Dependence of excited-state properties of tellurium on dimensionality: From bulk to two dimensions to one dimensions

The dependence of excited-state properties on dimensionality is the most prominent character of nanostructures. Using first-principles many-body perturbation theory, we show how those excited-state properties, i.e., quasiparticle energies and excitons, evolve with the dimensionality of tellurium nanostructures that have attracted significant interest because of their high carrier mobility and air stability. Even though the elementary atomistic structures are similar, dimensionality dictates many-electron interactions and excited-state properties: the self-energy correction to the band gap is increased from 0.22 eV in bulk to 0.90 eV in a two-dimensional (2D) monolayer, and ultimately to 2.70 eV in a one-dimensional (1D) spiral tube; excitonic effects are weak in bulk with an exciton binding energy less than 10 meV, while the exciton binding energy is substantially enhanced to be 0.67 eV in the monolayer and 2.40 eV in the 1D structure. Interestingly, reduced dimensionality also produces substantial anisotropic optical response through many-electron interactions: local-field effects dominate the optical spectra of 2D and 1D structures and induce highly anisotropic optical responses. These results not only reveal a systematic picture for understanding the evolution of excited-state properties with dimensionality but also suggest the possibility of designing macroscopic electronic and optical properties by engineering nanosized building blocks.