Analytical Description of Strain-Controlled Transport Anisotropy in Graphene

We develop an analytical framework to describe the impact of in-plane strain on the electronic and transport properties of graphene. Starting from a strain-modified nearest-neighbor tight-binding model, we derive the energy spectrum and group velocities, explicitly incorporating bond-dependent hopping renormalization. A dimensionless anisotropy parameter, derived from velocity fluctuations, is introduced to quantify directional transport imbalance. We show that this parameter admits a closed-form expression entirely determined by the strain tensor, linking lattice deformation directly to measurable transport quantities. In the small-strain regime, a compact expression is obtained, η≈ϵ1+νcos2θ, revealing an angular dependence controlled solely by the orientation of the applied deformation. This establishes that strain acts as a purely geometric control parameter, separating magnitude and orientation effects. Within the semiclassical Boltzmann framework, the same parameter fully determines the conductivity tensor, leading to simple expressions for the longitudinal components σx,y=σ01∓η and a clear identification of the preferred transport direction. Importantly, the total conductivity remains constant, while strain redistributes transport between orthogonal directions. These results provide a transparent and predictive description of strain-induced transport anisotropy, demonstrating that the directional electronic response can be tuned without modifying the material composition, offering a practical route to control electronic response in graphene through purely mechanical means.