Abstract
We investigate the low energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study both in-plane and out-of-plane deformations and obtain a closed expression for the effective gauge field due to arbitrary nonuniform sheet deformations. The obtained results reveal a remarkable relation between the local-pseudo magnetic field and the Riemann curvature, so far overlooked.
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