  We have calculated numerically electron exchange, correlation energies and
dynamical polarization function for newly discovered silicene, germanene and
black phosphorus (BP), consisting of puckered layers of elemental phosphorus
atoms, broadening the range of two-dimensional (2D) materials at various
temperatures. As a matter of fact, monolayer BP, produced by mechanical and
liquid exfoliation techniques, has been predicted to be an insulator with a
large energy splitting 1.6 eV for the quasiparticle band structure. We compare
the dependence of these energies on the chemical potential, field-induced gap
and the temperature and concluded that in many cases they behave qualitatively
similarly, i.e., increasing with the doping, decreasing significantly at
elevated temperatures, and displaying different dependence on the asymmetry gap
at various temperatures. Furthermore, we used the dynamical polarizability to
investigate the new "split" plasmon branches in the puckered lattices and
predict a unique splitting, different from that in gapped graphene, for various
energy gaps. Our results are crucial for stimulating electronic, transport and
collective studies of these novel materials, as well as for enhancing
silicene-based fabrication and technologies for photovoltaics and transistor
devices.
