Engineering of robust topological quantum phases in graphene nanoribbons

Abstract

Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin-momentum locked transport channels or Majorana fermions. 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. The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states. In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model. 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. 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. We demonstrate the controlled periodic coupling of topological boundary states 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 or superconductivity, and may allow the realization of Kitaev-like Hamiltonians and Majorana-type end states.

Massive Dirac Fermion Behavior in a Low Bandgap Graphene Nanoribbon Near a Topological Phase Boundary

“…Figure 4b shows the different wave functions of the HOMO between topologically trivial and non‐trivial pGNR by TB calculations. The absence of end states at the termini of the pGNRs in experiment confirms their topologically trivial nature 7,17…”

“…In conclusion, inspired by the principle of topological band engineering,7,8 we have demonstrated a new kind of GNR with an extremely low bandgap which is even lower than the one of the “quasi‐metallic” 5‐AGNR that has a similar width. This GNR has mixed armchair and zigzag edge structure, and the origin of its low bandgap can be rationalized within an SSH‐type model.…”

“…The synthesis of GNRs with smaller bandgaps would hence be highly desirable. To this end, width‐modulated AGNRs are promising candidates, because their periodically arranged and overlapping electronic states give rise to 1D topological bands within the bandgap of the pristine AGNR backbone 7,8. According to the Su–Schrieffer–Heeger (SSH) model, their fundamental electronic properties such as bandgap, bandwidth, and topological class can be widely tuned by varying the intra‐ and the interdimer coupling strength which are related to the overlap between the corresponding electronic states located at the ribbon edge extension.…”

Tuning the Electronic Properties of Atomically Precise Graphene Nanoribbons by Bottom‐Up Fabrication

“…Special molecular structures such as molecule 13 and molecule 14 can synthesize 7‐ AGNR‐S(1,3) and 7‐ AGNR‐I(1,3), respectively (Figure f, Figure g and Figure i). Electronic features of them are shown in Figure e and Figure i …”

Effect of Edge Functionalization on the Bottom‐Up Synthesis of Nano‐Graphenes

“…Besides potential application of atomically‐precise GNRs for qubits in quantum information technology, another promising application of extremely‐narrow GNRs is a detector diode, which rectifies THz‐waves into a direct‐current (DC) output voltage. Due to its negligible junction capacitance of sub‐nm wide GNR p‐n junction, it was predicted that the backward diode with GNR heterojunction can outperform the state‐of‐the‐art diodes made from III–V compound semiconductors .…”