Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe$_6$ ($X=$ Ta, Nb)

摘要

Nonsymmorphic space group symmetries can generate exotic band-crossings intopological metals and semimetals. Here, based on symmetry analysis andfirst-principles calculations, we reveal rich band-crossing features in theexisting layered compounds Ta$_3$SiTe$_6$ and Nb$_3$SiTe$_6$, enabled bynonsymmorphic symmetries. We show that in the absence of spin-orbit coupling(SOC), these three-dimensional (3D) bulk materials possess accidental Diracloops and essential fourfold nodal lines. In the presence of SOC, there emergesan hourglass Dirac loop---a fourfold degenerate nodal loop, on which each pointis a neck-point of an hourglass-type dispersion. We show that this interestingtype of band-crossing is protected and dictated by the nonsymmorphic spacegroup symmetries, and it gives rise to drumhead-like surface states.Furthermore, we also investigate these materials in the monolayer form. We showthat these two-dimensional (2D) monolayers host nodal lines in the absence ofSOC, and the nodal lines transform to essential spin-orbit Dirac points whenSOC is included. Our work suggests a realistic material platform for exploringthe fascinating physics associated with nonsymmorphic band-crossings in both 3Dand 2D systems.