Quasinodal lines in rhombohedral magnetic materials

Two-dimensional antiferromagnetic nodal-line semimetal and spin Hall effect in MnC4

“…These anticrossing points are induced by the low SOC interaction in the MnC 4 material and range from approximately 0.0-2.0 meV. However, the hybridization points extend along the first BZ, generating a quasi-Diracnodal line behavior [21]. To verify the existence of the quasi-Dirac-nodal line, we calculated the energy difference between the Ec and Ev bands, as shown in figure 4(c).…”

“…This suggests that the mentioned family exhibits a wide range of topological characteristics. Nodal lines also emerge in ferromagnets, such as K 2 N or XF 3 (X = Pd, Mn and Ir), which hold excellent promise for room-temperature spintronics applications [21,22]. Additionally, antiferromagnetic monolayers provide compelling evidence for the existence of nodal lines.…”

Band inversion and quasi-nodal spheres

“…1 b) we notice that the signal of the bracket ϕ 1 − | ĵz x |ϕ 2 − , where ĵz x = {v x , 2 τ 0 σ 3 }/2 is the spin current operator, is localized on the k-points with mixed orbital type. From the Kubo formula for the spin Hall conductivity (30) we deduce that the signal of Ω z n,xy appears whenever the states have mixed orbital type and peaks on the k-points inside the quasi-nodal sphere. This feature could be appreciated on the materials YH 3 and CaTe on Fig.…”

“…In the case of interest, the band inversion is due to the hybridization of the energy bands inside the Brillouin zone, thus producing a sphere of points where the energy gap is small. This 2-dimensional sphere in momentum space with small energy gap (comparable to room temperature ∼ 25 meV) has been coined Quasi-nodal Sphere, generalizing the concept of quasi-nodal line that was presented by the first and third authors in [30].…”