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.

arXiv comment12 pages, 7 figures

References in corpus (37)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• On-surface synthesis of graphene nanoribbons with zigzag edge topology
• Magnetism in graphene nano-islands
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Moiré heterostructures as a condensed matter quantum simulator
• Bottom up synthesis of multifunctional nanoporous graphene
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array
• Topological Frustration in Graphene Nanoflakes: Magnetic Order and Spin Logic Devices
• Observation of fractional edge excitations in nanographene spin chains
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Collective All-Carbon Magnetism in Triangulene Dimers
• Designer quantum states of matter created atom-by-atom
• Magnetism and correlations in fractionally filled degenerate shells of graphene quantum dots
• 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
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Exchange rules for diradical π-conjugated hydrocarbons
• Flat-Bands-Enabled Triplet Excitonic Insulator in a Di-atomic Kagome Lattice
• Quantum Simulation of the Hubbard Model with Dopant Atoms in Silicon
• Magnetic edge anisotropy in graphene-like honeycomb crystals
• Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to Néel order
• Quantum paramagnets on the honeycomb lattice and field-induced Néel order: Possible application to Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)
• Quantum phase diagram of the spin-$1$ $J_1-J_2$ Heisenberg model on the honeycomb lattice
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal 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
• Designer fermion models in functionalized graphene bilayers

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