Local electronic interaction effects on electronic properties of tetragonal Germanene under bias voltage

We study the effects of a transverse magnetic field and bias voltage on the electronic properties of buckled tetragonal Germanene in the context of Hubbard model with ferromagnetic ordering. In particular, the behavior of density of states and temperature dependence of specific heat, thermoelectric properties and magnetic susceptibility have been investigated. Mean field approximation has been employed in order to obtain the effects of local coulomb interaction on the band structure of the system. Our results show the band gap in the density of states decreases with increase of bias voltage. Also the low temperature dependence of specific heat of tetragonal Germanene is found to be exponentially increasing behavior with temperature for all magnetic field and local coulomb interaction strength values. Seebeck coefficient shows an increasing behavior in terms of temperature with positive sign for all values of interaction strength. However Seebeck coefficient gets both positive and negative signs due to variation of transverse magnetic field strength in the absence of coulomb interaction and bias voltage.