Semiconductors and their oxides, when properly doped, are potential promising plasmonic material alternatives due to their special properties such as low loss and tunability. The hydrodynamic theory has been applied to describe the nonlocal response of pint-sized nanostructures even when several different kinds of charge carriers are considered, but when an external static magnetic field is presented the interplay between the gyrotropy and nonlocality needs to be considered, which is important and critical for semiconductors. We derive an analytical approach to calculate the optical properties of a plasmonic semiconductor nanowire in an external dc magnetic field within the multi-fluid hydrodynamic framework. The extended nonlocal Mie theory to magnetized multi-fluid plasmas predicts the existence of multiple acoustic and optical longitudinal modes within the multi-fluid hydrodynamic theory and the resonance splitting due to the applied bias magnetic field. We further focus on the nonlocal magneto-plasmonic response of nanowires that consist of thermally excited InSb, and predict the modified Zeeman splitting of the plasmonic extinction resonances due to the interplay between nonlocality and gyrotropy.
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