(color online) (a) Structure deformation of 8-ZGNR induced by temperature effect. The C and H atoms at two different moments are represented by gray and silver, and red and green, respectively. (b) and (c) The spin I–V curve of the ideal 8-ZGNR and 8-ZGNR with phonon effect. (d) The phonon band structure of infinite GNRs. The widths of the red bands are proportional to the weight function of electron-phonon interaction, where the (1-6) represent the phonon modes at the Γ point of the six most effective bands. The dashed line shows the structural symmetric mirror plane δ through the center of GNR. (e) The magnetoresistances (MR) of ferromagnetic 6-ZGNR with (solid line) and without (dashed line) consideration of electron-phonon interaction at 4.2 K. (f) The spin up current of the elastic I_el and phonon-influenced I_ph parts in parallel and antiparallel configurations at 4.2 K. Reprinted Figs. 10(a)–10(c) and 10(d)–10(f) with permissions from Ref. [177] and Ref. [180], respectively. Copyright (2017) by AIP Publishing LLC and copyright (2016) by IOP Publishing.