Valley and spin quantum Hall conductance of silicene coupled to a ferroelectric layer

We study the quantum valley and Hall conductances in silicene coupled to a ferroelectric (FE) layer. The spin orbit interaction in silicene couples the valley, pseudospin, and real spin degrees of freedom resulting in a topological Berry curvature in the system. The finite Berry curvature in turn induces a transverse Hall conductance. In particular, if the Fermi level E-f is within the bulk energy gap, the Hall conductance is quantized to integer multiples of pi. We study the quantum spin and valley Hall conductivities (QSH and QVH) as functions of the applied out-of-plane electric field for different values of E-f and temperature. Both conductivities vary linearly as 1/|E-f| when E ( f ) is within the conduction or valence bands but reach a quantized plateau value when E ( f ) is within the bulk gap. Further, by coupling silicene to a FE layer, the QSH and QVH signals can be modulated by means of the coupling strength. This can potentially provide a robust topological memory read-out with distinct binary outputs over a wide temperature range.