Origins of Valley Current Reversal in Partially Overlapped Graphene Layers

TL;DR

This study investigates valley current reversal in partially overlapped graphene layers, revealing how vertical electric fields influence valley current behavior through interlayer and monolayer-bilayer matching effects.

Contribution

It provides a detailed analysis of valley current reversal mechanisms in specific graphene junctions using tight-binding models and introduces the role of interlayer matching under electric fields.

Findings

VCR is less than half without vertical field due to monolayer-bilayer matching.

Vertical field increases VCR to about 0.8 in low-bi-up junction, decreases in low-bi-low.

Analytic models clarify the matching effects influencing VCR.

Abstract

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 $T_{\nu,\nu'}$ 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 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.