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We investigate the longitudinal and transverse piezoresistance effect insuspended graphene in the ballistic regime. Utilizing parametrized tightbinding Hamiltonian from ab initio calculations along with Landauer quantumtransport formalism, we devise a methodology to evaluate the piezoresistanceeffect in 2D materials especially in graphene. We evaluate the longitudinal andtransverse gauge factor of graphene along armchair and zigzag directions in thelinear elastic limit ($0\%$-$10\%$). The longitudinal and transverse gaugefactors are identical along armchair and zigzag directions. Our model predictsa significant variation ($\approx 1000\% $ change) in transverse gauge factorcompared to longitudinal gauge factor along with sign inversion. The calculatedvalue of longitudinal gauge factor is $\approx 0.3$ whereas the transversegauge factor is $\approx -3.3$. We rationalize our prediction using deformationof Dirac cone and change in separation between transverse modes due tolongitudinal and transverse strain, leading to an inverse change in gaugefactor. The results obtained herein may serve as a template for high strainpiezoresistance effect of graphene in nano electromechanical systems.

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