Generation and control of charge, spin and valley currents in armchair silicene nanoribbons

It is well known that future information technology relies upon electronic states other than charge, through the feasibility of constructing spintronic and valleytronic devices. The main challenge in such applications is the generation and control of the corresponding state currents. The present paper is thus concerned with charge, spin and valley currents which intrinsically develop in armchair silicene nanoribbons (ASNs). In pursuing this consideration the well established Kubo formula is employed. Taking the symmetries of the ASN into account, we analyze the structure of total Hamiltonian and demonstrate how the matrix elements along with the summations involved in the suitably adopted Kubo formula, may be analytically calculated. The results so-obtained along with the corresponding figures reveal that all three currents develop in a step-wise manner. The heights, indicating a jump in the current, and the plateaus, indicating a constant current, are shown to be tunable by adjusting the width and/or the buckled effect. Moreover, we demonstrate that for particular (critical) widths an inversion in band gaps may occur, giving rise to quantum phase transitions. More practical result of this paper, as we show, is the fact that the ASN can generate pure spin or valley current under specific conditions placed on the width, buckled effect and Fermi energy. The material presented in this paper thus provides novel means of generation and control of the charge, spin and valley currents.