Metallic-Substrate-Induced\nRenormalization of Quasiparticle\nBand Gaps and Excitonic Effects in Biphenylene Nanoribbons

Biphenylene networks, as well as their nanoribbons, have\nbeen fabricated\nsuccessfully by a two-step dehydrofluorination polymerization method\non Au(111) [<i>Science</i> <b>2021</b>, <i>372</i>, 852–856]. Their band gap measured by differential conductance\nshows a monotonic decrease with the increasing width of the nanoribbon.\nHowever, the metallic substrate (Au(111)) induced band gap renormalization\nchallenges the direct comparison with the theoretical result. In this\nstudy, based on density functional theory with the many-body perturbation\nmethod, we include the additional screening from the metallic substrate\nand study its effects on quasiparticle electronic structure and electron–hole\nexcitation in these one-dimensional systems. The obtained quasiparticle\nband gap is in good agreement with the experimental value. Significantly,\ncompared with the pristine system, the screening effect of the substrate\non the attractive interaction of electron–hole (the direct\nterm of the kernel) decreases the exciton binding energy strongly\nby about 1.2 eV. Moreover, its influence on the repulsive interaction\nof electron–hole (the exchange term of the kernel) further\nincreases the exciton binding energy by about 0.3 eV, leading to a\nfinal variation of 0.9 eV. For biphenylene nanoribbons with six C–C\ndimers, the exciton with the metallic substrate effect exhibits a\ntransition from a bound exciton state to a resonant one. The exciton\nprofile, on the other hand, also shows obvious renormalization in\nboth real space and reciprocal space when the screening of the substrate\nis considered to be in the exchange term of the kernel. Our study\nhas provided a deep understanding of environmental dielectric screening\nand its effects on electronic excited states in low-dimensional systems.