Two-dimensional topological semimetals protected by symmorphic symmetries

Two-dimensional (2D) band crossing semimetals (BCSMs) could be used to build a range of novel nanoscale devices, such as superlenses and transistors. We find that symmorphic symmetry can protect a new type of robust 2D BCSM, unlike the previously proposed 2D essential BCSMs protected by nonsymmorphic symmetry [Young and Kane, Phys. Rev. Lett. 115, 126803 (2015)]. This type of symmorphic symmetry-protected (SSP) 2D essential BCSM cannot be pair annihilated without destroying the crystalline symmetries as opposed to the 2D BCSM caused by the accidental band crossing. Through group-theory analysis, we find that 2D SSP BCSMs can only exist at the K(K') point of the Brillouin zone of four-layer groups and identify nonmagnetic 2D FeB2 as a candidate. Interestingly, nonmagnetic 2D SSP BCSMs can host a single pair of band crossing points (BCPs), whereas nonmagnetic three-dimensional Weyl semimetals have, at least, two pairs of band crossing Weyl points. It is found that the single pair of BCPs is robust against any kind of strain. Furthermore, our calculation suggests that essential 2D SSP BCSMs can be used to realize electric-field control of spin texture and, thus, are promising candidates for spintronic devices.