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We present a theoretical study on the Landau levels (LLs) and magneto-opticalabsorption of a two-dimensional semi-Dirac electron system under aperpendicular magnetic field. Based on an effective k.p Hamiltonian, we findthat the LLs are proportional to the two-thirds power law of the magnetic fieldand level index, which can be understood as a hybridization of the LL ofSchrodinger and Dirac electrons with new features. With the help of Kuboformula, we find the selection rule for interband (intraband) magneto-opticaltransition is anisotropic (isotropic). Specifically, the selection rules forinterband magneto-optical transitions are $\Delta n$=0, $\pm2$ ($\pm2$, $\pm4$)for linearly polarized light along the linear (parabolic) dispersion direction,while the selection rules for the intraband transition are $\Delta n$=$\pm1$,$\pm3$ regardless of the polarization direction of the light. Further, themagneto-optical conductivity for interband (intraband) transition excited bylinearly polarized light along the linear dispersion direction is two (one)orders of magnitude larger than that along the parabolic dispersion direction.This anisotropic magneto-optical absorption spectrum clearly reflects thestructure of the LLs, and results in a strong linear dichroism. Importantly, aperfect linear dichroism with magnetic-field tunable wavelength can be achievedby using the interband transition between the two lowest LLs, i.e, from Ev0 toEc0. Our results shed light on the magneto-optical property of the twodimensional semi-Dirac electron systems and pave the way to design magneticallycontrolled optical devices.

Anisotropic magneto-optical absorption and linear dichroism in two-dimensional semi-Dirac electron systems