Pseudogap in electron-doped superconducting ${\mathrm{Sm}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ by interlayer magnetotransport

$c$-axis interlayer magnetoresistivity is measured for an electron-doped ($n$-type) superconducting cuprate ${\mathrm{Sm}}_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ with $x=0.14–0.16$ using $30\mathrm{nm}$ thick small mesa structures. A systematic doping dependence is observed in the negative interlayer magnetoresistance (MR) component, from which the pseudogap onset temperature $T^{*}$ is determined as the negative MR appearance temperature. For a doping level close to the phase boundary between superconductivity and antiferromagnetism, a $T^{*}$ of $48\mathrm{K}$ is observed. It is also found that $T^{*}$ decreases systematically with increasing $x$ but is still higher than $T_c$. For all the doping levels, the result represents features characteristic of hole-doped ($p$-type) cuprates in the overdoped region, suggesting that the phase diagrams for the pseudogap are primarily similar for both the $n$- and $p$-type cuprates.

Figure 1

$T$ dependence of ${\rho }_c$ for samples A–D with various $x$. Excitation current is $2\mu \mathrm{A}$. Top-left inset: $x$ dependence of $T_c$ for the same samples. The vertical error bars for $T_c$ indicate the transition width from the onset to the zero resistance. The superconducting onset temperature is defined as the temperature at which ${\rho }_c$ reaches the peak. The horizontal error bars represent the standard deviation of the composition analysis. Bottom-right inset: Schematic illustration of the mesa structure in the present study (not to scale).

Figure 2

(a)–(d) ${\rho }_c\text{−}T$ curves for $H\Vert c$ for the SCCO mesas (samples A–D). (e)–(h) $H$ dependences of ${\rho }_c$ at various temperatures for $H\Vert c$ for the same samples.

Figure 3

Plots for $T_{\text{peak}}\left(H\right)$ (filled symbols) and $H_{\text{peak}}\left(T\right)$ (open symbols) for samples A–D in the $H\text{−}T$ plane.

Figure 4

(a) ${\rho }_{cN}\text{−}T$ curves for samples A–D. The low temperature part of each curve is assumed to have the form ${\rho }_0+A{T}^{\beta }$. Values for ${\rho }_0$, $A$, and $\beta$ were determined for the calculated curve to fit the experimental ${\rho }_c\text{−}T$ curve at ${\mu }_{0}H=9\mathrm{T}$. (b) $T$ dependence of ${\rho }_{cN}$ and ${\rho }_{c\mathrm{PG}}$ for sample $A$ in the absence of a field. (c)–(f) $H$ dependence of the estimated ${\rho }_{c\mathrm{PG}}$ values at various temperatures for samples A–D.

Figure 5

(a) Schematic illustration of ${\rho }_c-\alpha H^2$, ${\rho }_{c\mathrm{PG}}$, and $\Delta {\rho }_{c\mathrm{PG}}$ as a function of $T$, showing diminishing ${\rho }_{c\mathrm{PG}}$ and a shift of $T^{*}$ with increasing $H$. (b),(c) $T$ dependence of $\Delta {\rho }_{c\mathrm{PG}}={\rho }_c(T,H)-{\rho }_c(T,0)-\alpha \left(50\mathrm{K}\right)H^2$ for sample A and C. (d) $\Delta {\rho }_{c\mathrm{PG}}-T$ at $9\mathrm{T}$ for samples A–D. Inset to (b): $\Delta {\rho }_c\left(H\right)-H^2$ for sample A at 50, 70, and $100\mathrm{K}$. Inset to (d): Plots for $\alpha ∕{\mu }_0^2$ vs $x$ at $50\mathrm{K}$.

Figure 6

(a) $T$ dependence of $\Delta {\rho }_{c\mathrm{PG}}(T,H)-\Delta {\rho }_{c\mathrm{PG}}(T,6\mathrm{T})$ at ${\mu }_{0}H=8$ and $9\mathrm{T}$ for sample $A$. (b) $H$ dependence of ${\rho }_c$ at $40\mathrm{K}$ for the same sample. The dashed line represents ${\rho }_{cN}\left(40\mathrm{K}\right)+\alpha \left(50\mathrm{K}\right)H^2={\rho }_c(40\mathrm{K},9\mathrm{T})-\alpha \left(50\mathrm{K}\right){(9∕{\mu }_0)}^2+\alpha H^2$. Both curves coincide for ${\mu }_{0}H>6\mathrm{T}$, indicating consistency with $T^{*}\left(6\mathrm{T}\right)=40\mathrm{K}$.

Figure 7

(a) $x$ dependence of $T^{*}\left(0\right)$, $T^{*}\left(6\mathrm{T}\right)$, $T_c$ at $H=0$. Filled diamonds show the values for $T^{*}$ obtained by an extreme definition of $\Delta {\rho }_{c\mathrm{PG}}=-0.02\Omega \mathrm{cm}$ at $9\mathrm{T}$. These plots indicate the lower bound for the ambiguity associated with the arbitrariness of the definition of $T^{*}$, demonstrating that even in such a case it holds that $T^{*}>T_c$. The $T^{*}$ values for PCCO obtained by Alff et al. (Ref. 11) at $14\mathrm{T}$ are also plotted. The bars at the top indicates approximate values for $n$, the number of electrons per Cu site when $\delta =0.03$. (b) The phase diagram for the $n$-type $L_{2-x}{\mathrm{Ce}}_x\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ system on the semilogarithmic scale in the absence of a magnetic field. The values for $T^{*}$ from the optical conductivity data (Ref. 6) and the values for Néel temperature $T_N$ by the muon spin rotation and relaxation measurements (Ref. 26) for NCCO are used as the data for the antiferromagnetic region. The dashed lines are guides to the eyes.