Pseudo magnetic field in strained graphene: Revisited

•We introduce a novel effective Hamiltonian for strained graphene.•We obtained the pseudo magnetic field up to the second order in strain.•We examine the accurateness of the pseudo fields expressions and compared with the full solution.•Beyond 3% strain the contribution of higher order in strain is important.

We revisit the theory of the pseudo magnetic field as induced by strain in graphene using the tight-binding approach. A systematic expansion of the hopping parameter and the deformation of the lattice vectors is presented from which we obtain an expression for the pseudo magnetic field for low energy electrons. We generalize and discuss previous results and propose a novel effective Hamiltonian. The contributions of the different terms to the pseudo field expression are investigated for a model triaxial strain profile and are compared with the full solution. Our work suggests that the previous proposed pseudo magnetic field expression is valid up to reasonably high strain (15%) and there is no K-dependent pseudo-magnetic field.