The electronic properties of curved graphene nanoribbons in the presence of uniform electric fields are investigated by using the tight-binding method. The energy dispersion, density of states, and wave function depend sensitively on the magnitude and direction of the electric field, and the curvature of the nanoribbon. An electric field separates the partial flat bands, causes band-mixing, creates new band-edge states, and induces semiconductor-metal transitions. The energy difference between the partial flat bands grows as the curvature, or the central angle, diminishes. The energy gap demonstrates a declining behavior with rising ribbon width. There are many density-of-states divergent peaks in the curved graphene nanoribbon, owing to the 1D subbands. The number, height, and energy of the density-of-states peaks are found to be dependent on the magnitude and direction of the electric field, and the curvature of the nanoribbon. The electric field causes electron transfer between different sublattices and among different atoms within the same sublattice, and introduces extra nodes into the wave function.
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