A novel two-dimensional system of colloidal particles with absolutely calibrated magnetic interaction is used to investigate static and dynamic properties at the 2D crystal to liquid phase transition. We observe two successive transitions from the solid to the liquid phase with an intermediate hexatic phase, in perfect agreement with the theory of Kosterlitz and Thouless. The absolute values of the transition temperatures are given, and we demonstrate that they depend neither on the system size nor on the cooling rate. [S0031-9007(99)08831-6]
Diffusive transport is among the most common phenomena in nature [1]. However, as predicted by Anderson [2], diffusion may break down due to interference. This transition from diffusive transport to localization of waves should occur for any type of classical or quantum wave in any media as long as the wavelength becomes comparable to the transport mean free path ℓ * [3]. The signatures of localization and those of absorption, or bound states, can however be similar, such that an unequivocal proof of the existence of wave localization in disordered bulk materials is still lacking. Here we present measurements of time resolved non-classical diffusion of visible light in strongly scattering samples, which cannot be explained by absorption, sample geometry or reduction in transport velocity. Deviations from classical diffusion increase strongly with decreasing ℓ * as expected for a phase transition. This constitutes an experimental realization of the critical regime in the approach to Anderson localization.Diffusive transport controls many phenomena in biology, chemistry, physics and engineering, where undirected transport is characterized by a linear increase of the mean square displacement r 2 with time [1]. As a consequence, transmission of particles through a slab of length L is proportional to ℓ * /L known in the context of electrons in metals as Ohm's law. However, when the wave-nature of the diffusing particles is taken into account, constructive interference of waves propagating on reciprocal multiple scattering paths may lead to a breakdown of diffusion and the particles are "trapped" on closed multiple scattering loops. This means that the probability of returning to the starting point of such a closed loop is increased twofold due to the fact that the path has the same length in both counter-propagating directions. Thus diffusive transport away from this starting point is reduced. Anderson first predicted this destruction of diffusion in 1958 [2] to explain the metal-insulator transition. If the scattering power of the medium is high, i.e. the transport mean free path ℓ * is small, the density of closed loops increases which leads to a reduced transport inside the material. This can be described by a rescaling of the diffusion coefficient [4]. For strong localization the rescaled diffusion coefficient becomes zero at finite length scales, such that the spread of r 2 comes to an end at a length scale corresponding to the localization length. The transition from a diffusive to a localized state should occur when the wavelength λ becomes comparable to ℓ * , as quantified by the Ioffe-Regel criterion kℓ * ≃ 1 where k = 2π/λ is the wavenumber [3].While localization of electrons in metals was widely studied [5], an unequivocal demonstration of the pure interference effect as predicted by Anderson turned out to be difficult in this case, as electrons bound in deep minima of a random potential are virtually impossible to distinguish from those in closed loops. However, photons in disordered materials revealed an...
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