Weak-coupling $d$-wave BCS superconductivity and unpaired electrons in overdoped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ single crystals

Weak-coupling $d$ -wave BCS superconductivity and unpaired electrons in overdoped ${La}_{2 - x} {Sr}_{x} Cu O_{4}$ single crystals

Yue Wang, Jing Yan, Lei Shan, Hai-Hu Wen, Yoichi Tanabe, Tadashi Adachi, and Yoji Koike

Phys. Rev. B 76, 064512 – Published 10 August 2007

Abstract

The low-temperature specific heat (SH) of overdoped ${La}_{2 - x} {Sr}_{x} Cu O_{4}$ single crystals $(0.178 ⩽ x ⩽ 0.290)$ has been measured. For the superconducting samples $(0.178 ⩽ x ⩽ 0.238)$ , the derived gap values (without any adjusting parameters) approach closely onto the theoretical prediction $Δ_{0} = 2.14 k_{B} T_{c}$ for the weak-coupling $d$ -wave BCS superconductivity. In addition, the residual term $γ (0)$ of SH at $H = 0$ increases with $x$ dramatically when beyond $x \sim 0.22$ , and finally evolves into the value of a complete normal metallic state at higher doping levels, indicating a growing amount of unpaired electrons. We argue that this large $γ (0)$ cannot be simply attributed to the pair breaking induced by the impurity scattering, instead the phase separation is possible.

Received 19 June 2007

DOI:https://doi.org/10.1103/PhysRevB.76.064512

Authors & Affiliations

Yue Wang, Jing Yan, Lei Shan, and Hai-Hu Wen^*

National Laboratory for Superconductivity, Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, People’s Republic of China

Yoichi Tanabe, Tadashi Adachi, and Yoji Koike

Department of Applied Physics, Graduate School of Engineering, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

^*hhwen@aphy.iphy.ac.cn

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Vol. 76, Iss. 6 — 1 August 2007

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Figure 1
(Color online) (a) Temperature dependence of dc magnetization measured in ZFC mode at $10 Oe$ . The curves are normalized to unity with the value at the lowest temperatures. (b) Doping dependence of $T_{c}$ (squares). The empirical formula (see text) is plotted as the solid line.Reuse & Permissions
Figure 2
(Color online) Temperature and magnetic field dependence of SH in $C ∕ T$ vs $T^{2}$ plot. (a)–(e) Raw data for all six samples (symbols). $μ_{0} H$ varies up to $12 T$ for $0.178 ⩽ x ⩽ 0.238$ while up to $2 T$ for $x = 0.259$ and 0.290. The solid lines represent the theoretical fit (see text). The fits are limited to $T = 7$ , 6, 5, and $4 K$ for $x = 0.178$ , 0.202, 0.218, and 0.238, respectively. For $x = 0.259$ and 0.290, the fits are ranged to $7 K$ . (f) Replot of the data at $μ_{0} H = 0 T$ for all samples (symbol: $◻ = 0.178$ , $엯 = 0.202$ , $▵ = 0.218$ , $▿ = 0.238$ , $◇ = 0.259$ , $◁ = 0.290$ ). The dotted lines are extrapolations of the data down to $T = 0 K$ with the Schottky anomaly subtracted.Reuse & Permissions
Figure 3
(Color online) Coefficient of the field-induced linear- $T$ specific heat for $0.178 ⩽ x ⩽ 0.238$ , $γ (H) = γ - γ (0)$ at $T = 0 K$ (symbols). The solid lines are the fits to $γ (H) = A \sqrt{H}$ . Inset: Doping dependence of the prefactor $A$ $(mJ {mol}^{- 1} K^{- 2} T^{- 0.5})$ .Reuse & Permissions
Figure 4
(Color online) Doping dependence of the superconducting gap $Δ_{0}$ obtained from SH measurements. (a) $Δ_{0}$ vs $x$ . The dashed line is a guide to the eye. (b) $Δ_{0} ∕ k_{B} T_{c}$ vs $x$ . The values from Ref. 16 (half filled squares) and Ref. 25 (triangle) are also included. The weak-coupling $d$ -wave BCS value $Δ_{0} = 2.14 k_{B} T_{c}$ $(Δ_{0} ∕ k_{B} T_{c} = 2.14)$ is plotted as a dotted curve (horizontal line) in (a) [(b)]. For $x ⩾ 0.19$ , the experiments are consistent with the BCS prediction.Reuse & Permissions
Figure 5
(Color online) (a) Doping dependence of the $γ (0)$ in zero field (filled squares) and the normal-state SH coefficient, $γ_{N}$ (circles). The $γ (0)$ from Ref. 19 (half filled square) and Ref. 25 (up triangles) are also shown. The $γ_{N}$ is quoted from Ref. 29. (b) Doping dependence of the $γ (0)$ in (a) normalized by $γ_{N}$ , $γ (0) ∕ γ_{N}$ . The same for Tl2201 (diamonds) is quoted from Ref. 36. The normalized residual spin Knight shift in LSCO (Ref. 35), $N_{res} ∕ N_{N}$ , is also shown for comparison (down triangles).Reuse & Permissions
Figure 6
(Color online) Fit low field $γ (H)$ to the $H \ln H$ function (see text). (a) Fit1 with $Λ$ and $H_{c 2}$ as both free fitting parameters. The yielded parameters ( $Λ$ translating to $γ_{res}^{imp}$ ) are shown in (b) and (c). (d) Fit2 with $H_{c 2}$ fixed within the values shown in the shaded region in (e). The dotted and dashed lines in (e) denote $H_{c 2} = 1 T_{c}$ and $1.5 T_{c}$ , respectively. The yielded parameter $γ_{res}^{imp}$ is shown in (f) as the shaded region. For comparison, the experimental $γ (0)$ is shown in (c) and (f) (circles).Reuse & Permissions

Physical Review B

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Weak-coupling $d$ -wave BCS superconductivity and unpaired electrons in overdoped ${La}_{2 - x} {Sr}_{x} Cu O_{4}$ single crystals

Yue Wang, Jing Yan, Lei Shan, Hai-Hu Wen, Yoichi Tanabe, Tadashi Adachi, and Yoji Koike

Phys. Rev. B 76, 064512 – Published 10 August 2007

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Physical Review B

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Weak-coupling d-wave BCS superconductivity and unpaired electrons in overdoped La2−xSrxCuO4 single crystals

Yue Wang, Jing Yan, Lei Shan, Hai-Hu Wen, Yoichi Tanabe, Tadashi Adachi, and Yoji Koike

Phys. Rev. B 76, 064512 – Published 10 August 2007

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Weak-coupling $d$ -wave BCS superconductivity and unpaired electrons in overdoped ${La}_{2 - x} {Sr}_{x} Cu O_{4}$ single crystals