Topological end states and Zak phase of rectangular armchair ribbon

Abstract

We consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron-electron interactions into account we find that, as the strength of the staggered potential varies, three types of couplings between the end states can occur: antiferromagnetic without or with spin splitting, and paramagnetic without spin-splitting. We find that a spin-splitting is present only in the staggered potential region $0<\Delta <{\Delta }_c$. The transition from the antiferromagnetic state at $\Delta =0$ to the paramagnetic state goes through an intermediate spin-split antiferromagnetic state, and this spin-splitting disappears suddenly at ${\Delta }_c$. For small and large values of $\Delta$ the end charge of a RAGR can be connected to the Zak phase of the periodic armchair graphene ribbon (PARG) with the same width, and it varies continuously as the strength of the potential changes.

References in corpus (11)

• The electronic properties of graphene
• Boron nitride substrates for high-quality graphene electronics
• Half-Metallic Graphene Nanoribbons
• Substrate-induced band gap opening in epitaxial graphene
• Electronic States of Graphene Nanoribbons
• STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride
• Spin qubits in graphene quantum dots
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• End states in a 1-D topological Kondo insulator
• Dirac equation description on the electronic states and magnetic properties of a square graphene quantum dot
• Topological gap states of semiconducting armchair graphene ribbons

Cited by in corpus (2)

• Soliton fractional charges in graphene nanoribbon and polyacetylene: similarities and differences
• Topological entanglement entropy of interacting disordered zigzag graphene ribbons