Abstract
It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length diverges as in the long-wavelength limit () with a universal exponent , independent of the type of disorder. Here, we show rigorously that pseudospin-1 systems exhibit nonuniversal critical behavior when they are subjected to 1D random potentials. In such systems, we find that with depending on the type of disorder. For binary disorder, and the fast divergence is due to a super-Klein-tunneling effect. When we add additional potential fluctuations to the binary disorder, the critical exponent crosses over from 6 to 4 as the wavelength increases. Moreover, for disordered superlattices, in which the random potential layers are separated by layers of background medium, the exponent is further reduced to 2 due to the multiple reflections inside the background layer. To obtain the above results, we developed an analytic method based on a stack recursion equation. Our analytical results are in excellent agreement with the numerical results obtained by the transfer-matrix method. For pseudospin-1/2 systems, we find both numerically and analytically that for all types of disorder, same as ordinary 1D disordered systems. Our analytical method provides a convenient way to obtain easily the critical exponent for general 1D Anderson localization problems.
- Received 29 November 2018
DOI:https://doi.org/10.1103/PhysRevB.99.014209
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