Nonsymmorphic symmetry protected spin-orbit semi-Dirac fermions in two dimensions

Semi-Dirac fermions (SDFs) in two-dimensional (2D) systems, which simultaneously exhibit linear and quadratic dispersion around them, are a bridge linking linear and quadratic Dirac cones. However, the so-called SDFs in the reported 2D materials are doubly degenerate (namely semi-Weyl fermions), and are vulnerable against spin-orbital coupling (SOC). Here, we propose a 2D SOC-robust SDF which arises from nonsymmorphic symmetries. Unlike the known 2D SDFs, due to the presence of inversion and time reversal symmetries (IT), each crossing band is doubly degenerate, making the SDF of fourfold degeneracy. By high throughput screening, we find that 26 candidate 2D materials (such as CuCN2, CaI2, TlF) can hold SDFs, which belong to layer groups 40 (pmam), 43 (pbaa), and 45 (pbma), respectively. Furthermore, the symmetry protection mechanism, associated Fermi arc edge states, the catalytic performance, and the topological phase transitions under symmetry breaking of SDFs are revealed, providing a way for understanding 2D SOC-robust SDFs. Overall, our work proposes a class of topological phases, and provides a platform to study their fascinating physical effects.