Symmetry-engineered nodal lines and hourglass fermions in patterned two-dimensional electron gas

In most cases, the formation of topological quantum states requires intrinsic crystalline symmetry to protect either discrete or continuous degeneracies in real materials, which greatly hinders their realization in practice. Patterned two-dimensional electron gas (2DEG), on the other hand, has become a very effective external means to manipulate the symmetry to whatever we want. Here, taking nonsymmorphic symmetries as the focus of attention, based on patterned 2DEG decoration, we reveal rich band-crossing features in two-dimensional systems. It is demonstrated that in the presence of intrinsic spin-orbital coupling (SOC), wallpaper groups p2mg, p2gg, and p4mg possess fourfold-degenerate Dirac nodal lines, and if Rashba SOC is further considered, the fourfold-degenerate nodal lines disappear and hourglass Weyl fermions then emerge. Our results not only afford an attractive route for designing robust nodal-line and hourglass Weyl semimetals in reality, but also pave the way for designing ideal macroscale materials through rational extrinsic symmetry engineering.