Strong- to weak-coupling superconductivity in high-$T_c$ bismuthates: revisiting the phase diagram via $\mu$SR

TL;DR

This study systematically investigates the evolution of superconducting properties in hole-doped Ba$_{1-x}$K$_{x}$BiO$_3$, revealing a transition from strong to weak electron-phonon coupling with increased doping through muon-spin rotation and susceptibility measurements.

Contribution

It provides a comprehensive phase diagram and microscopic evidence of the changing electron-phonon coupling strength in bismuthates across different doping levels.

Findings

Superfluid density indicates an isotropic fully-gapped superconducting state.

The superconducting gap varies from strong to weak coupling with doping.

Lattice parameter increases linearly with potassium content.

Abstract

Several decades after the discovery of superconductivity in bismuthates, the strength of their electron-phonon coupling and its evolution with doping remain puzzling. To clarify these issues, polycrystalline hole-doped Ba$_{1-x}$K$_{x}$BiO$_3$ ($0.1 \le x \le 0.6$) samples were systematically synthesized and their bulk- and microscopic superconducting properties were investigated by means of magnetic susceptibility and muon-spin rotation/relaxation ($\mu$SR), respectively. The phase diagram of Ba$_{1-x}$K$_{x}$BiO$_3$ was reliably extended up to $x = 0.6$, which is still found to be a bulk superconductor. The lattice parameter $a$ increases linearly with K-content, implying a homogeneous chemical doping. The low-temperature superfluid density, measured via transverse-field (TF)-$\mu$SR, indicates an isotropic fully-gapped superconducting state with zero-temperature gaps $\Delta_0/k_\mathrm{B}T_c$ = 2.15, 2.10, and 1.75, and magnetic penetration depths $\lambda_0$ = 219, 184, and 279 nm for $x$ = 0.3, 0.4, and 0.6, respectively. A change in the superconducting gap, from a nearly ideal BCS value (1.76 $k_\mathrm{B}$$T_c$ in the weak coupling case) in the overdoped $x$ = 0.6 region, to much higher values in the optimally-doped case, implies a gradual decrease in electron-phonon coupling with doping.