# Multilayered cuprate superconductor Ba$_2$Ca$_5$Cu$_6$O$_{12}$(O$_{1-x}$,F$_x$)$_2$ studied by temperature-dependent scanning tunneling microscopy and spectroscopy

## TL;DR

This study uses STM/STS to investigate a multilayered cuprate superconductor, revealing coexistence of small superconducting gaps and larger pseudogaps with distinct spatial and temperature behaviors, highlighting the inhomogeneity and disorder effects.

## Contribution

First detailed STM/STS analysis of a multilayered cuprate superconductor showing coexistence and spatial variation of superconducting and pseudogap states.

## Key findings

- Small gap follows BCS temperature dependence with a reduced ratio
- Large pseudogap persists above T_c and increases with temperature
- Spatially homogeneous small gap coexists with inhomogeneous pseudogap

## Abstract

Scanning tunneling microscopy/spectroscopy (STM/STS) measurements were carried out on a multi-layered cuprate superconductor Ba$_2$Ca$_5$Cu$_6$O$_{12}$(O$_{1-x}$,F$_x$)$_2$. STM topography revealed random spot structures with the characteristic length $\le 0.5$ nm. The conductance spectra dI/dV(V) show the coexistence of smaller gaps $\Delta_S$ and large gaps (pseudogaps) $\Delta_L$. The pseudogap-related features in the superconducting state were traced with the spatial resolution of $\sim$ 0.07 nm. Here, $I$ and $V$ are the tunnel current and bias voltage, respectively. The temperature, $T$, dependence of $\Delta_S$ follows the reduced Bardeen-Cooper-Schrieffer (BCS) dependence. The hallmark ratio 2$\Delta_{S}(T=0)/k_B T_c$ equals to 4.9, which is smaller than those of other cuprate superconductors. Here, $T_c$ is the superconducting critical temperature and $k_B$ is the Boltzmann constant. The larger gap $\Delta_L$ survives in the normal state and even increases with $T$ above $T_c$. The $T$ dependences of the spatial distributions for both relevant gaps ($\Delta$ map), as well as for each gap separately ($\Delta_S$ and $\Delta_L$) were obtained. From the histogram of $\Delta$ map, the averaged gap values were found to be $\bar \Delta_S = \sim 24$ meV and $\bar \Delta_L = \sim 79$ meV. The smaller gap $\Delta_S$ shows a spatially homogeneous distribution while the larger gap $\Delta_L$ is quite inhomogeneous, indicating that rather homogeneous superconductivity coexists with the patchy distributed pseudogap. The spatial variation length $\xi_{\Delta_L}$ of $\Delta_L$ correlates with the scale of the topography spot structures, being approximately 0.4 nm. This value is considerably smaller than the coherence length of this class of superconductors, suggesting that $\Delta_L$ is strongly affected by the disorder of the apical O/F.