Magnetic Dirac Semimetals in Three Dimensions

Abstract: We present a new type of three-dimensional essential Dirac semimetal with magnetic ordering. The Dirac points are protected by the magnetic space groups and cannot be gapped without lowering such symmetries, where the combined antiunitary symmetry of half-translation operator and time-reversal plays an essential role. We introduce two explicit tight-binding models for space groups $16$ and $102$, which possesses Dirac point at time-reversal-invariant momenta of surface Brillouin zone. In contrast to the time-reversal-invariant essential Dirac semimetal, the magnetic space groups here can be either symmorphic or non-symmorphic, and the magnetic DSM is symmetry tuned to the boundary between weak topologically distinct insulating phases. Interestingly, the symmetry-breaking perturbations could lead to an ideal Weyl semimetal phase with only two minimal Weyl points pinned exactly at the Fermi energy for filling $\nu\in4\mathbb{Z}+2$. By reducing the dimensionality we are able to access the Dirac and Weyl semimetal phases in two dimensions.