Magnetic barriers in graphene nanoribbons: Theoretical study of transport properties

Abstract

A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps towards higher energies. The magnetic barrier also induces Fabry − Pérot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbons tend to localize the lowest propagating state, which get delocalized in the magnetic barrier region. Thus, in sharp contrast to the case of two-dimensional graphene, the charge carriers in graphene nanoribbons cannot be confined by magnetic barriers. We also present a novel method based on the Green's function technique for the calculation of the magnetosubband structure, Bloch states and magnetoconductance of the graphene nanoribbons in a perpendicular magnetic field. Utilization of this method greatly facilitates the conductance calculations, because, in contrast to excising methods, the present method does not require self-consistent calculations for the surface Green's function.

Effect of zigzag and armchair edges on the electronic transport in single-layer and bilayer graphene nanoribbons with defects

“…We also calculate the local density of states (LDOS) of graphene nanoribbons with a defect, expressing it via the imaginary part of the Green's function of the ribbon in a standard way. 18,35 …”

“…The calculation of the conductance in monolayer graphene nanoribbons with many defects and all calculations for bilayer graphene nanoribbons (BGNs) are performed numerically on the basis of the recursive Green's function technique. 18,35 In this technique, a ribbon of width W is divided into three regions, namely a left lead, a scattering region, and a right lead. The scattering potential is defined in the scattering region of length L, whereas both semi-infinite leads are considered to be ideal (no scattering).…”

“…II we present the tight-binding model of p-orbital electrons in monolayer and bilayer nanoribbons with edge disorder. The conductance calculations in graphene nanoribbons with edge defects are performed on the basis of the recursive Green's function technique, 35 which is briefly presented in Sec. II A.…”

Interactions and screening in gated bilayer graphene nanoribbons

“…In order to determine the charge density, the local density of states ͑LDOS͒ D͑r , E͒ at site r and energy E is calculated with the help of the real-space Green's-functions technique described in Ref. 32. The electron density at site r is then given by…”

Electronic properties of quantum dots formed by magnetic double barriers in quantum wires

“…Alternatively, nonplanar 2DEGs may be used. 31 Furthermore, magnetic confinement concepts have attained increased attention recently due to their potential application to graphene, 32,33 where electrostatic confinement is inhibited due to Klein tunneling. 34 It will be interesting to see whether the concept discussed here can be transferred to graphene nanoribbons.…”