Theory of triangulene two-dimensional crystals

Abstract

Equilateral triangle-shaped graphene nanoislands with a lateral dimension of $n$ benzene rings are known as $[n]$triangulenes. Individual $[n]$triangulenes are open-shell molecules, with single-particle electronic spectra that host $n-1$ half-filled zero modes and a many-body ground state with spin $S=(n-1)/2$. The on-surface synthesis of triangulenes has been demonstrated for $n=3,4,5,7$ and the observation of a Haldane symmetry-protected topological phase has been reported in chains of $[3]$triangulenes. Here, we provide a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices whose unit cell contains a pair of triangulenes with dimensions $n_a,n_b$. Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for $n_a=n_b=2$), spin-1 Dirac electrons (for $n_a=2,n_b=3$), $p_{x,y}$-orbital physics (for $n_a=n_b=3$), as well as a gapped system with flat valence and conduction bands (for $n_a=n_b=4$). All these results are rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states that generalize the graphene honeycomb model to the case of fermions with an internal pseudospin degree of freedom with $C_3$ symmetry.

12 pages, 7 figures

References in corpus (16)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Magnetism in graphene nano-islands
• Moiré heterostructures as a condensed matter quantum simulator
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Observation of fractional edge excitations in nanographene spin chains
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Aza-Triangulene: On-Surface Synthesis, Electronic and Magnetic Properties
• On-surface synthesis and collective spin excitations of a triangulene-based nanostar
• Engineering the eigenstates of coupled spin-1/2 atoms on a surface
• Flat-Bands-Enabled Triplet Excitonic Insulator in a Di-atomic Kagome Lattice
• Theory of intermolecular exchange in coupled spin-1/2 nanographenes
• Renormalization of spin excitations and Kondo effect in open shell nanographenes
• Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model
• Hubbard model for spin-1 Haldane chains
• Topological junction states and their crystalline network in chiral-symmetric systems: application to graphene nanoribbons

Cited by in corpus (7)

• Metal-free Stoner and Mott-Hubbard magnetism in 2D polymers with honeycomb lattice
• Broken-symmetry magnetic phases in two-dimensional triangulene crystals
• Conformational tuning of magnetic interactions in coupled nanographenes
• Superexchange Mechanism in Coupled Triangulenes Forming Spin-1 Chains
• Magnetic frustration and fractionalization in oligo(indenoindenes)
• Quantum Monte Carlo study of artificial triangular graphene quantum dots
• Modulated Dirac bands and integer hopping ratios in a honeycomb lattice of phenalenyl-tessellation molecules