Full analytical solution of finite-length armchair/zigzag nanoribbons

Abstract

Finite-length armchair graphene nanoribbons can behave as one dimensional topological materials, that may show edge states in their zigzag-terminated edges, depending on their width and termination. We show here a full solution of Tight-Binding graphene rectangles of any length and width that can be seen as either finite-length armchair or zigzag ribbons. We find exact analytical expressions for both bulk and edge eigen-states and eigen-energies. We write down exact expressions for the Coulomb interactions among edge states and introduce a Hubbard-dimer model to analyse the emergence and features of different magnetic states at the edges, whose existence depends on the ribbon length. We find ample room for experimental testing of our predictions in N = 5 armchair ribbons. We compare the analytical results with ab initio simulations to benchmark the quality of the dimer model and to set its parameters. A further detailed analysis of the ab initio Hamiltonian allows us to identify those variations of the Tight-Binding parameters that affect the topological properties of the ribbons.

References in corpus (20)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Phosphorene: A New 2D Material with High Carrier Mobility
• Topological Insulators with Inversion Symmetry
• Half-Metallic Graphene Nanoribbons
• Electronic States of Graphene Nanoribbons
• Topological Band Engineering of Graphene Nanoribbons
• Engineering of robust topological quantum phases in graphene nanoribbons
• The Zak phase and the existence of edge states in graphene
• SIESTA: recent developments and applications
• Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers and Quantum Spin Chains
• Giant edge state splitting at atomically precise zigzag edges
• Carrier Density and Magnetism in Graphene Zigzag Nanoribbons
• Robustness of edge states in graphene quantum dots
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Probing the magnetism of topological end-states in 5-armchair graphene nanoribbons
• Hidden multiferroic order in graphene zigzag ribbons
• Electronic states in finite graphene nanoribbons: Effect of charging and defects

Cited by in corpus (1)

• Kagome edge states under lattice termination, spin-orbit coupling, and magnetic order