Origins of Valley Current Reversal in Partially Overlapped Graphene Layers

Using the tight-binding model, we investigate the valley current of the low-bi-up' and low-bi-low’ graphene junction, where low' and up’ are respectively the lower and upper graphene layers extended from the central AB stacking bilayer graphene layer, `bi’. Source and drain electrodes connect with the left and right monolayer regions, respectively, and thus the total current is forced to flow through the interlayer path in the low-bi-up junction. We measure valley current reversal (VCR) using the average of $\frac{1}{2}{\sum }_{\nu =\pm }(T_{\nu ,-\nu }-T_{\nu ,\nu })$ per lateral wave number, where $T_{\nu ,{\nu }^{\mathrm{\prime }}}$ denotes the electron transmission rate from the left $K_{{\nu }^{\mathrm{\prime }}}$ valley to the right $K_{\nu }$ valley. Without the vertical electric field, the VCR is less than half in both junctions. This VCR is attributed to monolayer–bilayer matching. As the vertical field intensifies, the VCR declines in the low-bi-low junction, but increases to about 0.8 in the low-bi-up junction. This VCR enhancement originates from interlayer matching. Analytic scattering matrixes elucidate these matching effects. Experiments of VCR detection are also proposed.