Quantum capacitance in bilayer graphene nanoribbon

We address a physically based analytical model of quantum capacitance (CQ)(CQ) in a bilayer graphene nanoribbon (BGN) under the application of an external longitudinal static bias. We demonstrate that as the gap (ΔΔ) about the Dirac point increases, a phenomenological population inversion of the carriers in the two sets of subbands occurs. This results in a periodic and composite oscillatory behavior in the CQCQ with the channel potential, which also decreases with increase in ΔΔ. We also study the quantum size effects on the CQCQ, which signatures heavy spatial oscillations due to the occurrence of van Hove singularities in the total density-of-states function of both the sets of subbands. All the mathematical results as derived in this paper converge to the corresponding well-known solution of graphene under certain limiting conditions and this compatibility is an indirect test of our theoretical formalism.

Quantum capacitance (CQCQ) as a function of channel potential (VchVch) in highly asymmetric bilayer graphene nanoribbon has been investigated analytically. Figure optionsDownload as PowerPoint slideHighlights
► Analytical model of quantum capacitance in graphene nanoribbon has been exhibited.
► Phenomenological population inversion of the carriers in subbands occurs.
► Periodic and composite oscillatory behavior in quantum capacitance is shown.
► Size effects on the quantum capacitance have also been studied.