Effect of uni-axial and bi-axial strains and vertical electric field on free standing buckled germanene

In this work, the effects of small uni-axial and bi-axial strains and vertical electric field on the band dispersion and dielectric response of germanene are studied by density functional theory. The results show that by applying the vertical electric field a small band gap at the K point is opened in germanene. The created band gap increases with electric field. The vertical electric field only affects the optical spectra in the low energy range below 1 eV. The band structure of germanene under small biaxial strain maintains the feature of bands near the K point without applying the strain, including a pair of two linear dispersive bands crossing at the Fermi level and the Dirac point position. The CBM at the Γ point moves downward as the biaxial strain increases. By applying the small uniaxial strain, a direct gap at K point is observed and the value of band gap increases with increasing of strain. Imaginary part of dielectric function shows that the inter-band transitions are red-shifted for uni- and bi-axial tensile strains and are blue shifted for uni- and bi-axial compressive strains. The predicted tunability of the band gap and dielectric response by applying the strain and electric field may leads to a wide range of applications of germanene in electronic and optoelectronic devices.