We study the electronic properties of GaAs-AlGaAs superlattices with intentional correlated disorder by means of photoluminescence and vertical dc resistance. The results are compared to those obtained in ordered and uncorrelated disordered superlattices. We report the first experimental evidence that spatial correlations inhibit localization of states in disordered low-dimensional systems, as our previous theoretical calculations suggested, in contrast to the earlier belief that all eigenstates are localized. [S0031-9007(99) PACS numbers: 73.20.Dx, 73.20.Jc, In recent years, a number of tight-binding [1][2][3] and continuous [4] models of disordered one-dimensional (1D) systems have predicted the existence of sets of extended states, in contrast to the earlier belief that all the eigenstates are localized in 1D disordered systems. These systems are characterized by the key ingredient that structural disorder is short-range correlated. Because of the lack of experimental confirmations, there are still some controversies as to the relevance of these results and their implications on physical properties. In this context, some authors have proposed finding physically realizable systems that allow for a clear cut validation of the above-mentioned purely theoretical prediction [5][6][7][8]. Given that semiconductor superlattices (SL's) have been already used successfully to observe electron localization due to disorder [9][10][11][12][13][14], these authors have suggested SL's as ideal candidates for controllable experiments on localization or delocalization and related electronic properties [5][6][7][8].To the best of our knowledge, up to now there is no experimental verification of this theoretical prediction owing to the difficulty in building nanoscale materials with intentional and short-range correlated disorder. However, the confirmation of this phenomenon is important both from the fundamental point of view and for the possibility to develop new devices based on these peculiar properties. In this work we present an experimental verification of this phenomenon in semiconductor nanoscale materials, taking advantage of the molecular beam epitaxy growth technique, which allows the fabrication of semiconductor nanostructures with monolayer controlled perfection.We grew several GaAs-Al 0.35 Ga 0.65 As SL's and we studied their electronic properties by photoluminescence (PL) at low temperature and dc vertical transport in the dark. Indeed PL has been proven to be a good technique to study the electronic properties of disordered SL's [9-11], giving transition energies comparable with theoretical calculations of the electronic levels. The electronic states were calculated using a Kronig-Penney model that has been shown to hold in this range of well and barrier thicknesses, with precise results [15]. This allows the analysis of the experimental transition energies for PL and the ascertainment of the localization and delocalization properties of the SL's. The details of the calculations and a schematic view of the cond...

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Propagating light beams with widths down to and below the optical wavelength require bulky large-aperture lenses and remain focused only for micrometric distances 1,2 . Here, we report the observation of light beams that violate this localization/depth-of-focus law by shrinking as they propagate, allowing resolution to be maintained and increased over macroscopic propagation lengths. In nanodisordered ferroelectrics 3,4 we observe a non-paraxial propagation of a sub-micrometresized beam for over 1,000 diffraction lengths, the narrowest visible beam reported to date [5][6][7][8] . This unprecedented effect is caused by the nonlinear response of a dipolar glass, which transforms the leading optical wave equation into a Klein-Gordon-type equation that describes a massive particle field 9 . Our findings open the way to high-resolution optics over large depths of focus, and a route to merging bulk optics into nanodevices.As monochromatic light travels through a transparent material its optical field E is governed by the Helmholtz equation (HE) (∇ 2 + n 2 k 2 0 )E = 0, where k 0 = 2π/λ is the wavevector, λ is the wavelength of the beam, and n is the index of refraction 10 . The HE includes diffraction, which smears out the fine details of spatial information. In nanodisordered ferroelectrics, the photorefractive nonlinearity can cause light to obey a Klein-Gordon equation0 )E = 0, which corresponds to a relativistic particle with mass given by the Einstein relation mc 2 = h − n m k 0 c (see Methods). In terms of propagation, a basic signature of the KGE regime is anti-diffraction; that is, diffraction-limited optical spots shrink instead of spreading. The simplest description of anti-diffraction can be formulated in the paraxial approximation, which predicts that(see Supplementary Section 'Beam anti-diffraction law in the paraxial regime'), which connects the beam spot size w(z) at a given distance z along the propagation direction to the minimum spot size w 0 at z = 0 through λ and n and the characteristic length scale L 11 . For L ≪ λ the standard diffraction law holds, so for sufficiently large values of z, the beam has an angular spread that scales as Δθ ≈ λ/nw 0 . In turn, for L > λ, equation (1) predicts beams that converge like funnels into a point-like focus at the critical value z c = (nπ/λ)w 0 2 [(L/λ) 2 -1] -1/2 . Anti-diffraction at λ = 633 nm was observed with the set-up presented in Fig. 1a. To achieve values of L/λ > 1 we applied a rapid change in temperature to the crystal before launching the propagating light (see description of thermal shocks in the Methods). The L ≪ λ (diffraction) and the L > λ (anti-diffraction) cases are shown in Fig. 1b and c, respectively. In Fig. 1b, a round Gaussian beam is focused to its diffraction-limited spot at the input of the sample and naturally diffracts through the sample when standard cooling is performed, a behaviour compatible with L ≪ λ. In this case the beams obey the HE in its paraxial approximation and spread following the basic Gaussian beam law. If a therm...