Bias-tunable resonances and device metrics in M-graphene nanoribbons

We report a comparative first-principles study of electronic transport in M-graphene nanoribbons with zigzag and chiral edge terminations for widths W = 1-4. Density functional theory combined with nonequilibrium Green's function (DFT-NEGF) calculations were used to compute relaxed geometries, band structures, bias-dependent transmission spectra and two-terminal current-voltage characteristics. A coordinated diagnostic suite comprising Fowler-Nordheim and Millikan-Lauritsen transforms, WKB estimates, empirical power-law fitting, transmission eigenchannel decomposition and first-principles inelastic electron tunnelling spectroscopy (IETS) was applied to identify conduction mechanisms and discriminate smooth barrier tunnelling from resonance-mediated transport. Narrow nanoribbons display sharp, bias-tunable transmission resonances that localise on ring motifs and produce abrupt increases in differential conductance, while wider nanoribbons exhibit a smoother bias dependence, consistent with field-assisted tunnelling and barrier thinning. IETS signatures correlate with changes in eigenchannel character and provide vibrational corroboration of resonance-assisted conduction. Extracted device metrics such as threshold bias for resonance, peak differential conductance and the bias evolution of the leading eigenvalue τ₁ indicate that M-graphene nanoribbons are promising candidates for nanoscale switching and resonant tunnelling elements, with predictions that map directly to measurable two-terminal observables.