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  diverges as m  in the long wavelength limit (  ) with a universal exponent m=2, independent of the type of disorder. Here, we show rigorously that pseudospin-1 systems exhibit non-universal critical behaviors when they are subjected to 1D random potentials. In such systems, we find that 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 (SKTE). 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 a new analytic method based on a stack recursion equation. Our analytical results are in excellent agreements with the numerical results obtained by the transfer-matrix method (TMM). For pseudospin-1/2 systems, we find both numerically and analytically that 2   for all types of disorder, same as ordinary 1D disordered systems. Our new analytical method provides a convenient way to obtain easily the critical exponent m for general 1D Anderson localization problems.

Pseudospin-1 Physics of Photonic Crystals

“…Also, the absence of complex interactions between photons facilitates the advances of theories and makes the experimental observations and characterizations much easier. With the rapid development of the field of pseudospin-1 physics, there emerge lots of interesting phenomena, such as the superscattering of pseudospin-1 waves from a circular potential barrier [54], perfect caustics inside a circular barrier [53], current enhancement induced by the flat band in nonequilibrium transport of pseudospin-1 particles [55], and nonuniversal long-wavelength critical behavior of Anderson localization [51]. We expect that photonic crystals can be a good platform to test experimentally these theoretical predictions of pseudospin-1 physics.…”

“…When pseudospin-1 systems are subjected to 1D disordered potentials, two unconventional localization behaviors are found for obliquely incident waves. One is nonuniversal critical behavior for which the critical exponent of the localization length depends strongly on the type of disorder [51]. Another is the existence of a minimum localization length at some critical disorder strength beyond which the waves become less localized [52].…”

Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

“…For the i-th scattering element, we let t i+ (r i+ ) be the transmission (reflection) amplitude for waves incident from the left (forward waves), and t i− (r i− ) for waves incident from the right (backward waves). Then, for forward waves, the transmission amplitude t + (N + 1) through the stack of N + 1 scattering elements can be obtained from the following recurrence relations [33][34][35][36]…”

“…i 2 ln |1 − r i+ r − (i − 1)| involves both the modulus and phase of the reflection amplitudes and we will refer to it as the interference term. The stack recursion equation method has been discussed in detail in the literature [33][34][35][36].…”

“…In both scenarios, it is expected that the presence of coherent backscattering can lead to the Anderson localization of waves, i.e., the transmission will decay exponentially to zero when the sample is sufficiently large. Our results will be compared with the Anderson localization behaviors found in some special Hermitian random systems, where localization length is also known to be infinite at normal incidence such as random layered media with the same impedance in all layers [31] and pseudospin-1 systems in 1D random potential [32,33].…”