Dirac wave transmission in Lévy-disordered systems

Extended states in random dimer gated graphene superlattices

Ordered and disordered semiconductor superlattices represent structures with completely opposed properties. For instance, ordered superlattices exhibit extended Bloch-like states, while disordered superlattices present localized states. These characteristics lead to higher conductance in ordered superlattices compared to disordered ones. Surprisingly, disordered dimer superlattices, which consist of two types of quantum wells with one type always appearing in pairs, exhibit extended states. The percentage of dissimilar wells does not need to be large to have extended states. Furthermore, the conductance is intermediate between ordered and disordered superlattices. In this work, we explore disordered dimer superlattices in graphene. We calculate the transmission and transport properties using the transfer matrix method and the Landauer-Büttiker formalism, respectively. We identify and discuss the main energy regions where the conductance of random dimer superlattices in graphene is intermediate to that of ordered and disordered superlattices. We also analyze the resonant energies of the double quantum well cavity and the electronic structure of the host gated graphene superlattice (GGSL), finding that the coupling between the resonant energies and the superlattice energy minibands gives rise to the extended states in random dimer GGSLs.

Impact of Correlated Disorder on Surface Superconductivity: Revealing the Robustness of the Surface Ordering Effect

Surface superconductivity, wherein electron pairing occurs at material surfaces or interfaces, has attracted a remarkable amount of attention since its discovery. Recent theoretical predictions have unveiled increased critical temperatures, especially at the surfaces of certain compounds and/or structures. The notion of "surface ordering" has been advanced to elucidate this phenomenon. Employing the framework of self-consistent Bogoliubov-de Gennes equations and a model incorporating correlated disorder, our study demonstrates the persistence of the surface ordering effect in the presence of weak to moderate bulk disorder. Intriguingly, our findings indicate that under moderate disorder conditions the surface critical temperature can be further increased, depending on the intensity and correlation of the disorder.

Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon, and Dirac equations

We investigate the propagation of waves in one-dimensional systems with Lévy-type disorder. We perform a complete analysis of nonrelativistic and relativistic wave transmission submitted to potential barriers whose width, separation, or both follow Lévy distributions characterized by an exponent 0<α<1. For the first two cases, where one of the parameters is fixed, nonrelativistic and relativistic waves present anomalous localization, 〈T〉∝L^{-α}. However, for the latter case, in which both parameters follow a Lévy distribution, nonrelativistic and relativistic waves present a transition between anomalous and standard localization as the incidence energy increases relative to the barrier height. Moreover, we obtain the localization diagram delimiting anomalous and standard localization regimes, in terms of incidence angle and energy. Finally, we verify that transmission fluctuations, characterized by its standard deviation, are universal, independent of barrier architecture, wave equation type, incidence energy, and angle, further extending earlier studies on electronic localization.

Delay time of waves performing Lévy walks in 1D random media

The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder—Lévy disorder—leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.