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 nanoribbon 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 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 containing a long constriction support formation of localized resonances which induce a system of conductance peaks that is reentrant in the Fermi energy, with the form of the probability density that can be resolved by the 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 of the system is low compared to the narrower part.

Graphene through the looking glass of QFT

“…A remarkable property of the DC conductivity (32) is its quantization in a square-root manner, not a stepwise one obtained for the conductance quantization in Landauer approach [36]. Such behavior is in accordance with numerical simulations [37], and is induced by averaging the Fabry-Perot oscillations of the propagating modes between the leads, and not the presence of impurities. This behavior is given at the Fig.…”

Aharonov-Bohm interferometer based onn−pjunctions in graphene nanoribbons

“…The incident amplitude c l in is set to 1 for each subsequent subband. The backscattered d in and transferred amplitudes c out are evaluated with the quantum transmitting boundary method [52][53][54][55][56][57]. The scattering amplitudes with the current fluxes allow to evaluate the transfer probability T l for the incident subband as T l = m T ml , where T ml may also include transfer between propagating modes in different valleys.…”

Valley filtering in graphene due to substrate-induced mass potential

“…Valley filtering has been seen as a promising path to manipulate the two non-equivalent valley states in graphene. Previous theoretical proposals for valley filtering in monolayer graphene involve cutting it in specific directions [5,6], using specific strain distributions that yield uniform [7][8][9][10] or piece-wise uniform [11] pseudomagnetic fields, or using a line of heptagon-pentagon defects in its honeycomb lattice [12][13][14][15][16], just to mention a few. Notice that all the mentioned proposals share the feature of requiring manipulation of the graphene crystal structure, be it by cutting, straining, or creating defects on its honeycomb lattice, which is not always an easy task.…”