Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems

Through a group theoretical analysis, we provide the complete list of nodal semimetals that can be created by accidental band crossing in two-dimensional noncentrosymmetric systems with time-reversal symmetry. Although a direct transition between two insulators is generally predicted in such a system, various stable semimetal phases with point or line nodes can also arise from accidental band crossing in the presence of additional crystalline symmetries. By analyzing the 49 noncentrosymmetric layer groups, we find that there are only three types of symmetries that can stabilize the semimetallic phase. First, two-fold rotation about the z-axis (normal to the system) combined with time reversal always stabilizes two-dimensional Weyl nodes. Second, two-fold rotation (mirror) symmetry with the rotation (normal) axis lying in the two-dimensional plane may stabilize Weyl nodes. Finally, mirror symmetry about the plane embracing the whole system may stabilize nodal lines. Our classification table can be used to help search for semimetals in two dimensional systems.