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We study the optical response of nanoribbons made from the $\alpha-T_3$lattice under a weak magnetic field in the terahertz to far-infrared regime. Itis found that the magnetic field can open a gap in the band structure andinduce a new absorption peak with much reduced frequency in metallic armchairribbons and a class of zigzag ribbons with particular boundaries. This tunablemagneto-optical modulation effect is attributed to the interband transitionsbetween the flat band and the propagating bands. By contrast, this magneticmodulation of gap opening and optical conductance is much weaker in metallicarmchair graphene ribbons (the case of $\alpha=0$) in which the flat band isabsent. The enhancement in the $\alpha-T_3$ model is analytically investigatedand explained within the perturbation theory for metallic armchair ribbons. Themagnetic field induced valley degeneracy lifting and valley splitting of theabsorption peak are also discussed in the case of zigzag ribbons. Thesefindings pave the way for magneto-optics devices based on the $\alpha-T_3$model materials.

Enhanced magneto-optical response due to the flat band in nanoribbons made from the $\alpha-T_3$ lattice