topological nodal line (TNL) in SGSMs. The proposed TNLSGSMs are protected by space-time inversion symmetry or glide mirror symmetry with two-dimensional (2D) fully spin-polarized nearly flat surface states. Based on first-principles calculations and effective model analysis, a series of high-quality materials with $R\overline{3}c$ and $R3c$ space groups are predicted to realize such TNLSGSMs (chainlike). The 2D fully spin-polarized nearly flat surface states may provide a route to achieving equal spin pairing topological superconductivity as well as topological catalysts.

Figure 1

Schematic illustration of the simplest TNLSGSMs between two inverted subbands and the corresponding density of states (DOS) for (a) concentric loops that come from different spin channels separately, and (b) NLs that come from a single spin channel. (c) Schematic figure showing nodal chain SGSMs consisting of TNLSGSMs. The red (blue) pattern represents the spin-up (spin-down) channel.

Figure 2

(a) The primitive unit cell with a nonsymmorphic $R\overline{3}c$ rhombohedral lattice of ${\mathrm{TMF}}_3$ ($\mathrm{TM}=\mathrm{Mn}$, Pd) and (b) $AB{O}_3$-type perovskites (i.e., ${\mathrm{FeCO}}_3$, ${\mathrm{MnBO}}_3$, ${\mathrm{TiBO}}_3$, ${\mathrm{LaMnO}}_3$, and ${\mathrm{LaNiO}}_3$). (c) The primitive unit cell with $R3c$ rhombohedral $A^{\prime }AB{O}_3$-type perovskites [i.e., $X\mathrm{TiMn}({\mathrm{PO}}_4{)}_3$; $X=\mathrm{Ca}$, Mg, Zn]. Spin-resolved band structures and DOS of (d) ${\text{PdF}}_3$ and (e) $\mathrm{ZnTiMn}({\mathrm{PO}}_4{)}_3$ ($U=4\mathrm{eV}$). The red and blue lines represent spin-up and spin-down channels, respectively.

Figure 3

The band structures of DFT (black solid curves) agree with that of the effective lattice model (red solid curves) calculations in (a) ${\text{PdF}}_3$ and (b) $\mathrm{ZnTiMn}({\mathrm{PO}}_4{)}_3$ systems.

Figure 4

(a)–(d) The profile of the nodal chainlike SGSMs in three-dimensional k space, including the top views (a) ${\text{PdF}}_3$ and (c) $\mathrm{ZnTiMn}({\mathrm{PO}}_4{)}_3$ along the [111] direction, the side views (b) ${\text{PdF}}_3$ and (d) $\mathrm{ZnTiMn}({\mathrm{PO}}_4{)}_3$. Different colors (i.e., the red, blue, green, and purple lines) correspond to different orientations of the NLs (i.e., NL1, NL2, NL3, and NL4). Band structures and DOSs for surface (111) and in (e) ${\text{PdF}}_3$ and (f) $\mathrm{ZnTiMn}({\mathrm{PO}}_4{)}_3$. The purple dashed lines labeled ${\mathrm{L}}_1$, ${\mathrm{L}}_2$, and ${\mathrm{L}}_3$ represent three respective loops along which the Berry phase is calculated.