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After having derived boundary conditions for dressed-state electrons in adice lattice, we investigate the electron tunneling through a squareelectrostatic potential barrier in both dice lattices and graphene under alinearly-polarized off-resonance and high-frequency dressing field, anddemonstrate the anomalous Klein paradox for a nonzero incident angle, resultedfrom the misalignment of optically-controllable elliptical dispersion forDirac-cone dressed states and the direction of incoming kinetic particles inour system. This finite incident angle is found depending on the type of lightpolarization, the light-induced anisotropy in energy dispersion and thestrength of electron-light coupling. Meanwhile, we also observe much largeroff-peak transmission amplitudes in dice lattices in comparison with graphene.We expect the theoretical results in this paper could be used for wide range ofDirac materials and applied to controlling both coherent tunneling andballistic transport of electrons for constructing novel optical and electronicnano-scale switching devices.

Anomalous Klein paradox due to misalignment of optically-tunable  elliptical dispersion for Dirac-cone dressed states and direction of incoming  particles