*3.1.2 Hall and pressure effects of Pr*2*Ba*4*Cu*7*O*<sup>15</sup>�*<sup>δ</sup>*

Furthermore, in **Figure 7**, we show the temperature dependences of the Hall coefficients *RH* for the as-sintered non-superconducting and 48-h-reduced superconducting samples of Pr2Ba4Cu7O15�*<sup>δ</sup>*. For comparison, the *RH* values of the assintered sample are taken from our previous work [33], which are similar, in magnitude and temperature dependence, to *RH* of Pr124 with a metallic CuO double-chain block. (**Figure 1a**) For the 48-h-reduced sample, the *RH* data exhibit negative values in the limited temperature range between 30 and 100 K, accompanied by electron doping due to the reduced heat treatment in a vacuum. Moreover, we estimate *RH* ¼ �1*:*<sup>1</sup> � <sup>10</sup>�<sup>3</sup> cm3 /C at 30 K, which is in good agreement with the published data [33].

In **Figure 7b**, we show the temperature dependences of electrical resistivities of the 48-h-reduced superconducting sample under hydrostatic pressures up to 2.0 GPa. The application of external pressure on the 48-h-reduced sample suppressed the superconductivity with increasing the applied pressure. In the case

**Figure 7.**

*(a) Temperature dependences of Hall coefficients for the as-sintered non-superconducting and 48-h-reduced superconducting Pr247 compounds. For comparison, the as-sintered data are cited from our previous paper [34]. (b) Temperature dependences of electrical resistivities of the 48-h-reduced superconducting Pr247 under various pressures up to 2.0 GPa. (c) Magneto-resistance effect (up to 14 T) of the 48-h-reduced superconducting Pr247 for temperatures close to 30 K under a maximum pressure of 2.0GPa.*

of applied pressures above 0.8 GPa, the zero-resistance state vanished and the hightemperature metallic properties were transferred to the semi-conducting behaviors, accompanied by a rapid increase in *ρ*. The onset temperature of superconducting transition *T*c,on declined gradually from 26.5 K at ambient pressure through 24.1 K at 0.8 GPa down to 18.0 K at 1.6 GPa. However, the onset temperature was enhanced up to 30 K under a maximum pressure of 2.0 GPa.

The electronic phase diagram between normal and superconducting phases of a CuO double chain model has been clarified using the Tomonaga-Luttinger Liquid theory [32]. In the case of a shrinkage of the lattice spacing along *c*-axis between the two single chains of a CuO double-chain block, we expect the enhancement of both carrier hopping energies, *tpp* and *tdd*. Here, we define the hoping term between 2*p<sup>σ</sup>* orbitals at the nearest neighbor oxygen sites and that between 3*dx*<sup>2</sup>*<sup>y</sup>*<sup>2</sup> orbitals at the nearest neighbor copper sites, as *tpp* and *tdd*, respectively (see **Figure 5b**). If we apply the external pressure on Pr247 including the CuO double chain block, it is theoretically predicted that the pressure induced enhancement of the hopping terms will result in a phase transition from the superconducting to normal phase. This theoretical prediction is qualitatively in agreement with the negative pressure effect on the superconducting phase observed in Pr247 [34].

We examined the magneto-resistance effect (up to 14 T) of the 48-h-reduced superconducting Pr247 for temperatures close to 30 K under a maximum pressure of 2.0 GPa, to establish a phase boundary between the superconducting and normal states. In **Figure 7c**, the MR data around 30 K tend to increase according to the upward covey behaviors at low fields. On the other hand, the MR around 40 K shows weak increases in the downward convey forms which is related to the model of slightly warped Fermi surfaces. (in details, see [27]) This finding indicates that the applied magnetic field destroyed the superconducting isolated regions and enlarged further the normal-state majority phase, resulting in the observed MR phenomena near 30 K. The re-entrant superconducting behavior observed at 2.0 GPa is an open question to be resolved in future through the structure analysis under applied pressures [35].

### **3.2 Double perovskite photocatalytic semiconductor**
