2D-ACAR

Scintillators like NaI(Tl) can be made position-sensitive for applications like 2D-ACAR (section 7) and medical imaging [19]. Light from a large-diameter crystal is detected by a close-packed array of PM tubes. 

These have been used for detecting gamma rays with high positional resolution in 2D-ACAR experiments (see 7.2) [20], although—principally for reasons of availability, lower complexity and more straightforward maintenance—scintillation detectors are more common. Very briefly, a spark chamber is modified to detect gamma radiation with positional... 

Figure 3.11 Schematic diagram of a 2D-ACAR system [36]. he camera-camera...

The limited application of positron beams is explained by the fact that Doppler-broadening spectroscopy is the only detection method that works with beams without any difficulty. Although angular correlation measurements are possible with positron beams, it requires a very high efficiency beamline. Only very few beams fulfill the requirements of ACAR measurements, but their results are very impressive. The combination of low-energy positron beams and 2D-ACAR measurements is the only possibility to gain direct information on the momentum distribution of electrons at the surface of metals and semiconductors (Chen et al. 1987). 

Positrons can be used as particle probes, suitable to detect low concentrations of defects in materials. Positron physicists generally are in need of intense positron beams for applying positron annihilation techniques such as two dimensional (2D) Angular Correlation of Annihilation Radiation (ACAR) for investigating surfaces and interfaces of materials. The 2D-ACAR technique allows high resolution measurements of the electron momentum distribution for depth, localized defects, thin layer systems, and interfaces. In addition, a submicrometer size positron beam can be created for defect depth profiling on a lateral scale smaller than a micrometer. Vacancy type defects can be mapped in a three dimensional fashion. 

Due to the nature of the electron wave fimctions involved in this case, p (p) is not periodic, but its shape carries information on the electronic structure of the defect. This can be measured by 2D-ACAR and lineshape spectroscopies. Another important quantity to consider in this case is the total annihilation rate A ... 

As the positron is thermalized, px and py are, to a good approximation, momentum components of the annihilated electron. The 2D-ACAR measurement yields N(px,Py), the projection of the two-photon momentum density p (p) ... 

The typical value for the resolution of a 2D-ACAR measurement is 0.03-0.05 a.u. of momentum on both px and Py. Compared to 0.35 a.u., the T-X length of the Brillouin zone of YBa2Cu307, one notices that 2D-ACAR spectroscopy has an excellent resolution. Tliis high resolution and the 2D character of N px,Py) are the main advantages of this technique. The main limitation of the 2D-ACAR is the long time (several days) required to complete one N(px,Py)- This is due to the small ( 10 ) solid angle covered... 

Anisotropies in the 2D-ACAR are often considered to enhance the interesting structures. If N(r,6) denotes the 2D-ACAR in polar coordinates, the anisotropy A(r,9) is given by... 

D-ACAR spectroscopy, eq. (14) Lineshape spectroscopy has two advantages (1) it is rapid a profile is obtained in less than one hour (2) it is technically simple, making use either of one (Hautojarvi and Vehanen 1979) or two (Ashoka-Kumar et al. 1996) high-purity Ge detectors. The rather low resolution of lineshape spectroscopy (0.4-0.6 a.u.)... 

Some alternative approaches have been taken to study the positron annihilation characteristics without explicit band-structure calculations. As far as YBa2Cu307 is concerned, the LCAO-MO approach developed by Chiba (1976) for oxides has been applied by Chiba (1992), Turchi et al. (1988, 1990) and Saul and Weissmann (1990). Although the Fermi surface is not a concept in the LCAO-MO description, this method is quite appropriate for the direct physical insights it provides for the analysis of the anisotropies A(r,d) of the 2D-ACAR distribution, eq. (15). 

Fig. 5. The position of the ridge in momentum space, as seen in a 2D-ACAR projection along the r Z direction. (From Manuel 1995.)...

The turning point in the study of the Fermi surface of YBa2Cu30y was the availability of high-quality untwirmed single crystals. It provided the possibility to obtain 2D-ACAR distributions of lower S)mimetry (c2v instead of C4v) and hence to differentiate... 

Fig. 6. (a) Isometric and (b) contom plots of the anisotropy of the T-Z-projected 2D-ACAR obtained with an untwirmed YBa CujO, sample. (From Haghighi et al. 1991.)... 

How is the Fermi surface reflected in the 2D-ACAR distribution Consider to... 

Fig. 7. Feami surface of YBajCujO,. Calculations are from Yu et al. (1987). The thick lines are the 2D-ACAR results (From Shukla et al. 1995a.)...

Besides YBa2Cu307, 2D-ACAR has been measured in compounds of the same structure but with different rare earths R=Dy, Ho and Pr (Hoffmann et al. 1993a, 1995). It has been concluded that the electronic structure of these compounds is similar to that of YBa2Cu307, as suggested by band-structure calculations. The ridge, i.e. the Fermi surface sheet originating from the Cu-O chains, is almost unchanged, as probably are the other sheets of the Fermi surface. 

One striking fact is that the ridge, predicted for the metallic PrBa2Cu307 (Singh 1994), is observed by 2D-ACAR, despite the insulating behavior of the crystal. The existence of the Fermi surface in this case is supported by the model of Fehrenbacher and Rice (1993). 

We can ascribe the macroscopic insulating behavior of this compound to its extreme sensitivity to disorder on the chains, which themselves remain metallic at the microscopic level, until their ID character is strongly damaged by defects and impurities. The recent observation of metallicity in PrBa2Cu307 (Blackstead et al. 1995, Zhou Zliigang et al. 1997) is not in opposition with the conclusions drawn from the positron 2D-ACAR study. 

D-ACAR measurements (Mosley et al. 1994) have led to the identification of a Fermi surface in Bai j Kj Bi03. It is a cubic structure, centered around F, with rounded corners. Its location is in excellent agreement with that predicted by band-structure calculations. The observed large, parallel sheets of Fermi surface suggest the presence of effects due to Fermi surface nesting which may drive the superconducting state. 

Manuel, A.A., 1995, 2D-ACAR studies and positron beam developements in Switzerland, in Positron Spectroscopy of Solids, eds A. Dupasquier and A.P. Mills Jr (lOS Press, Amsterdam) pp. 155-178. Manuel, A.A., B. Barbiellini, M. Gauthier, L. Hoffmann, T. Jarlborg, S. Massidda, M. Peter, W. Sadowski, A. Shukla and E.J. Walker, 1993,... 

Tanigawa, S., 1989, Recent 2D-ACAR results in highly scattered electron systems from Tsukuba, in Proc. Conf. on Positron Annihilation, Gent, Belgium, 1988, eds L. Dorikens, M. Dorikens and D. Segers (World Scientific, Singapore) pp. 119-121. 

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