Influence of electric and magnetic fields and $\sigma$-edge bands on the electronic and optical spectra of graphene nanoribbons

TL;DR

This paper systematically investigates how electric and magnetic fields, along with edge types, influence the electronic and optical properties of graphene nanoribbons using a detailed tight-binding model.

Contribution

It introduces a comprehensive multi-orbital tight-binding approach to analyze the combined effects of external fields and edge structures on GNRs' spectra.

Findings

Electric fields split energy bands and shift Fermi levels.

Magnetic fields induce quantized Landau levels and unique optical spectra.

Edge types significantly affect the electronic and optical responses.

Abstract

The unusual electronic and optical properties of armchair and zigzag graphene nanoribbons (GNRs) subject to in-plane transverse electric and perpendicular magnetic fields have been systematically investigated. Our calculations were carried out within the generalized multi-orbital tight-binding model based on a Hamiltonian which takes into account hopping integrals among the (s, $p_x$, $p_y$, $p_z$) atomic orbitals as well as the external electric and magnetic fields. The electronic structure consists of $\pi$ bands arising from the $p_z$ orbital and $\sigma$ bands originating from the (s, $p_x$, $p_y$) orbitals. The energy bands and optical spectra are diversified by both the nature of the edge of the nanoribbon and strength of the external fields. Armchair GNRs display a width-dependent energy gap in addition to low-energy $\sigma$ bands while the zigzag system has the unfilled flat band with $\pi$ edge states at zero energy and partially filled wide-range $\sigma$ bands. An applied in-plane electric field leads to the splitting of energy bands and shifted Fermi level, thereby enriching the inter-band and intra-band optical conductivities. The interplay between an external magnetic field and the edge geometry gives rise to extraordinary quantized Landau levels and special optical spectra.