Landau Quantized Dynamics and Spectrum of the Diced Lattice

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Abstract

In this work the role of magnetic Landau quantization in the dynamics and spectrum of Diced Lattice charge carriers is studied in terms of the associated pseudospin 1 Green's function. The equations of motion for the 9 matrix elements of this Green's function are formulated in position/frequency representation and are solved explicitly in terms of a closed form integral representation involving only elementary functions. The latter is subsequently expanded in a Laguerre eigenfunction series whose frequency poles identify the discretized energy spectrum for the Landau-quantized Diced Lattice as $\epsilon_n = \pm\sqrt{2(2n+1)\alpha^2 eB}$ ($\alpha\sqrt{2}$ is the characteristic speed for the Diced Lattice) which differs significantly from the nonrelativistic linear dependence of $\epsilon_n$ on $B$, and is similar to the corresponding $\sqrt{B}-$dependence of other Dirac materials (Graphene, Group VI Dichalcogenides).