Spin structure of germanene quantum dot as a function of normal electric field

Germanene quantum dot consisting of 13 germanium atoms is studied numerically within the nearest neighbor tight-binding model. Both the energy spectra and the spin structure of the corresponding Eigen-functions are obtained. Due to strong spin-orbit interaction in germanene the spin polarization of the germanene quantum dot strongly depends on the energy of the corresponding Eigen-state and on the external electric field, $E_{\mathrm{z}}$. There are two states with energies close to zero, for which the direction of the spin is along z-axis, where z-axis is perpendicular of the quantum dot layer. For the higher energy levels the spin deviates from the z-axis with maximum angle $\theta _{\mathrm{max}}=$3.9$^{\mathrm{0}}$ for the levels with energy 1128 meV (for electron channel) and -1128 meV (for hole channel) and zero electric field, $E_{\mathrm{z}}=$0. The angle $\theta_{\mathrm{max}}$ increases almost linearly with $E_{\mathrm{z\thinspace }}$and takes the value of 4.2$^{\mathrm{0}}$ at $E_{\mathrm{z}}=$100 meV/{\AA}. The in-plane direction of spin is also sensitive to external electric field. With increasing electric field, the in-plane spin rotates in the anticlockwise and clockwise directions for the 1128 meV and -1128 meV levels, respectively. Due to such sensitivity of spin polarization to external electric field, applying a bias voltage can control the spin current through germanene quantum dot.