Nonuniversal critical behavior in disordered pseudospin-1 systems

Abstract

It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $\ensuremath{\xi}$ diverges as ${\ensuremath{\lambda}}^{m}$ in the long-wavelength limit ($\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$) with a universal exponent $m=2$, 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 $\ensuremath{\xi}\ensuremath{\propto}{\ensuremath{\lambda}}^{m}$ with $m$ depending on the type of disorder. For binary disorder, $m=6$ 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 $m$ 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 $m$ 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 $\ensuremath{\xi}\ensuremath{\propto}{\ensuremath{\lambda}}^{2}$ for all types of disorder, same as ordinary 1D disordered systems. Our analytical method provides a convenient way to obtain easily the critical exponent $m$ for general 1D Anderson localization problems.