Conductance response of graphene nanoribbons and quantum point contacts in scanning gate measurements

Abstract

We provide a theoretical study of the conductance response of systems based on graphene nanoribbons to the potential of a scanning probe. The study is based on the Landauer approach for the tight-binding Hamiltonian with an implementation of the quantum transmitting boundary method and covers homogenous nanoribbons, their asymmetric narrowing and quantum point contacts (QPCs) of various profiles. The response maps at low Fermi energies resolve formation of n–p junctions induced by the probe potential and a presence of zigzag-armchair segments of the edges for inhomogeneous ribbons. For an asymmetric narrowing of the nanoribbons the scanning probe resolves formation of standing waves related to backscattering within the highest subband of the narrower part of the system. The QPCs contain a long constriction support formation of localized resonances. These resonances result in a series of conductance peaks that are reentrant in the Fermi energy, and the form of the probability density can be resolved by conductance mapping. For shorter constrictions the probe induces smooth conductance minima within the constrictions. In general, besides the low-energy transport gap, in the wider parts of the ribbon the variation of the conductance is low compared to the narrower part.