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Using the tight binding and Pariser-Parr-Pople (PPP) model Hamiltonians, westudy the electronic structure and optical response of multilayer armchairgraphene nanoribbons (AGNRs), both with and without a gate bias. In particular,the influence of the number of layers ($n$), and the strength of the electricfield applied perpendicular to layers, for different types of edge alignments,is explored on their electro-optical properties. As a function of increasing$n$, the energy gap initially decreases, eventually saturating for large $n$.The intensity of the linear optical absorption in these systems also increaseswith increasing $n$, and depends crucially on the polarization direction of theincident light, and the type of the edge alignment. This provides an efficientway of determining the nature of the edge alignment, and $n$, in theexperiments. In the presence of a gate bias, the intensity of opticalabsorption behaves in a nontrivial way. The absorption becomes more intense forthe large fields in narrow ribbons exhibiting a red shift of the band gap withthe increasing field strength, while in broad ribbons exhibiting a blue shift,the absorption becomes weaker. However, for smaller electric fields, theabsorption intensity exhibits more complicated behavior with respect to thefield strength. Thus, the effect of the gate bias on optical absorptionintensity in multilayer AGNRs is in sharp contrast to the bilayer graphene,which exhibits only enhancement of the absorption intensity with the increasingelectric field.

Band Structure and Optical Absorption in Multilayer Armchair Graphene Nanoribbons: A Pariser-Parr-Pople Model Study