Triply degenerate point in three-dimensional spinless systems

As the rise of quantum topological materials, a number of fermionic qusaiparticle are identified in solids, associated with exotic properties. Beyond the conventional Dirac and Weyl fermions, multifold fermions attract lots of attention without analog in quantum field theory. Here, we perform an exhaustive search of triply degenerate points (TDPs) in 230 nonmagnetic space groups in the absence of SOC. Different from Dirac points with up to cubic dispersions, TDPs are found to hold only up to quadratic dispersions either at high-symmetry points (HSPs) or on high-symmetry lines (HSLs). While QTDPs at HSPs possess quadratic dispersions in all directions, the ones on HSLs only disperse quadratically in k_x-k_y plane. When located at high-symmetry points in chiral SGs, TDPs are found to host a topological charge of ±2 with linear dispersions, which are also known as spin-1 Weyl points. We also break certain symmetry to investigate their phase transitions. Though the results support their existences in a range of space groups, their stable material realization is still limited.