1. Introduction
The superconductor-insulator transition (SIT) has been intensively studied in homogeneously disordered twodimensional (2D) thin films since the late 1980s [1-3]. In some theory it is expected that the SIT may be the quantum phase transition and the threshold of SIT is related to the universal constant, i.e. the quantum resistance
. A lot of attention has been directed towards a clear separation between superconducting and insulating in a sequence of films of different sheet resistances. Experimental works have been investigated about the critical sheet resistances which were compared with
. So that, the SIT is done experiments for several materials (high Tc superconductors, organic superconductor etc.) and several shape of samples (thick films, polycrystals, singlecrystals etc.).
High-Tc cuprate superconductors (HTSC) are quasi-2D system, and the SIT of them has been reported on many kinds of samples [3]. These reports indicate the existence of a threshold sheet resistance. However not all the threshold sheet resistances were close to Rq. Furthermore several methods to calculate a sheet resistance were used: the sheet resistance per a CuO2 bilayer [4], per individual CuO2 plane [5]. Then, a mechanism of the SIT for HTSCs may not be the same one for 2D thin films.
We have so far investigated the SIT for HTSC thin films and single crystals [6-8]. One of the reasons why we use single crystals is that the SIT was observed on even thick samples. We are interested in the origin of the SIT for thick samples. Then the thickness driven SIT is inappropriate for our study. Extreme huge magnetic field is necessary to study the magnetic field tuned SIT for nondoped HTSCs. The doping controlled SIT may be related to competition between Mott transition (electronelectron interaction) and Anderson transition (disorder). Bi2Sr2CaCu2O8+y (Bi2212) is one of the highest anisotropy systems among HTSCs. Therefore the doping control SIT for Bi2212 single crystals is selected as our research target.
Inhomogeneity is one of the most important problems for studying the doping controlled SIT. We have reported the relation between microscopic inhomogeneous structure and transport properties for SIT [8]. Since superconducting properties relate to dimensionality, it is easily expected that the dimensionality of samples relate to properties of SIT. Therefore we have studied the transport properties of Y and Pb doping Bi2212 crystals. Y substitution is due to the doping level and Pb substitution is mainly due to dimensionality. However it found that Pb substitution drives Y inhomogeneity in our study. In this report the effect of Pb substitution on the inhomogeneity and transport property is studied in order to analyze atomic compositions and to measures transport properties.
2. Experimental
The Y and Pb co-doped Bi2212 crystals used for the present work were grown using a self-flux method in Al2O3 crucibles. Starting materials for the crystal growth were powder Bi2O3, PbO, SrCO3, CaCO3, Y2O3 and CuO, and were weighted out to yield an atomic ratio Bi:Pb:Sr:Ca:Y:
. Here x and y are nominal compositions of Y and Pb, respectively. Excess Bi2O3 and PbO acts as a flux for the crystal growth. Those materials was mixed and fired at 800˚C for 48 h. This process was repeated two times. The product were melted at 1100˚C for 5 h, then fast cooled down to 940˚C, then slowly cooled down to about 790˚C - 810˚C at a rate 0.6˚C - 1˚C/h, followed by a furnace cooling down to room temperature. The crystals were removed after breaking the crucible. The crystals were cleaved mechanically. Typical sample size is about 3 × 6 × 0.01 mm3. Hereafter PbY-Bi2212 stands for Y and Pb co-doped Bi2212 crystals, while Y-Bi2212 represents Y only doping Bi2212 crystals.
The c-axis lattice parameter was measured by X-ray diffraction (XRD). The Kα radiation from a copper anode was selected. The temperature dependence of resistivity was measured by dc four-probe method. The real atomic compositions of the resulting crystals were determined by wavelength-dispersive X-ray spectroscopy (WDS).
3. Results and Discussion
Figure 1 shows the real atomic compositions of Y (measured Y-content) determined by WDS as a function of nominal composition of Y, x. Measured Y-content is much larger than nominal content like other groups reports [9] and is distribute even in the same batch. While we have reported the inhomogeneity of the Y-content for Y-Bi2212 crystals [8], Y-content is much wide distribute for PbY-Bi2212 crystal rather than for Y-Bi2212 ones.
All peaks on crystal XRD patterns can be indexed using (00l). Figure 2 shows the relation between c-axis lattice constant and measured Y-content gotten by WDS for PbY-Bi2212 crystals. It is well known that c-axis lattice constant is linearly dependent to Y-content for YBi2212 crystals [9]. From Figure 2 it is found that the similar relation exists not only for Y-Bi2212 crystals but also for PbY-Bi2212 ones.
Samples with single phase were selected in order to plot Figure 2 because we want to find the relation between c-axis lattice constant and Y-content. However, the crystal Pb5Y10a07 is a three-phase sample. Here the sample name Pb5Y10a07 represents the 7th sample cleaved from the 1st batch (represented by “a”) of the following nominal content: Y 10% (x = 0.1) and Pb 5% (y = 0.05). The same hereinafter for sample names. Many cleaved samples were observed multi-peaks for (00l) on XRD spectra. Therefore it is expected that there are multi-phase with different Y-content for these crystals. A typical example for the two-phase sample is shown in Figure 3 which shows a XRD spectra on Pb5Y10a13. There are multi-peaks which correspond to two phases. Existence of multi-phases was confirmed by transport properties (R-T curves) and chemical compositions measured by WDS. Y-content component and existence of multi-phases were estimated by XRD, owing to the convenience of measurement of many cleaved samples.
Figure 4 shows c-axis lattice constant as a function of measured Y-content for PbY-Bi2212 crystals. For WDS a radius of the measured area which corresponds to electron distribution area is several μm. While measured X-ray