Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP

In this work, we report the existence ofnodal-arc, which acts as the building block of all the nodal-rings in TaAs & TaP. Thisnodal-arcis found to be capable of generating all the nodal-rings in these materials upon the application of space-group symmetry operations including time-reversal symmetry. The arcs are obtained to be dispersive with the energy spread of ∼109 (∼204) meV in TaAs (TaP). Also, the orbitals leading to bands-inversion and thus the formation ofnodal-arcsare found to be Ta-5d& As-4p(P-3p) in TaAs (TaP). The area of nodal-rings is found to be highly sensitive to the change in hybridization-strength, where the increase in hybridization-strength leads to the decrease in the area of nodal-rings. In the presence of spin-orbit coupling (SOC), all the points on these arcs get gaped-up and two pairs of Weyl-nodes are found to evolve from them. Out of the two pair, one is found to be situated close to the joining point of the two arcs forming a ring. This causes the evolution of each nodal-ring into three pairs of Weyl-nodes. The coordinates of these Weyl-nodes are found to be robust to the increase in SOC-strength from ∼0.7-3.5 eV. All the results are obtained at thefirst-principlelevel. This work provides a clear picture of the existence ofnodal-arcdue to accidental degeneracy and its evolution into Weyl-nodes under the effect of SOC.