Parabolic refractive x-ray lenses with short focal distance can generate intensive hard x-ray microbeams with lateral extensions in the 100 nm range even at a short distance from a synchrotron radiation source. We have fabricated planar parabolic lenses made of silicon that have a focal distance in the range of a few millimeters at hard x-ray energies. In a crossed geometry, two lenses were used to generate a microbeam with a lateral size of 380 nm by 210 nm at 25 keV in a distance of 42 m from the synchrotron radiation source. Using diamond as the lens material, microbeams with a lateral size down to 20 nm and below are conceivable in the energy range from 10 to 100 keV.

Parabolic refractive x-ray lenses with short focal distance can generate intensive hard x-ray microbeams with lateral extensions in the 100 nm range even at a short distance from a synchrotron radiation source. We have fabricated planar parabolic lenses made of silicon that have a focal distance in the range of a few millimeters at hard x-ray energies. In a crossed geometry, two lenses were used to generate a microbeam with a lateral size of 380 nm by 210 nm at 25 keV in a distance of 42 m from the synchrotron radiation source. Using diamond as the lens material, microbeams with a lateral size down to 20 nm and below are conceivable in the energy range from 10 to 100 keV.

To study the phase breaking scattering events in single-wall carbon nanotubes ͑SWNTs͒, ropes of SWNTs are intentionally damaged by Ar ϩ ion milling. Due to this treatment, the average distance an electron can travel before being elastically scattered is reduced to about 10 nm. This significantly increases the probability of one-dimensional localization and allows us to obtain the phase coherence length (L ⌽ ) in ropes of SWNTs as a function of temperature. We find that Nyquist scattering ( ⌽ ϳT Ϫ2/3 ) as well as another dephasing mechanism with a ⌽ ϳT Ϫ1 dependence are involved in limiting the phase-coherent transport. We also investigate the scattering of hot electrons in the system. The results support the statement that two different scattering mechanisms dominate the phase coherence length for different rope samples.Extensive studies of the electrical transport in singleand multiwall carbon nanotubes ͑SWNTs and MWNTs͒ have deepened our insight into the electrical properties of onedimensional metallic and semiconducting systems. The main impact of the reduced dimensionality on electrical transport is the decrease in the phase space available for different kinds of scattering events. In the case of metallic nanotubes it has been shown for example that the scattering rate in the case of the scattering of electrons by acoustic phonons follows a ϳT dependence 1 instead of a ϳT 5 power law as expected for three-dimensional metallic structures in the Grüneisen regime.While it is possible to investigate momentum changing scattering processes in a standard transport experiment, not every scattering event can be detected in this way. In particular, there are phase breaking mechanisms limiting the phase coherence length L ⌽ , such as Thouless scattering, which do not cause backscattering of the current carrying electrons and therefore cannot be measured in such an experiment. A common way to obtain information about L ⌽ in two-and threedimensional samples is to evaluate the magnetoresistance in a transport experiment. This approach was successfully used for MWNTs by different groups 2-5 and the analysis of the data clearly showed the two-dimensional character of electron motion in these systems. However, in one-dimensional systems such as SWNTs, no magnetic field dependence of resistance is expected, unless the fields are extremely high such that the dispersion relation of the sample is significantly changed, 6 or the tubes are used as building blocks for more complicated geometries, e.g., a ring geometry. 7 Because of this lack of a direct process for measuring L ⌽ , little is known about phase-coherent transport in SWNTs.This paper examines the nature of the major phase breaking scattering mechanisms in single-wall nanotubes and the dependence of L ⌽ on temperature. In order to perform a phase sensitive measurement, a rope of SWNTs is intentionally damaged by Ar ϩ ion bombarding at an energy of 500 eV. Simulations 8 suggest that this treatment would reduce the elastic mean free path L 0 from several micrometers 9 to L...

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