We report herein existence of a critical tunnelling width beyond which graphitic tunnelling nanostructures exhibit asymmetric spin polarized negative differential resistance feature. Our theoretical foray quite clearly establishes that even with a simple two-dimensional tunnelling nanostructure created by an assembly of ferromagnetic graphitic carbon nitride (g-C4N3) electrodes separated by insulating graphene sheet of variable lengths, there exists a critical tunnelling width at which the system switches from symmetric to asymmetric negative differential resistance feature. Presence of robust spin filer efficiency (100%) over a wide range of bias variation (- 1.0 to +1.0 V) added with negative differential resistance action makes the device with shorter tunnelling width of 22.36 A and 31. 96 A potentially useful as multifunctional spintronic device. However, at the critical tunnelling width of 36.69 A and beyond the forward bias negative differential resistance features completely switches off and same is observed only in reverse bias. This switching action certainly opens up the prospect of logic gates operation in quantum circuits. Results obtained has been explained through transmission spectra, transmission pathways and molecular projected self-consistent Hamiltonian states analysis. Emergence of asymmetric I-V curve beyond critical tunnelling width has been explained by examining differences in spin injection coefficients.
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