1. Valley current reversal in partially overlapped graphene layers
- Author
-
Tamura, Ryo
- Subjects
Condensed Matter - Mesoscale and Nanoscale Physics ,Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ,FOS: Physical sciences - Abstract
Using the tight-binding model, we investigate the valley current of partially overlapped graphene layers with the two arrangements, $\Box \,_-\,_-^-\,^-\Box$ and $\Box \,_-\,_-^-\,_-\Box$, where symbols $\Box$, $\,_-$ ($\,^-$) and $\,_-^-$ represent the current probe, the lower (upper) monolayer region, and the AB stacking bilayer region, respectively. In the arrangement $\Box \,_-\,_-^-\,^-\Box$, there is no intra-layer current path connecting both the current probes; thus, the total current must flow through the interlayer path. We measure valley current reversal (VCR) by the average of $\frac{1}{2} \sum_{\nu =\pm}(T_{\nu,-\nu}-T_{\nu,\nu})$ per lateral wave number, where $T_{\nu,\nu'}$ denotes the electron transmission rate from the left $K_{\nu'}$ valley to the right $K_{\nu}$ valley. Without the vertical electric field, the VCR is less than half in both arrangements. As the vertical field intensifies, the VCR increases to about 0.8 in the $\Box \,_-\,_-^-\,^-\Box$ arrangement, but declines in the other arrangement. We derive an analytic scattering matrix $S_\downarrow$ ($S_\uparrow$) between the monolayer $\,_-$ ($\,^-$ ) and bilayer regions for the normal incidence. These $S_\downarrow$ and $S_\uparrow$ are real symmetric unitary matrixes ($S^{-1}=S=\;^tS=S^*$) and elucidate the vertical field effects on the VCR., Comment: 14 pages, 15 figures
- Published
- 2023