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Giant enhancement of Piezo-resistance in ballistic graphene due to transverse electric fields

We investigate the longitudinal and transverse piezoresistance effect in suspended graphene in the ballistic regime. Utilizing parametrized tight binding Hamiltonian from ab initio calculations along with Landauer quantum transport formalism, we devise a methodology to evaluate the piezoresistance effect in 2D materials especially in graphene. We evaluate the longitudinal and transverse gauge factor of graphene along armchair and zigzag directions in the linear elastic limit ($0\%$-$10\%$). The longitudinal and transverse gauge factors are identical along armchair and zigzag directions. Our model predicts a significant variation ($\approx 1000\% $ change) in transverse gauge factor compared to longitudinal gauge factor along with sign inversion. The calculated value of longitudinal gauge factor is $\approx 0.3$ whereas the transverse gauge factor is $\approx -3.3$. We rationalize our prediction using deformation of Dirac cone and change in separation between transverse modes due to longitudinal and transverse strain, leading to an inverse change in gauge factor. The results obtained herein may serve as a template for high strain piezoresistance effect of graphene in nano electromechanical systems.