  Graphene nanoribbons (GNRs) possess distinct symmetry-protected topological
phases. We show, through first-principles calculations, that by applying an
experimentally accessible transverse electric field (TEF), certain boron and
nitrogen periodically co-doped GNRs have tunable topological phases. The
tunability arises from a field-induced band inversion due to an opposite
response of the conduction- and valance-band states to the electric field. With
a spatially-varying applied field, segments of GNRs of distinct topological
phases are created, resulting in a field-programmable array of topological
junction states, each may be occupied with charge or spin. Our findings not
only show that electric field may be used as an easy tuning knob for
topological phases in quasi-one-dimensional systems, but also provide new
design principles for future GNR-based quantum electronic devices through their
topological characters.
