  The engineering of the optical response of materials is a paradigm that
demands microscopic-level accuracy and reliable predictive theoretical tools.
Here we compare and contrast the dispersive permittivity tensor, using both a
low-energy effective model and density functional theory (DFT). As a
representative material, phosphorene subject to strain is considered. Employing
a low-energy model Hamiltonian with a Green's function current-current
correlation function, we compute the dynamical optical conductivity and its
associated permittivity tensor. For the DFT approach, first-principles
calculations make use of the first-order random-phase approximation. Our
results reveal that although the two models are generally in agreement within
the low-strain and low-frequency regime, the intricate features associated with
the fundamental physical properties of the system and optoelectronic device
implementation such as band gap, Drude absorption response, vanishing real
part, absorptivity, and sign of permittivity over the frequency range show
significant discrepancies. Our results suggest that the random-phase
approximation employed in widely used DFT packages should be revisited and
improved to be able to predict these fundamental electronic characteristics of
a given material with confidence. Furthermore, employing the permittivity
results from both models, we uncover the pivotal role that phosphorene can play
in optoelectronics devices to facilitate highly programable perfect absorption
of electromagnetic waves by manipulating the chemical potential and exerting
strain and illustrate how reliable predictions for the dielectric response of a
given material are crucial to precise device design.
