Spin-orbit coupling driven crossover from a starfruitlike nodal semimetal to Dirac and Weyl semimetal state in CaAuAs

Band crossings that occur on a mirror plane are compelled to form nodal loops in the momentum space in the absence of spin-orbit coupling (SOC). When other equivalent mirror planes are present, multiple such nodal loops can combine to form interesting topological structures involving crossed nodal lines. Here, based on first-principles calculations and an effective k.p model analysis, we show that CaAuAs hosts a unique starfruitlike crossed-nodal-line structure in the bulk electronic dispersion, which is comprised of three nodal loops that cross each other at the time-reversal-invariant momentum point A. When the SOC is turned on, the nodal loops are gapped out, resulting in a stable Dirac semimetal state with a pair of Dirac points along the Gamma-A direction in the Brillouin zone. These Dirac points are protected by the combination of time-reversal, inversion, and C-3 rotation symmetries. We discuss how a systematic elimination of the symmetry constraints yields a Weyl semimetal and eventually a topological insulator state.