Intrinsic two-dimensional states on the pristine surface of tellurium

Atomic chains configured in a helical geometry have fascinating properties, including phases hosting localized bound states in their electronic structure. We show how the zero-dimensional state---bound to the edge of a single one-dimensional helical chain of tellurium atoms---evolves into two-dimensional bands on the $c$-axis surface of the three-dimensional trigonal bulk. We give an effective Hamiltonian description of its dispersion in $k$ space by exploiting confinement to a virtual bilayer, and elaborate on the diminished role of spin-orbit coupling. These intrinsic gap-penetrating surface bands were neglected in the interpretation of seminal experiments, where two-dimensional transport was otherwise attributed to extrinsic accumulation layers.