Tunable spin and conductance in porphyrin-graphene nanoribbon hybrids

Graphene nanoribbons (GNRs) exhibit width-dependent band gaps, edge states, and long spin relaxation times, making them promising for nanoelectronics and spintronics. Porphyrins possess tunable spin properties depending on the central metal and ligand field. Integrating porphyrins into GNRs could enable control over band gaps, topological phases, and spin-dependent transport. On-surface bottom-up synthesis offers atomically precise nanostructures, making Por-GNR hybrids feasible and overcoming issues like random molecular placement. Prior work has largely focused on porphyrin oligomers, polymers, and nanotapes rather than GNR-backbone hybrids, with only finite nanostructures realized that include porphyrins connected by short GNR segments. Quantum interference has been observed in porphyrin nanoribbon devices with graphene electrodes, motivating a study of charge and spin transport in Por-GNRs with magnetic centers. This work proposes two Por-GNR hybrid structures and investigates their electronic structure and spin-transport behavior, including tunability via mechanical and chemical stimuli.

• Bottom-up on-surface synthesis can create atomically precise 1D nanostructures from precursor molecules or porphyrin building blocks, enabling Por-GNR hybrid fabrication.
• Prior synthesized systems include porphyrin oligomers/polymers and porphyrin nanotapes, which typically lack extended GNR backbones. Finite nanostructures with two metal-free porphyrins connected by a short GNR segment have been realized experimentally.
• Charge transport through nickel-porphyrin nanoribbon devices with graphene electrodes shows quantum interference, raising questions about transport in Por-GNR hybrids, especially with magnetic centers.
• The study builds on known GNR precursors used to grow 7-AGNRs and 13-AGNRs, integrating a porphyrin center to form straight (hybrid1) and S-shaped (hybrid2) Por-GNRs.

First-principles calculations were carried out using DFT and NEGF. The SIESTA/TranSIESTA codes were employed with the GGA-PBE exchange-correlation functional and a double-zeta polarized (DZP) basis set. A real-space grid cutoff of 400 Ry and low electronic temperature of 50 K were used, including spin polarization. The k-point mesh was 1×6×1, and a vacuum layer of 25 Å was included. All atoms were relaxed until forces were below 0.01 eV/Å. A Hubbard U correction of 3 eV was applied to Fe 3d orbitals. Computational parameters were checked for convergence and trends were cross-validated with VASP using PBE and HSE06 functionals. DOS, transmission, current, and spin density were analyzed with SISL. Zak phases (Z2 topology) were obtained from electronic contributions to macroscopic polarization computed with SIESTA. For transport, a two-terminal device was modeled with one Fe-porphyrin hybrid2 unit between semi-infinite H2-hybrid2 electrodes (periodically repeated), and zero-bias transmissions and eigenchannel scattering states were evaluated. Spin-crossover was studied by applying 3% uniaxial strain along the GNR backbone and by modeling CO adsorption on Fe (adsorption geometry optimized and binding energy computed).

• Two Por-GNR hybrids were proposed: straight hybrid1 and S-shaped hybrid2, constructed from known GNR precursor units with an integrated porphyrin.
• Electronic structure (H2-porphyrin cases): hybrid1 exhibits a larger band gap (0.75 eV with PBE; 0.9 eV with HSE06), while hybrid2 displays a small gap (0.1 eV with PBE; 0.25 eV with HSE06). Both have Z2=1, indicating a topologically non-trivial phase with expected localized end states.
• Embedding Fe in the porphyrin center induces spin polarization with an S=1 ground state. Fe-hybrid2 remains planar (approximate D4h symmetry) with Fe–N ≈ 2.00 Å; the 3d shell favors a 3E configuration (dxz)1(dyz)1(dxy)2(dx2−y2)1(dz2)1. A metastable 3A2g-like state lies ~0.1 eV higher.
• Transport in a two-terminal device with H2-hybrid2 electrodes and a central Fe-hybrid2 unit shows a small electrode-induced gap (~0.1 eV) at EF. A pronounced Fano anti-resonance appears in the spin-down transmission at −0.15 eV (relative to EF), linked to the Fe dxz state; spin-up transmits while spin-down is reflected at this energy.
• Mechanical strain (3% uniaxial) increases Fe–N bonds from 2.00 Å to ~2.10 Å and drives a spin-crossover from S=1 to S=2, removing the Fano feature and yielding nearly equal spin up/down transmission in −0.5 to 0.5 eV.
• CO adsorption atop Fe (binding energy 2.03 eV; Fe–CO 1.73 Å; C–O 1.16 Å; ~0.2 e charge transfer) strengthens crystal-field splitting and quenches the magnetic moment to S=0 with minimal structural distortion of the porphyrin plane (Fe–N ~2.0 Å), producing distinct transmission characteristics consistent with spin quenching.
• The small-gap hybrid2 is promising as an electrode material for spintronic devices, with conductance highly sensitive to Fe spin state and external stimuli.

The study addresses how integrating porphyrins into GNRs enables tunable spin-dependent transport. Hybrid2’s small band gap makes it suitable as an electrode, and embedding Fe yields an S=1 ground state whose d-levels couple to GNR bands, producing a spin-selective Fano anti-resonance near EF. This feature renders conductance highly sensitive to the Fe spin state. External stimuli provide practical control: modest mechanical strain induces a spin-crossover to S=2, erasing the Fano dip and equalizing spin channels, while CO adsorption leads to S=0 and distinct transmission changes. Thus, Por-GNR hybrids offer a controllable platform for carbon-based spintronics and chemical sensing. Considerations about experimental realization are noted: although synthesis typically occurs on metallic substrates that may quench spins, techniques such as STM lifting and transfer to insulating substrates can preserve the magnetic properties, supporting feasibility for device applications.

First-principles DFT-NEGF calculations predict that S-shaped Por-GNR hybrid2 has a small band gap and, with embedded Fe, exhibits an S=1 ground state due to coupling between GNR bands and Fe-porphyrin states. In a two-terminal device with hybrid2 electrodes, a spin-down Fano anti-resonance appears near EF, enabling spin-sensitive conductance. The spin state, and thus transport, can be tuned via 3% uniaxial strain (S=2) or CO adsorption (S=0), demonstrating routes for mechanically driven spin filters and chemical sensing. Future directions include exploring substrate-induced effects (e.g., Kondo resonance), topological quantum phases, spin–spin interactions, and extending to 2D Por-GNR-based structures.

• The results are purely theoretical; experimental validation is pending.
• Band gaps and relative spin-state energetics depend on the choice of exchange-correlation functional and Hubbard U; near-degeneracy of spin multiplets in Fe-porphyrins is a known theoretical challenge.
• Real devices are often fabricated on metallic substrates where spin quenching can occur; careful device architectures (e.g., lifting with STM tips, transfer to insulating substrates) are needed to preserve spin properties.
• Transport analysis focuses on zero-bias characteristics; finite-bias and temperature effects beyond the chosen electronic temperature were not explored.