Charge density response of 2D polymorphs: borophene as a prototypical case

The aim of this thesis is to elucidate the charge dynamics in 2D materials with complex atomic structures.
To this end, borophene was chosen as a prototypical material that exhibits numerous allotropes, such that the influence of the atomic structure on the electronic properties
can be investigated directly. Among the multiple allotropes I identified eight structures of theoretical and experimental relevance and computed their electronic band structure. I then
used the shared characteristics of the electronic structure of the different polymorphs to relate them to a common parent structure, and I built a theoretical model based on a confined
three-dimensional homogeneous electron gas. This model explain several findings for the electronic structure of the different polymorphs studied in this work. The electronic structure of the different polymorphs showed common features  among different allotropes, but it also showed differences in the form of weakly-dispersive bands. 
These flat bands show up as a signature of the specific atomic structure. We refer
to them as defect-like states that appear from the creation
of point defects in a common borophene atomic structure.
Moreover, I investigated the effect of buckling on the electronic structure and showed that we can use this parameter
to tune electronic properties of the material such that semi-metallicity and eventually even superconductivity might be
impacted. The study of the electronic structure also showed the potential of this class of materials to be used as a
transparent conductor. I described the mechanism for which
certain electronic transitions do not appear in the absorption spectra by symmetry : the position of the Fermi energy
in the band structure is an important parameter to determine the optical properties of borophene, and the relative
positions of p-states in-plane and out-of-plane plays also an
important role around the Fermi level. I therefore described
nesting of the Fermi surface based on the information of
the electronic transitions. The study of the nesting of the
Fermi surface was complemented with the computation of
the static linear response, which allowed me to we unravel
the nature of two Kohn anomalies appearing in borophene
δ6 . The calculation of the response functions is computationally very expensive. I addressed this problem by developing an approximated method that allows us to write the
static response as an explicit functional of the density matrix. This is of both fundamental and practical interest since
it is one of the few examples of explicit density matrix functionals for observables, and since it leads to an order of magnitude gain in computer time.