Persistence of vortexlike phase fluctuations in underdoped to heavily overdoped Bi-2201 cuprates

Abstract

The mechanism that controls the superconducting (SC) transition temperature $T_{\mathrm{c}}^{0}$ as a function of doping is one of the central questions in cuprate high-temperature superconductors. While it is generally accepted that $T_{\mathrm{c}}^{0}$ in underdoped cuprates is not determined by the scale of pairing but by the onset of global phase coherence, the role of phase fluctuations in the overdoped region has been controversial. Here, our transport measurements in perpendicular magnetic fields ($H$) on underdoped Bi-2201 reveal immeasurably small Hall response for $T>T_{\mathrm{c}}(H)$ as a signature of SC phase with vortexlike phase fluctuations. We find that the extent of such a regime in $T$ and $H$ is suppressed near optimal doping but becomes strongly enhanced in heavily overdoped Bi-2201. Our results thus show that vortexlike phase fluctuations play an important role in the field-tuned SC transition in the heavily overdoped region, in contrast to conventional mean-field Bardeen-Cooper-Schrieffer description. The unexpected nonmonotonic dependence of phase fluctuations on doping provides a new perspective on the SC transition in cuprates.

Figures (14)

• Figure 1: In-plane magnetotransport in underdoped Bi-2201 ($\bm{p \approx 0.10}$).a$\rho_\mathrm{xx}$ vs $H \parallel c$ at several $T$, as shown. Right axis: the corresponding $R_{\square/\mathrm{layer}}$ in units of quantum resistance for Cooper pairs, $R_\mathrm{Q}=h/4e^2$. b$\rho_\mathrm{yx}$ vs $H$ up to 18 T at several $T$, as shown. Inset: Difference in the onsets of nonzero $\rho_\mathrm{yx}$ (blue curve) and $\rho_\mathrm{xx}$ (black curve) at $T= 0.07$ K; red arrow indicates $T_{\mathrm{c}} (H)$, i.e. the onset of nonzero $\rho_\mathrm{xx}$. c$\rho_\mathrm{xx}(T)$ for several $H$ up to 45 T; the data for $1\leq H$(T)$\leq 45$ are shown in steps of 1 T. Blue arrows indicate the peak in $\rho_\mathrm{xx}(T)$, $T_{\mathrm{peak}}(H)$; right axis: the corresponding $R_{\square/\mathrm{layer}}$. Open black circles: $T_{R_\mathrm{H} =0}(H)$, onset of zero Hall coefficient $R_\mathrm{H} = 0$, for $0.25\leq H$[T] $\leq 15$; solid black line guides the eye. d$T$--$H$ phase diagram ($H\parallel c$); color map: $d\rho_{\mathrm{xx}}/dT$. $T_{\mathrm{c}} (H)$ (black dots): boundary of the pinned vortex lattice in which $\rho_\mathrm{xx} (T < T_{\mathrm{c}} )= 0$ and $\rho_\mathrm{yx}=0$, as expected for a superconductor. The quantum melting field of the vortex lattice where $T_{\mathrm{c}} (H)\rightarrow 0$ is $\sim 12.8$ T. Open blue diamonds: $T_{\mathrm{peak}}(H)$; solid blue diamonds: $H_{\mathrm{c}}' (T)$, the fields above which Gaussian SC fluctuations are not observed. The error bars for $H_{\mathrm{c}}' (T)$ correspond to $\pm 1$ SD (standard deviation) in the slopes of the linear fits in Supplementary Fig. 1a. The dashed line is a fit with $\mu_0 H_{\mathrm{c}}'$ [T] $= (25\pm 2)[1-(T [\mathrm{K}]/(18.9\pm 0.9)^2]$. $H^{\ast}(T)$ (neon squares): boundary between the viscous vortex liquid with non-Ohmic $dV/dI$ for $H<H^{\ast}(T)$ and Ohmic behavior at $H>H^{\ast}(T)$; error bars reflect the uncertainty in determining $H^{\ast}(T)$ within experimental resolution. Open green circles separate the low-$T$, high-$H$ regime where $R_{{\square}/\mathrm{layer}} > R_Q$ from the regime where $R_{{\square}/\mathrm{layer}} < R_Q$. Red diamonds: $T_{R_\mathrm{H} =0}(H)$, boundary between the regime with $R_\mathrm{H}>0$, found at higher $H$ and $T$, and the $R_\mathrm{H}=0$ regime; the dashed red line guides the eye.
• Figure 1: In-plane resistance $\bm{R_{\mathrm{xx}}}$ vs $\bm{H^2}$ at several $\bm{T}$ for Bi-2201. Dashed lines are linear fits representing the contributions from normal state transport. Deviations of the measured resistance from the fits are due to the onset of Gaussian fluctuations of the superconducting amplitude and phase, with the onset field indicated by $H_\mathrm{c}'$ for a underdoped ($p\approx 0.10$), b weakly overdoped ($p\approx 0.18$), and c heavily overdoped ($p\approx 0.25$) samples. In c, the curves have been offset for clarity, such that the 1.1 K curve is offset by $0.4~\Omega$ and 0.3 K curve is offset by $0.8~\Omega$.
• Figure 2: In-plane magnetotransport in weakly overdoped Bi-2201 ($\bm{p \approx 0.18}$).a$\rho_\mathrm{xx}$ vs $H \parallel c$ at several $T$, as shown. Right axis: the corresponding $R_{\square/\mathrm{layer}}$ in units of quantum resistance for Cooper pairs, $R_\mathrm{Q}=h/4e^2$. b$\rho_\mathrm{yx}$ vs $H$ up to 18 T at several $T$, as shown. Inset: Difference in the onsets of nonzero $\rho_\mathrm{yx}$ (blue curve) and $\rho_\mathrm{xx}$ (black curve) at $T= 5$ K; red arrow indicates $T_{\mathrm{c}} (H)$, i.e. the onset of nonzero $\rho_\mathrm{xx}$. c$\rho_\mathrm{xx}(T)$ for several $H$ up to 45 T, as shown; the data for $1\leq H$(T)$\leq 19$ are given in steps of 1 T, while the highest $H$ curves correspond to 45 T, 38 T, and 35 T, respectively. The right axis shows the corresponding $R_{\square/\mathrm{layer}}$. Open black circles: $T_{R_\mathrm{H} =0}(H)$, onset of zero Hall coefficient $R_\mathrm{H} = 0$, for $0.5\leq H$[T] $\leq 19$; solid black line guides the eye. d$T$--$H$ phase diagram ($H\parallel c$); color map: $d\rho_{\mathrm{xx}}/dT$. $T_{\mathrm{c}} (H)$ (black dots): boundary of the pinned vortex lattice, in which $\rho_\mathrm{xx} (T < T_{\mathrm{c}} )= 0$ and $\rho_\mathrm{yx}=0$, as expected for a superconductor. Solid blue diamonds: $H_{\mathrm{c}}' (T)$, the fields above which Gaussian SC fluctuations are not observed. The error bars for $H_{\mathrm{c}}' (T)$ correspond to $\pm 1$ SD in the slopes of the linear fits in Supplementary Fig. 1b. The dashed line is a fit with $\mu_0 H_{\mathrm{c}}'$ [T] $= (24\pm 3)[1-(T [\mathrm{K}]/(19\pm 2)^2]$. Red diamonds: $T_{R_\mathrm{H} =0}(H)$, boundary between the regime with $R_\mathrm{H}>$ 0, found at higher $H$ and $T$, and the $R_\mathrm{H}= 0$ regime; the dashed red line guides the eye.
• Figure 2: Hall resistivity $\bm{\rho_{\mathrm{yx}}}$ vs $\bm{H}$ for Bi-2201. The data are shown for a - d$p\approx 0.10$ underdoped, e - h$p\approx 0.18$ weakly overdoped, and i - l$p\approx 0.25$ heavily overdoped samples.Dark gray and cyan traces correspond to data measured using different systems up to 18 T, while light gray and magenta traces correspond to data measured using different systems up to 28 T and 41 T, respectively. The same ${\rho_{\mathrm{yx}}}$ data, averaged over 1 T bins, are shown by red symbols (for dark gray trace), blue symbols (for cyan trace), orange symbols (for light gray trace), and black symbols (for magenta trace). Error bars correspond to $\pm$1 SD (standard deviation) of the data points within each bin. At low $T$, the signals appear relatively noisy because extremely small excitation currents $I$ are used to avoid heating and to ensure that the measurements are taken in the $I\rightarrow 0$ limit (see Methods). At higher $T$, the signal-to-noise ratio increases.
• Figure 3: In-plane magnetotransport in heavily overdoped Bi-2201 ($\bm{p \approx 0.25}$).a The in-plane longitudinal resistivity $\rho_\mathrm{xx}$ vs $H\parallel c$ at several $T$, as shown. The right axis shows the corresponding $R_{\square/\mathrm{layer}}$ in units of quantum resistance for Cooper pairs, $R_\mathrm{Q}=h/4e^2$. b Hall resistivity $\rho_\mathrm{yx}$ vs $H$ up to 18 T at several $T$, as shown. Inset: Difference in the onsets of nonzero $\rho_\mathrm{yx}$ (blue curve) and $\rho_\mathrm{xx}$ (black curve) at $T = 0.510$ K; red arrow indicates $T_{\mathrm{c}}(H)$, i.e. the onset of nonzero $\rho_\mathrm{xx}$. c$\rho_\mathrm{xx}(T)$ for several $H$ up to 41 T, as shown; the data for $1\leq H$(T)$\leq 18$ are shown in steps of 1 T. The right axis shows the corresponding $R_{\square /\mathrm{layer}}$. Open black circles indicate $T_{R_\mathrm{H} =0}(H)$, the onset of zero Hall coefficient $R_\mathrm{H }= 0$, for $0.5\leq H$[T] $\leq 12$; solid black line guides the eye. d$T$--$H$ phase diagram ($H \parallel c$); color map: $d\rho_{\mathrm{xx}}/dT$. $T_{\mathrm{c}} (H)$ (black dots) mark the boundary of the pinned vortex lattice, which is a superconductor with $\rho_\mathrm{xx} = 0$ for all $T < T_{\mathrm{c}} (H)$. Open blue diamonds: $T_{\mathrm{peak}}(H)$; solid blue diamonds: $H_{\mathrm{c}}' (T)$ , the fields above which Gaussian superconducting fluctuations are not observed. The error bars for $H_{\mathrm{c}}' (T)$ correspond to $\pm~1$ SD in the slopes of the linear fits in Supplementary Fig. 1c. The dashed line is a fit with $\mu_0 H_{\mathrm{c}}'$ [T] $= (27\pm 1)[1-(T [\mathrm{K}]/(26.9\pm 0.7)^2]$. Red diamonds: $T_{R_\mathrm{H} =0}(H)$, the boundary between the region with $R_\mathrm{H}(T)>$ 0 at higher $H$ and $R_\mathrm{H}(T) = 0$ at lower $H$. The latter generally extends above $T_\mathrm{c}(H)$. The dashed red line guides the eye.