Fresnel zone plates consisting of alternating transmissive and opaque circular rings can be used to focus X-rays. The spatial resolution that can be achieved with these devices is of the order of the width of the outermost zone and is therefore limited by the smallest structure (20-40 nm) that can be fabricated by lithography today. Here we show that a large number of pinholes distributed appropriately over the Fresnel zones make it possible to focus soft X-rays to spot sizes smaller than the diameter of the smallest pinhole. In addition, higher orders of diffraction and secondary maxima can be suppressed by several orders of magnitude. In combination with the next generation of synchrotron light sources (free-electron lasers) these 'photon sieves' offer new opportunities for high-resolution X-ray microscopy and spectroscopy in physical and life sciences.

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The electronic structure of the layered compound 1T-TiTe 2 has been studied in detail by high-resolution angle-resolved photoelectron spectroscopy ͑ARPES͒ and density-functional band calculations. The results confirm the semimetallic nature of this material as due to an overlap of Te 5p-and Ti 3d-like conduction bands. We find an overall good correspondence between experiment and theory, with all ARPES structures accounted for by the calculated band structure. Particular focus is applied to the bands near the Fermi level and to the Fermi-surface topology. Interesting behavior is observed for an essentially Ti 3d Z 2 -derived conduction band, whose measured Fermi vector and qualitative shape are excellently reproduced by the calculation. However, the experimental energy dispersion of the Ti 3d z 2 ARPES peak appears to be considerably reduced with respect to band theory. From these results we obtain a picture of the electronic structure of 1T-TiTe 2 as that of a Fermi liquid with renormalized quasiparticle dispersions and a Fermi surface in accordance with Luttinger's sumrule. We show that the experimental Ti 3d z 2 emission is quasi-two-dimensional near the Fermi surface, which, together with its being remarkably unobscured, virtually free of any interference with other spectral structures or inelastic background, makes it an ideal object for ARPES line-shape studies on a Fermiliquid system.

Angle-resolved photoelectron spectroscopy ͑ARPES͒ is commonly applied to map the shape of Fermi surfaces. Here we quantify the errors of simple criteria for extracting Fermi vectors by ARPES that are induced by strongly varying matrix elements. Sophisticated methods for determining the three-dimensional Fermi vector based on temperature and photon energy dependent photoemission are discussed with reference to data of the quasi-two-dimensional system 1T-TiTe 2 .

The local density of states (LDOS) of the adsorbate induced two-dimensional electron system (2DES) on n-InAs(110) is studied by low-temperature scan-

The importance of three-dimensional effects in the electronic structure of the quasi twodimensional layered crystal 1 r-TiSe 2 is demonstrated by means of high-resolution angle-resolved photoemission excited by synchrotron radiation. By resolving the spin-orbit splitting of the upper Se-4p valence band in TA we found strong evidence for hole states at r. The overlap (< 120 meV) between these states and the Ti-3Estates measured exactly at T and L, respectively, is much smaller than previously suggested and is discussed in relation to the structural phase transition below T c = 200 K.PACS numbers: 79.60. Eq. 71.25.Tn, Layered transition-metal dichalcogenides in the 1Tpolytype as well as their intercalates exhibit interesting physical properties 1 concerning conductivity, Hall effect, specific heat, and their temperature dependence. Because of their atomic components one finds metallic, semimetallic, or semiconducting behavior, and transitions between these types as well as structural phase transitions in special temperature regions. 1,2 Although recent experimental and theoretical studies on crystal and electronic structure reveal a good overall understanding of these materials, there remains the long-standing question of whether the stoichiometric Ti-derived compounds form semimetals or indirect semiconductors at room temperature: TiTe 2 was shown to form a semimetal with an overlap of about 0.6 eV between the top of the valence p bands at the Brillouin zone (BZ) center and the d conduction band minimum at the BZ boundary. 3 For TiS 2 the most accepted view now is that it is an extrinsic semiconductor 4, 5 with an indirect gap of a few tenths of an electronvolt. Its metallic behavior observed in transport properties can be explained by excess Ti.The most important experimental and theoretical challenge is TiSe 2 with its position between TiTe 2 and TiS 2 . Since selenium is less electronegative than sulfur it is expected that the band gap in TiSe 2 is smaller or even vanishes, tending to semimetallic behavior. This is supported by a positive Hall coefficient and thermopower, 6 the pressure dependence of the Hall coefficient, 4 and trends in the optical spectra. 7 On the other hand, band-structure calculations give different results as regards the gap and the values for the overlap, 8 " 11 and relativistic corrections, in particular the spin-orbit splitting in the vicinity of the Fermi level (Zip), are expected to play a significant role in materials containing Se. 11 The theoretical results concerning the band structure can be directly tested by high-resolution angleresolved photoemission spectroscopy (ARPES). Previous ARPES works 12 " 14 indicate values for the band overlap that vary between 0.18 and 0.5 eV, but no direct evidence for /?-like hole states at T. First, it has to be noted that in these investigations, with the photon energies used, the T and the L points in the BZ have not been investigated together which is absolutely necessary to understand the delicate overlap. This means that three-dimensional...