Effects of shear displacement on the conductance of monolayer/gapped bilayer/monolayer graphene junctions: Implications for ac-dc conversion

Abstract

Analytical treatments of tunneling in bilayer graphene have typically relied on minimal models including only the vertical interlayer hopping $\gamma_1$ and have been restricted to the weak interlayer-bias regime ($2\varepsilon \ll \gamma_1$). Consequently, they cannot adequately describe lattice deformations or strong electric-field effects. In this work, we present an analytical theory of evanescent states in electrically gapped bilayer graphene that overcomes both limitations. Our approach explicitly incorporates the skew interlayer hoppings $\gamma_3$ and $\gamma_4$ and remains valid even when the interlayer bias $2\varepsilon$ is comparable to $\gamma_1$. Focusing on low-energy electronic states near the charge neutrality point, we analytically derive the complex longitudinal wave numbers, the gap width, and the sublattice pseudospin within the electric-field-induced gap. We then systematically analyze the dependence of these quantities on the interlayer shear displacement $\vec{\delta}=(\delta_x,\delta_y)$, and find that skew interlayer hoppings, in particular $\gamma_3$, play an essential role. For transport along the zigzag ($x$) direction, the longitudinal wave vector becomes complex, whereas the transverse wave vector remains real. For a monolayer/bilayer/monolayer junction with transport along the zigzag direction, we find that $\delta_y$ has a significantly stronger impact on the conductance than $\delta_x$. Furthermore, we identify a shear-induced phase proportional to $\delta_y$ that appears universally in the analytical expressions for the gap width, the sublattice pseudospin, and the decay length. These results establish a unified framework for shear- and bias-controlled evanescent tunneling in bilayer graphene and suggest broader relevance to nonequilibrium transport phenomena in layered materials.