  In this paper, we present a Kane-Mele model in the presence of magnetic field
and next nearest neighbors hopping amplitudes for investigations the electronic
and optical properties of monolayer Germanene. Specially, we address the
dynamical conductivity of the structure as a function of photon frequency and
in the presence of magnetic field and spin-orbit coupling at finite
temperature. Using linear response theory and Green's function approach, the
frequency dependence of optical conductivity has been obtained in the context
of Kane-Mele model Hamiltonian. Our results show a finite Drude response at low
frequency at non zero value for magnetic field in the presence of spin-orbit
coupling. However Drude weight gets remarkable amount in the presence of
electron doping. The thermal conductivity and specific heat increase with
increasing the temperature at low amounts of temperature due to the increasing
of thermal energy of charge carriers and excitation of them to the conduction
bands. The results for Seebeck coefficient show the sign of thermopower is
negative in the presence of spin-orbit coupling. Also we have studied the
temperature dependence of electrical conductivity of Germanene monolayer due to
both spin orbit coupling and magnetic field factors in details.
