X-Ray Reflectivity of Fibonacci Multilayers

We have numerically computed the reflectivity of X-ray incident normally onto Fibonacci multilayers, and compared the results with those obtained in periodic approximant multilayers. The constituent layers are of low and high refractive indices with the same thickness. Whereas reflectivity of periodic approximant multilayers changes only slightly with increasing the number of layers, Fibonacci multilayers present a completely different behaviour. In particular, we have found a highly-fragmented and self-similar reflectivity pattern in Fibonacci systems. The behaviour of the fragmentation pattern on increasing the number of layers is quantitatively described using multifractal techniques. The paper ends with a brief discussion on possible practical applications of our results in the design of new X-ray devices.Comment: 8 pages, REVTeX 3.0, 3 figures available upon request from [email protected]. To appear in Physics Letters

Frenkel Excitons in Random Systems With Correlated Gaussian Disorder

Optical absorption spectra of Frenkel excitons in random one-dimensional systems are presented. Two models of inhomogeneous broadening, arising from a Gaussian distribution of on-site energies, are considered. In one case the on-site energies are uncorrelated variables whereas in the second model the on-site energies are pairwise correlated (dimers). We observe a red shift and a broadening of the absorption line on increasing the width of the Gaussian distribution. In the two cases we find that the shift is the same, within our numerical accuracy, whereas the broadening is larger when dimers are introduced. The increase of the width of the Gaussian distribution leads to larger differences between uncorrelated and correlated disordered models. We suggest that this higher broadening is due to stronger scattering effects from dimers.Comment: 9 pages, REVTeX 3.0, 3 ps figures. To appear in Physical Review

Feshbach-type resonances for two-particle scattering in graphene

Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshbach resonances in the identical-helicity channel. In the limit $Q \rightarrow 0$, one of the resonances survives and the opposite-helicity scattering amplitudes vanish.Comment: 8 pages, 2 figure

Spin-dependent THz oscillator based on hybrid graphene superlattices

We theoretically study the occurrence of Bloch oscillations in biased hybrid graphene systems with spin-dependent superlattices. The spin-dependent potential is realized by a set of ferromagnetic insulator strips deposited on top of a gapped graphene nanoribbon, which induce a proximity exchange splitting of the electronic states in the graphene monolayer. We numerically solve the Dirac equation and study Bloch oscillations in the lowest conduction band of the spin-dependent superlattice. While the Bloch frequency is the same for both spins, we find the Bloch amplitude to be spin dependent. This difference results in a spin-polarized ac electric current in the THz range.Comment: 4 pages, 6 figure

Bound states in the continuum driven by AC fields

We report the formation of bound states in the continuum driven by AC fields. This system consists of a quantum ring connected to two leads. An AC side-gate voltage controls the interference pattern of the electrons passing through the system. We model the system by two sites in parallel connected to two semi-infinite lattices. The energy of these sites change harmonically with time. We obtain the transmission probability and the local density of states at the ring sites as a function of the parameters that define the system. The transmission probability displays a Fano profile when the energy of the incoming electron matches the driving frequency. Correspondingly, the local density of states presents a narrow peak that approaches a Dirac delta function in the weak coupling limit. We attribute these features to the presence of bound states in the continuum.Comment: 5 pages, 3 figure

Comment on ``Periodic wave functions and number of extended states in random dimer systems'

There are no periodic wave-functions in the RDM but close to the critical energies there exist periodic envelopes. These envelopes are given by the non-disordered properties of the system.Comment: RevTex file, 1 page, Comment X. Huang, X. Wu and C. Gong, Phys. Rev. B 55, 11018 (1997

Fluorescence decay in aperiodic Frenkel lattices

We study motion and capture of excitons in self-similar linear systems in which interstitial traps are arranged according to an aperiodic sequence, focusing our attention on Fibonacci and Thue-Morse systems as canonical examples. The decay of the fluorescence intensity following a broadband pulse excitation is evaluated by solving the microscopic equations of motion of the Frenkel exciton problem. We find that the average decay is exponential and depends only on the concentration of traps and the trapping rate. In addition, we observe small-amplitude oscillations coming from the coupling between the low-lying mode and a few high-lying modes through the topology of the lattice. These oscillations are characteristic of each particular arrangement of traps and they are directly related to the Fourier transform of the underlying lattice. Our predictions can be then used to determine experimentally the ordering of traps.Comment: REVTeX 3.0 + 3PostScript Figures + epsf.sty (uuencoded). To appear in Physical Review

Localisation and finite-size effects in graphene flakes

We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large samples and can explain the divergence of results for finite-size graphene flakes

Subband energy in two-band delta-doped semiconductors

We study electron dynamics in a two-band delta-doped semiconductor within the envelope-function approximation. Using a simple parametrization of the confining potential arising from the ionized donors in the delta-doping layer, we are able to find exact solutions of the Dirac-type equation describing the coupling of host bands. As an application we then consider Si delta-doped GaAs. In particular we find that the ground subband energy scales as a power law of the Si concentration per unit area in a wide range of doping levels. In addition, the coupling of host bands leads to a depression of the subband energy due to nonparabolicity effects.Comment: REVTeX 3.0, 10 pages, 1 figure available upon request. To apper in Physics Letters