Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential

Abstract

We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range correlated dichotomous random potential at all strengths of disorder. We also consider a $\delta$-function correlated random potential at weak disorder. Using the invariant imbedding method, we calculate the localization length in a numerically precise way and analyze its dependencies on incident angle, disorder correlation length, disorder strength, energy, wavelength and average potential over a wide range of parameter values. In addition, we derive analytical formulas for the localization length, which are very accurate in the weak and strong disorder regimes. From the Dirac equation, we obtain an expression for the effective wave impedance, using which we explain several conditions for delocalization. We also deduce a condition under which the localization length vanishes. For all cases considered, the localization length depends non-monotonically on the disorder correlation length and diverges as $\theta^{-4}$ as the incident angle $\theta$ goes to zero. As the disorder strength is varied from zero to infinity, we find that there appear three different scaling regimes. As the energy or wavelength is varied from zero to infinity, there appear three or four different scaling regimes with different exponents, depending on the value of the average potential. The crossovers between different scaling regimes are explained in terms of the disorder correlation effect.