Dirac wave transmission in Lévy-disordered systems

Abstract

We investigate the propagation of electronic waves described by the Dirac equation subject to a Lévy-type disorder distribution. Our numerical calculations, based on the transfer matrix method, in a system with a distribution of potential barriers show that it presents a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schrödinger equation do not present such transitions. Moreover, we obtain the phase diagram delimiting anomalous and standard localization regimes, in the form of an incidence angle versus incidence energy diagram, and argue that transitions can also be characterized by the behavior of the dispersion of the transmission. We attribute this transition to an abrupt reduction in the transmittance of the system when the incidence angle is higher than a critical value which induces a decrease in the transmission fluctuations.

Electronic transport in disordered graphene superlattices with scale-free correlated barrier spacements

“…However, strong long-range correlations are known to induce a localization-delocalization transition [39,40,41,42,43,44,45,46], thus leading to the emergence of the reported transmission band. Notice that the average logarithmic transmission is not an appropriate quantity to clearly signal this delocalization transition, in agreement with the similar delocalization phenomenon reported in graphene superlattices with Levy-distributed barrier spacements [50].…”

“…On the other hand, transmission still results reminiscent of Klein tunneling at small incidence angles. Recently, it was shown that these two regimes leads to either standard or anomalous scaling of the transmission when the barrier widths are distributed following a scale-free Levy distributions [50]. Further, fractal [51], self-affine potentials [52] and long-range scale-free correlations in the barrier heights and widths [53] as well in the velocity profile [54] were also considered.…”

Wave Propagation and Localization in a Complex Random Potential with Power-law Correlations: A Numerical Study

“…Email address: nguyenbaphi@muce.edu.vn https//doi.org / 10.25073/2588-1124/vnumap.4498 During the recent few decades, the influence of spatially correlated disorder on the wave propagation and localization properties has been attracted much attention from theoretical as well as experimental researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. It has been demonstrated that some special kinds of short-range correlated disorder can produce delocalized eigenstates even in one dimension [7,8].…”

Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations

“…During the recent few decades, the influence of spatial disorder correlations on the localization properties has been studied extensively [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. It has been demonstrated both theoretically and experimentally that some special types of short-range correlated disorder can produce extended eigenstates even in one dimension [10,11,26].…”