Electrically-tunable ultra-flat bands and $\pi$-electron magnetism in graphene nanoribbons

Atomically thin crystals hosting flat electronic bands have been recently identified as a rich playground for exploring and engineering strongly correlated phases. Yet, their variety remains limited, primarily to two-dimensional moir\'e superlattices. Here, we predict the formation of reversible, electrically-induced ultra-flat bands and $\pi$-electron magnetism in one-dimensional chevron graphene nanoribbons. Our $ab$ $initio$ calculations show that the application of a transverse electric field to these nanoribbons generates a pair of isolated, nearly perfectly flat bands with widths of approximately 1 meV around the Fermi level. Upon charge doping, these flat bands undergo a Stoner-like electronic instability, resulting in the spontaneous emergence of local magnetic moments at the edges of the otherwise non-magnetic nanoribbon, akin to a one-dimensional spin-$\frac{1}{2}$ chain. Our findings expand the class of carbon-based nanostructures exhibiting flat bands and establish a novel route for inducing correlated electronic phases in chevron graphene nanoribbons.