Magnetoexcitons and Faraday rotation in single-walled carbon nanotubes and graphene nanoribbons

Abstract

The magneto-optical response of single-walled carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) is studied theoretically, including excitonic effects. Both diagonal and nondiagonal response functions are obtained and employed to compute Faraday rotation spectra. For single-walled CNTs in a parallel field, the results show field-dependent splitting of the exciton absorption peaks caused by brightening a dark exciton state. Similarly, for GNRs in a perpendicular magnetic field, we observe a field-dependent shift of the exciton peaks and the emergence of an absorption peak above the energy gap. Results show that excitonic effects play a significant role in the optical response of both materials, particularly for the off-diagonal tensor elements.

Enhanced magneto-optical response due to the flat band in nanoribbons made from the α−T3 lattice

“…The optical and magneto-optical spectroscopy can be used to probe the underlying electronic structure and as well as design optoelectronic devices. For graphene, the optical and magneto-optical conductivities have been extensively studied for both infinite sheet 33 and nanoribbon geometry [34][35][36][37][38][39][40] . The optical response at selective frequencies can be enhanced with the use of nanoribbons in graphene.…”

Excitonic magneto-optics in monolayer transition metal dichalcogenides: From nanoribbons to two-dimensional response

“…I, the relation between field strength and the supercell size makes the calculation of excitonic properties unfeasible for realistic magnetic fields. However, for a nanoribbon system, which is finite in the y-direction, the Landau gauge, A = −Byx, does not affect the translation symmetry of the system [35]. Hence, no restrictions on the magnetic field strength and no magnetic supercell are required.…”

“…However, if only the optical response and not the full eigenvalue decomposition is needed a significant reduction in computational complexity can be obtained by using the Lanczos approach in Refs. 35…”

“…( 17) are evaluated effectively as in Ref. 35, i.e. using the Lanczos-Haydock routine for tridiagonalization [47].…”

“…The translation symmetry can be restored by considering a magnetic supercell, but the size of the supercell is inversely proportional to the magnetic field strength [33]. Consequently, for realistic field strengths, a very large supercell is needed, thus, making the task of computing the excitonic properties unfeasible [35]. In the present work, we address this issue by using a system of finite width in the direction, for which translation symmetry is broken.…”