Effect of pressure on magneto-transport properties in the superconducting and normal phases of the metallic double chain compound Pr${}_2$Ba${}_4$Cu${}_7$O${}_{15-\delta }$

To examine the electronic phase diagram of superconducting CuO double chains, we report the effect of external pressure on the magneto-transport properties in superconducting and non-superconducting polycrystalline samples of Pr${}_2$Ba${}_4$Cu${}_7$O${}_{15-\delta }$ at low temperatures (1.8-40 K) under various magnetic fields (up to 14 T). In the as-sintered non-superconducting sample, the magneto-resistance (MR) follows a power law of $H^{3\mathrm{/}2}$ at low temperatures, which is in no agreement with the $H^2$ dependence of MR in the PrBa${}_2$Cu${}_4$O${}_8$ system. The negative pressure dependence of the superconducting phase is qualitatively consistent with a theoretical prediction on the basis of the Tomonaga-Luttinger Liquid theory. The 48-h-reduced superconducting sample at ambient pressure exhibits no clear increase in MR for $T>T_{c,on}=26.5$ K. In contrast, with the application of pressure to the superconducting sample, the MR effects reappear and are also well fitted by $H^{3\mathrm{/}2}$. The model of slightly warped Fermi surfaces explains not only the MR effect of the non-superconducting sample, but is also related to the reasons for the pressure-induced MR phenomena of the superconducting sample.