Spatial Correlation of Superconducting and Pseudogap Dynamics in a Bi-based Cuprate

TL;DR

This study addresses the spatial relationship between superconductivity and the pseudogap in cuprates by employing spatially and temporally resolved ultrafast pump-probe reflectivity on optimally doped La-Bi2201. The authors extract local destruction thresholds for the SC and PG states and show that these thresholds correlate with the superconducting transition temperature and the pseudogap energy, respectively, with their spatial variations tracking closely on micron scales. They find that the SC response is largely uniform at low excitation yet shows micrometer-scale modulation at higher fluence, while the PG response is inherently inhomogeneous, leading to a strong local correlation between the two destruction thresholds. The results demonstrate a bulk-sensitive optical pathway to visualize hidden spatial correlations in correlated materials and provide benchmarks for understanding intertwined orders in cuprates.

Abstract

Understanding the interplay between superconductivity and the pseudogap phase is essential for elucidating the mechanism of high-temperature superconductivity in cuprates. Here we provide direct spatial evidence that these two states are locally and intrinsically correlated. Using spatially and temporally resolved measurements of photoinduced quasiparticle dynamics in optimally doped Bi$_2$Sr$_{1.7}$La$_{0.3}$CuO$_{6+δ}$ (La-Bi2201), we reveal micrometer-scale spatial contrasts in the transient reflectivity that arise from local variations in the threshold fluence required to disrupt either the superconducting or pseudogap state. The superconducting response remains spatially uniform, whereas the pseudogap exhibits intrinsic inhomogeneity, yet the spatial variations of their threshold fluences closely track each other, establishing a robust local correlation between the two. These results introduce a bulk-sensitive ultrafast optical methodology for visualizing hidden spatial correlations in correlated materials and provide new benchmarks for understanding the intertwined phases in cuprates.

Figures (4)

• Figure 1: (a) Optical microscope image of the sample surface. The red box marks the two-dimensional (2D) scan region, while the white dashed line indicates the one-dimensional (1D) scan path. (b) Representative transient reflectivity changes $\Delta R/R$, recorded at selected temperatures and at two distinct positions, P$_{\rm A}$ (dashed line) and P$_{\rm B}$ (solid line), as indicated by the cross symbols in (a), under a pump fluence of ${\mathcal{F}}=15~\mu$J/cm$^{2}$. For clarity, $\Delta R/R$ at different temperatures are vertically offset. (c)-(e) 2D images of $\Delta R/R$, over a $90 \times 90\ \mu\mathrm{m}^2$ area corresponding to the region indicated by the red box in (a). Panels (c) and (d) present $\Delta R/R$ distributions acquired at $T=10$ K and a probe delay of $t_{\rm Ppr}=3.0$ ps, with pump fluence of ${\mathcal{F}}=0.6~\mu{\rm J/cm}^2$, and 6.0$~\mu{\rm J/cm}^2$, respectively. (e) 2D map of the PG response measured at $T=50$ K, $t_{\rm Ppr}=0.4$ ps, and ${\mathcal{F}}=6.2~\mu{\rm J/cm}^2$. Since $\Delta R_{\mathrm{PG}}/R$ is negative, $-\Delta R/R$ is plotted.
• Figure 2: 1D spatial distributions of $A_{\rm SC}$ and $A_{\rm PG}$ at different pump fluence, extracted from $\Delta R/R$ transients measured at 43 positions along the dashed line in Fig. \ref{['fig_2D']}(a) with a spacing of $\Delta x = 3.75\mu$m. $A_{\rm SC}$ is defined as the time-averaged reflectivity change $\langle \Delta R/R \rangle_{2-10~{\rm ps}}$ at $T = 10$ K, whereas $A_{\rm PG}$ is obtained from $\langle -\Delta R/R \rangle_{0.1-0.5~{\rm ps}}$ at $T = 50$ K.
• Figure 3: Fluence dependence of the transient reflectivity amplitudes for (a) SC ($A_{\rm SC}$) and (b) PG ($A_{\rm PG}$) responses. The amplitudes $A_{\rm SC}$ and $A_{\rm PG}$, extracted from the $\Delta R/R$ signals at the positions P$_{\rm A}$ and P$_{\rm B}$ in Fig. \ref{['fig_2D']}(a), are shown. Dashed (P$_{\rm A}$) and solid (P$_{\rm B}$) lines in each panel represent fits based on the finite-penetration-depth excitation model kusar2008naseska2018. Temperature dependence of the transient reflectivity amplitudes for (c) SC ($A_{\rm SC}$) and (d) PG ($A_{\rm PG}$) responses. Dashed (P$_{\rm A}$) and solid (P$_{\rm B}$) lines in (c) and (d) correspond to fits using (c) the Mattis-Bardeen formula with a BCS-like gap function mertelj2009distinct and (d) a temperature-independent gap model kabanov1999, respectively.
• Figure 4: Spatial distributions of the phase destruction thresholds for (a) the superconducting phase ${\mathcal{F}}_{\rm th}^{\rm SC}$ at $T=10$ K and (b) the PG phase ${\mathcal{F}}_{\rm th}^{\rm PG}$ at $T=50$ K. The threshold values are obtained from the fluence dependence of $\Delta R/R$ measured along the dashed line in Fig. \ref{['fig_2D']}(a). (c) Corresponding spatial distribution of the reflectivity with an enlarged view shown in the inset. (d) Correlation between ${\mathcal{F}}_{\rm th}^{\rm SC}$ and ${\mathcal{F}}_{\rm th}^{\rm PG}$ shown in (a) and (b).