Anomalous localization behaviors in disordered pseudospin systems: Beyond the conventional Anderson picture

Abstract

We discovered novel Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the wave localization behaviors are entirely different from those of normal disordered systems. We show both numerically and analytically that there exists a critical strength of random potential ($W_c$), which is equal to the incident energy ($E$), below which the localization length $\xi$ decreases with the random strength $W$ for a fixed incident angle $\theta$. But the localization length drops abruptly to a minimum at $W=W_c$ and rises immediately afterwards, which has never been observed in ordinary materials. The incidence angle dependence of the localization length has different asymptotic behaviors in two regions of random strength, with $\xi \propto {\sin }^{-4}\theta$ when $W<W_c$ and $\xi \propto {\sin }^{-2}\theta$ when $W>W_c$. Experimentally, for a given disordered sample with a fixed randomness strength $W$, the incident wave with incident energy $E$ will experience two different types of localization, depending on whether $E>W$ or $E<W$. The existence of a sharp transition at $E=W$ is due to the emergence of evanescent waves in the systems when $E<W$. Such localization behavior is unique to pseudospin-1 systems. For pseudospin-1/2 systems, there is a minimum localization length as randomness increases, but the transition from decreasing to increasing localization length at the minimum is smooth rather than abrupt. In both decreasing and increasing regions, the $\theta$ -dependence of the localization length has the same asymptotic behavior $\xi \propto {\sin }^{-2}\theta$.

44 pages, 5 figures

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• Effective medium theory for photonic pseudospin-1/2 system
• Non-Universal Critical Behaviors in Disordered Pseudospin-1 Systems
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