Topological States in Finite Graphene Nanoribbons Tuned by Electric Fields

TL;DR

This study theoretically explores how transverse electric fields influence topological states in finite graphene nanoribbons, revealing tunable energy shifts and transmission properties that could advance electronic and quantum device applications.

Contribution

It provides new insights into the Stark effect on topological states in finite graphene nanoribbons and heterostructures, highlighting controllable coupling and energy shifts under electric fields.

Findings

Blue Stark shift of formal topological states within specific energy ranges

Oscillatory Stark shift of interface states around the Fermi level

Electric field control of coupling strength between interface states

Abstract

In this comprehensive study, we conduct a theoretical investigation into the Stark shift of topological states (TSs) in finite armchair graphene nanoribbons (AGNRs) and heterostructures under transverse electric fields. Our focus centers on the multiple end zigzag edge states of AGNRs and the interface states of $9-7-9$ AGNR heterostructures. For the formal TSs, we observe a distinctive blue Stark shift in energy levels relative to the electric field within a range where the energy levels of TSs do not merge into the energy levels of bulk states. Conversely, for the latter TSs, we identify an oscillatory Stark shift in energy levels around the Fermi level. Simultaneously, we reveal the impact of the Stark effect on the transmission coefficients for both types of TSs. Notably, we uncover intriguing spectra in the multiple end zigzag edge states. In the case of finite $9-7-9$ AGNR heterostructures, the spectra of transmission coefficient reveal that the coupling strength between the topological interface states can be well controlled by the transverse electric fields. The outcomes of this research not only contribute to a deeper understanding of the electronic property in graphene-based materials but also pave the way for innovations in next-generation electronic devices and quantum technologies.