Goos-Hänchen-like shift in biased silicene

We have theoretically studied the Goos-Hänchen-like shift of spinor-unpolarized beams tunneling through various gate-biased silicene nanostructures. Following the stationary-phase method, lateral displacement in single-, dual-, and multiple-gated silicene systems has been systematically demonstrated. It is shown for simple single-gated silicene that lateral displacement can be generally enhanced by Fabry-Perot interference, and near the transition point turning on the evanescent mode a very large lateral shift could be observed. For the dual-gated structure, we have also shown the crucial role of localized modes like quantum well states in enhancing the beam lateral displacement, while for the multiple gate-biased systems the resulting superlattice subbands are also favorable for lateral displacement enhancement. Importantly, including the degeneracy-broken mechanisms such as gate-field and magnetic modulations, a fully spinor-resolved beam can be distinguished from the rest counterparts by aligning the incident beam with a proper spinor-resolved transition point, localized state, and subband, all of which can be flexibly modulated via electric means, offering the very desirable strategies to achieve the fully spinor-polarized beam for functional electronic applications.