$T$ linearity of in-plane resistivity in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ thin films

We performed a temperature and doping-dependent study of in-plane dc resistivity (IDCR) on molecular beam epitaxy grown ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ thin films. By analyzing the temperature dependence of normal state IDCR as a function of doping level, we show that long-known $T$-linear dependence of normal state IDCR occurs not at the optimal doping $(p=0.16∕\mathrm{Cu})$ but at an overdoping of $p=0.19∕\mathrm{Cu}$, which coincides with the recently proposed putative quantum critical point. This observation suggests that $p=0.19$ may be a sample-independent critical doping level at least for bilayer cuprate systems.

Figure 1

Temperature dependence of the normalized IDCR for three representative doping levels, $p=0.100$ (underdoping), 0.160 (optimal doping), and 0.233 (overdoping). These curves show that the upturn seen in overdoped samples transforms into downturn in the underdoped samples.

Figure 2

Normalized IDCR is replotted after linear high temperature part is subtracted. For $T>150\mathrm{K}$, transformation of the curvature from upturn to downturn is clearly seen. It shows that the widest (down to $150\mathrm{K}$) linear temperature dependence is observed at $p=0.189$, and not at the optimal doping $(p=0.160)$.

Figure 3

(a) Curvature of normal state IDCR and (b) critical temperature as a function of doping. The parabolic curve on top of the critical temperatures is the empirical formula $T_c=88.5[1-{(p-0.16)}^2]$, where 0.16 is the optimal doping. For the definition of the curvature, see the text. The curvature becomes zero at $p\approx 0.19$. Temperature dependence of normal state IDCR is linear at this point.