In-Plane Magnetoresistance Obeys Kohler’s Rule in the Pseudogap Phase of Cuprate Superconductors

We report in-plane resistivity ($\rho$) and transverse magnetoresistance (MR) measurements for underdoped ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg1201). Contrary to the long-standing view that Kohler’s rule is strongly violated in underdoped cuprates, we find that it is in fact satisfied in the pseudogap phase of Hg1201. The transverse MR shows a quadratic field dependence, $\delta \rho /{\rho }_0=a{H}^2$, with $a(T)\propto T^{-4}$. In combination with the observed $\rho \propto T^2$ dependence, this is consistent with a single Fermi-liquid quasiparticle scattering rate. We show that this behavior is typically masked in cuprates with lower structural symmetry or strong disorder effects.

Figure 1

(a) Temperature dependence of the in-plane resistivity for two Hg1201 samples. Dotted lines are linear fits to the high-temperature behavior. Inset: Magnetic susceptibility shows $T_{\mathit{c}}=70\pm 1$ and $80.5\pm 0.5\mathrm{K}$ for the two samples, HgUD70b (black) and HgUD81 (red). The $T_{\mathit{c}}$ values are defined as the midpoint of the transition, and the uncertainties correspond to 90% of the transition width. (b) Resistivity plotted versus $T^2$. Dotted lines are fits to $\rho =A_2{T}^2$. There is some uncertainty in the conversion to units of $\rho$ due to difficulties in measuring the exact cleaved sample dimensions [9]. For consistency, we have assumed the same magnitude of $\rho$ for the two $T_c=70\mathrm{K}$ samples. Inset: Schematic temperature-hole doping phase diagram. The superconducting (SC), strange metal (SM), and pseudogap (PG) phases as well as the characteristic temperatures $T^{*}$ and $T^{**}$ are indicated. The circles represent the two doping levels of the present study.

Figure 2

(a) Transverse MR with $H\parallel c$ and $j\parallel ab$ and (b) the corresponding Kohler plot for sample HgUD70a ($T_{\mathit{c}}=70\mathrm{K}$) measured in a maximum pulsed field of 30 T. ${\rho }_0$ is defined as the zero-field resistivity extrapolated from fitting the data above 20 T to the form $\rho ={\rho }_0+a^{\prime }{H}^2$. (c) Kohler plot of the orbital MR [$\rho (H\parallel c)-\rho (H\parallel j)$ with $j\parallel ab$] for HgUD70b measured in a Quantum Design, Inc. PPMS system up to 9 T. (d) Kohler plot of the orbital MR for HgUD81 measured in fields up to 9 T. Insets to (b)–(d) are low-field views of the respective panels.

Figure 3

(a) Log-log plot of the temperature dependence of the orbital MR coefficient $a_{\mathrm{orb}}\equiv (a_{\perp }-a_{\parallel })$ for HgUD70b and HgUD81 and of the transverse MR coefficient $a_{\perp }$ for HgUD70a. The dashed lines are fits to $a=(bT{)}^{-4}$. The arrows mark the characteristic temperatures $T^{*}$ and $T^{**}$. (b) and (c) show, respectively, representative data for $a_{\mathrm{orb}}$ and $a$-axis in-plane resistivity ${\rho }_a$ from Ref. [36] for YBCO6.5 (${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+y}$ with $y=0.5$, $T_{\mathit{c}}\approx 35\mathrm{K}$, $p\approx 0.073$) and YBCO6.6 ($y=0.6$, $T_c\approx 50\mathrm{K}$, $p\approx 0.085$). We estimate the doping levels by comparing the quoted $T_{\mathit{c}}$ values to Ref. [37]. The resistivity in (b) is plotted versus $T^2$ to highlight the ${\rho }_a\propto T^2$ behavior indicated by dashed lines below the characteristic temperature $T^{**}$, consistent with the inset of Fig. 1. (c) Log-log plot and the dashed lines are fits to the form $(c+b{T}^2{)}^{-2}$, with $c=0$ for YBCO6.6.

Figure 4

(a) Kohler plot for LSCO ($x=0.09$) from Ref. [23] (b) Modified Kohler plot, with ${\rho }_0$ replaced by ${\rho }_0-{\rho }_{\mathrm{res}}$. Inset: Temperature dependence of the planar resistivity $\rho$ in zero field. The dotted red line is a fit to $\rho ={\rho }_{\mathrm{res}}+A_2{T}^2$. ${\rho }_{\mathrm{res}}$ is determined from extrapolating to $T=0$.