Evidence for Universal Signatures of Zeeman-Splitting-Limited Pseudogaps in Superconducting Electron- and Hole-Doped Cuprates

We probe the “normal” state in electron-doped ($n$-type) ${\mathrm{Sm}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4-\delta }$ through interlayer tunneling transport in magnetic fields up to 45 T. The behavior of intrinsic high-field $c$-axis negative magnetoresistance (MR), which is accessed in small 30 nm-high mesa structures, is characteristic of the pseudogap state. It follows a universal correlation between the excess low-energy dissipation due to the pseudogap and its closing field $H_{\mathrm{pg}}$ and is in close correspondence with the hole-doped ($p$-type) ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$. The MR in the mesas and in the bulk crystals consistently gives a Zeeman relation between the pseudogap temperature $T^{*}$ and its closing field, pointing to a preeminent role of spin-singlet correlations in forming the pseudogap in cuprates, regardless of their $n$ or $p$ type.

Figure 1

(a) Schematic illustration of our mesa structure (not to scale). (b) Temperature dependence of ${\rho }_c$ in zero field for a mesa sample. (c) ${\rho }_c(T)$ curves in magnetic fields applied along the $c$ axis. A slight field spread of the curves at high $T$ is due to a small positive MR $\propto H^2$, see text. After subtracting this MR all high-$T$ data follow a single curve (inset). Negative MR is observed below $T^{*}\approx 38\mathrm{K}$. (d) Field dependence of ${\rho }_c$ for the SCCO mesa sample.

Figure 2

${\rho }_c$ vs $H^2$ at various temperatures in an SCCO bulk sample for (a) $H\parallel c$ and (b) $H\parallel ab$ [25]. Dashed lines are high-field fits to the $H^2$ dependence. Insets: (a) $H–T$ diagram for the mesa (closed symbols) and bulk (open symbols) samples. Lines are guides to the eye. Negative MR (shaded region) vanishes at $H_{\mathrm{pg}}(T)$. (b) ${\rho }_c(T)$ of the bulk sample without field (solid line) and in 45 T (filled symbols).

Figure 3

$\mathrm{d}{\rho }_c/\mathrm{d}T$ vs $T$ at 0 and 8 T in the mesa. The exposed downward departure of the zero-field $\mathrm{d}{\rho }_c/\mathrm{d}T$ from the high-field data highlights the ${\rho }_c(T)$ upturn due to DOS depletion below $T^{*}$. Inset: Temperature dependence of the negative MR term in the mesa and the bulk samples. All the data consistently indicate that the onset temperature $T^{*}$ is $38(\pm 2)\mathrm{K}$ (arrows) both in the mesa and the bulk—a witness to the intrinsic nature of the relevant features.

Figure 4

Maximum $\Delta {\rho }_c$ in SCCO (solid squares) and BSCCO (solid circles) as a function of obtained $H_{\mathrm{pg}}$ in units of T (upper axis) and K (lower axis). Also plotted are $\Delta {\rho }_c^{\max }$ vs $T^{*}$ estimated from our analysis of the ${\rho }_c(H,T)$ data in NCCO (open square) [28] and BSCO (open circles) [29]. Dashed line is a $H_{\mathrm{pg}}^3$ dependence [Eq. (2)]. Inset: $H_{\mathrm{pg}}$ (at low $T$) vs $T^{*}$ (at 0 T) in SCCO (square) and BSCCO (circles). Dotted line is the Zeeman scaling line with $g=2$.