Phonon polaritons are hybrid light-matter quasiparticles that enable confinement and control of electromagnetic modes at the nanoscale. Particular interest has been paid to hetero-bicrystals composed of molybdenum oxide (α-MoO) and isotopically pure hexagonal boron nitride (hBN), which feature polariton dispersion tailorable the spectral gap originating from polariton hybridization. In this work, we propose unexplored hetero-crystals assembled from Ca-intercalated metal oxide α'-(Ca)VO and α-MoO, allowing the polaritons to travel along closed trajectories inside the bicrystal within the spectral gap. We systematically study the dependence of the spectral gap on the twist angle and thickness ratio of constituting layers in α'-(Ca)VO/α-MoO and the initial hBN/α-MoO. We show that on-off switching and strong tuning of the spectral gap in polariton dispersion can be realized by varying the twist angle in both structures. In particular, the spectral gap in α'-(Ca)VO/α-MoO can exist over a wide range of twist angles, three times as broad as that in hBN/α-MoO. Moreover, the spectral gap can also be significantly tuned by altering the thickness ratio. The spectral gap in α'-(Ca)VO/α-MoO emerges in a higher frequency range that is not achievable in hBN/α-MoO. Our results demonstrate that α'-(Ca)VO/α-MoO and hBN/α-MoO provide two powerful bicrystal systems for polariton engineering tuning the twist angle and thickness ratio.
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