Electric field induced band tuning, optical and thermoelectric responses in tetragonal germanene: a theoretical approach

Abstract

In this article, we have systematically explored the electronic, optical and thermoelectric properties of tetragonal germanene (T-Ge) using first principles calculations. The ground state geometry of pristine T-Ge is buckled and exhibits nodal line semi-metallic behaviour. In addition, we have proposed a tight binding (TB) model Hamiltonian that efficiently explains the emergence of double Dirac points at the Fermi level of T-Ge. Furthermore, a hopping relation has been explored at which both Dirac points merge and then annihilate resulting in a direct band gap at the Γ point. To exploit the buckling of the system, we have employed a transverse electric field, which invariably breaks the sublattice symmetry and removes the degeneracies at the Fermi surface. Furthermore, the band gap at the Dirac points varies linearly with the external electric field strength. Our TB Hamiltonian adequately satisfies the first principles results even in the presence of an external electric field. Moreover, we have found that T-Ge offers efficient tuning of band gaps at the Dirac points compared to other buckled systems viz. hexagonal silicene and germanene. In addition, the optical behaviour of T-Ge has been explained in accordance with the electronic states of the system. The strong optical responses in a low energy region make the material efficient for optical nanodevice applications. Moreover, T-Ge shows relatively better thermoelectric behaviour than graphene. Therefore, the external electric field induced tunable band gap and intriguing low energy optical signals pave the way to choose T-Ge as a smart choice for optoelectronic device applications. Finally we have suggested probable routes for experimental realization of the T-Ge structure.