Symmetry-Enforced Dirac Fermions and Structural Metastability in Pentagonal Monolayers of Transition-Metal Ditellurides

The recent synthesis of pentagonal PdTe${}_2$ monolayer motivates broader research interests in transition-metal ditellurides whose electronic phases are governed by symmetry and structural reconstruction. The pentagonal phase of transition-metal ditellurides exhibits electronic properties that are dramatically different from those of its hexagonal counterpart due to its lower crystalline symmetry. Using first-principles calculations, we study monolayer $X$Te${}_2$ ($X=\mathrm{P}\mathrm{d},\mathrm{P}\mathrm{t},\mathrm{N}\mathrm{i}$) in both hexagonal and pentagonal polymorphs. By constructing a continuous structural interpolation between the hexagonal and pentagonal phases, we show that the semimetal (hex)-to-semiconductor (penta) transition occurs only after an intermediate structural threshold rather than at the onset of symmetry reduction. The gap opening coincides with the formation of Te–Te dimers, which drive the bonding–antibonding splitting of the Te $p$ states and reorganize the band edges. In addition, the nonsymmorphic symmetry of the pentagonal phase enforces band degeneracies at the Brillouin-zone boundary, leading to symmetry-protected two-dimensional (2D) Dirac states. These results establish pentagonal $X$Te${}_2$ monolayers as a new class of 2D semiconductors in which symmetry constraints and local bonding collectively shape the unconventional semiconducting electronic structure.