Strain engineering of graphene nanoribbons: pseudomagnetic versus external magnetic fields

Bandgap opening due to strain engineering is a key architect for making graphene's optoelectronic, straintronic, and spintronic devices. We study the bandgap opening due to strain induced ripple waves and investigate the interplay between pseudomagnetic fields and externally applied magnetic fields on the band structures and spin relaxation in graphene nanoribbons (GNRs). We show that electron-hole bands of GNRs are highly influenced (i.e. level crossing of the bands are possible) by coupling two combined effects: pseudomagnetic fields (PMF) originating from strain tensor and external magnetic fields. In particular, we show that the tuning of the spin-splitting band extends to large externally applied magnetic fields with increasing values of pseudomagnetic fields. Level crossings of the bands in strained GNRs can also be observed due to the interplay between pseudomagnetic fields and externally applied magnetic fields. We also investigate the influence of this interplay on the electromagnetic field mediated spin relaxation mechanism in GNRs. In particular, we show that the spin hot spot can be observed at approximately B = 65 T (the externally applied magnetic field) and B-0 = 53 T (the magnitude of induced pseudomagnetic field due to ripple waves) which may not be considered as an ideal location for the design of straintronic devices. Our analysis might be used for tuning the bandgaps in strained GNRs and utilized to design the optoelectronic devices for straintronic applications.