Engineering of robust topological quantum phases in graphene nanoribbons

Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin-momentum locked transport channels or Majorana fermions(1-3). The idea of using such states in spintronic devices or as qubits in quantum information technology is a strong driver of current research in condensed matter physics(4-6). The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states(7-9). In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model(10,11). Because the SSH model describes chiral topological insulators, charge fractionalization and spin-charge separation in one dimension, numerous efforts have been made to realize the SSH Hamiltonian in cold-atom, photonic and acoustic experimental configurations(12-14). It is, however, desirable to rationally engineer topological electronic phases into stable and processable materials to exploit the corresponding quantum states. Here we present a flexible strategy based on atomically precise graphene nanoribbons to design robust nanomaterials exhibiting the valence electronic structures described by the SSH Hamiltonian(15-17). We demonstrate the controlled periodic coupling of topological boundary states(18) at junctions of graphene nanoribbons with armchair edges to create quasi-one-dimensional trivial and non-trivial electronic quantum phases. This strategy has the potential to tune the bandwidth of the topological electronic bands close to the energy scale of proximity-induced spin-orbit coupling(19) or superconductivity(20), and may allow the realization of Kitaev-like Hamiltonians(3) and Majorana-type end states(21).