Superconducting energy gap in $\rm Ba_{1-x}K_xBiO_3$: Temperature dependence

TL;DR

This study measures the superconducting energy gap in Ba_{1-x}K_xBiO_3 using tunneling, revealing BCS-like behavior with a medium coupling strength and temperature dependence consistent with theoretical predictions.

Contribution

It provides experimental data on the energy gap and its temperature dependence in Ba_{1-x}K_xBiO_3, highlighting local variations affecting the transition temperature.

Findings

Energy gap scales with T_c

Reduced gap ratio of 4-4.3 indicating medium coupling

Temperature dependence follows BCS theory

Abstract

The superconducting energy gap of $\rm Ba_{1-x}K_xBiO_3$ has been measured by tunneling. Despite the fact that the sample was macroscopically single phase with very sharp superconducting transition $T_c$ at 32~$K$, some of the measured tunnel junctions made by point contacts between silver tip and single crystal of $\rm Ba_{1-x}K_xBiO_3$ had lower transition at 20~$K$. Local variation of the potassium concentration as well as oxygen deficiency in $\rm Ba_{1-x}K_xBiO_3$ at the place where the point contact is made can account for the change of $T_c$. The conductance curves of the tunnel junctions reveal the BCS behavior with a small broadening of the superconducting-gap structure. A value of the energy gap scales with $T_c$. The reduced gap amounts to $2\Delta/kT_c = 4\div 4.3$ indicating a medium coupling strength. Temperature dependence of the energy gap follows the BCS prediction.

Full text

Bismuthate superconductors in contrast to the cuprates with a quasi twodimensional lattice, are fully 3-dimensional with cubic symmetry and diamagnetism in the normal state. Their superconducting properties seem to be understood within the classical theory. Tunneling studies on $\rm Ba_{1-x}K_{x}BiO_{3}$ have shown a full superconducting energy gap $\Delta$ with the reduced value $2\Delta/kT_{c}$ ranging from the weak coupling limit 1 ; 2 to the medium coupling 3 . It is generally accepted that the electron-phonon interaction plays a role in the superconductivity here 1 ; 3 . There is on the other hand some similarity with the cuprates. Both perovskites are near the metal-insulator transition triggered by doping. Namely, for $\rm Ba_{1-x}K_{x}BiO_{3}$ the system becomes metallic (supeconducting) at $x\sim 0.35$. The highest transition temperature $T_{c}=32\ K$ is achieved near the metal-insulator transition and then it is decreased down to 20 $K$ for $x=0.5$, the solubility limit. Asymmetric linear background of the tunneling conductance may indicate strong electronic correlations in the normal state.

The $\rm Ba_{1-x}K_{x}BiO_{3}$ crystals used in this experiment were grown by electrochemical method 4 . They are characterized by the high and sharp superconducting transition at $T_{c}=32\ K$. They are macroscopically single phase. The point-contact technique has been used to make the tunnel junctions with a silver single crystal as a tip.

Figure 1 shows a typical tunneling conductance trace with the single gap structure, which could be fitted by the BCS density of states $N(E)=E/\sqrt{{{E}^{2}}-{{\Delta}^{2}}}$ at 4.2 $K$, taking into account a smearing factor $\Gamma$ by replacement $E$ by $E^{\prime}+i\Gamma$ as the only extra parameter (Dynes formula). Actually, the superconducting energy gap $\Delta$ equals to 6 $meV$ and very small smearing factor $\Gamma=0.35\ meV$, $T_{c}$ of the tunnel junction was 32 $K$.

We measured also the temperature dependence of the tunneling effect. In few cases we found the transition temperature of the tunnel junction different from the bulk $T_{c}$. As shown in Fig.2, the transition $T_{c}$ was achieved at about 20 $K$. Lower local $T_{c}$ can be caused by a presence of microphases of different stoichiometry, e.g. by variation in the concentration of potassium and/or the oxygen deficiency. Local deviations in stoichiometry seem to be a general problem of the bismuthates. It is worth noticing that our sample does not show multiphase character in acsusceptibility and it has a high metallic conductance above $T_{c}$ 4 . We fitted the experimental data by the Dynes formula with resulting values: $\Delta_{0}=3.5\ meV$, $\Gamma=0.5\ meV$.

In Fig.3 the temperature dependence of the superconducting energy gap obtained from the data of three different junctions is displayed in the reduced coordinates to account for different $T_{c}$, resp. $\Delta_{0}$. In all three cases the data follow the BCS prediction.

The reduced superconducting energy gap $2\Delta/kT_{c}$ amounts to $4\div 4.3$ for all junctions. Hence the gap scales with the $T_{c}$ in $\rm Ba_{1-x}K_{x}BiO_{3}$. Presence of microdomains of different phases observed by our point-contact method may affect several physical properties measured in the system.

This work was partially supported by the Commision of the European Communities Contract No.CIPA-CT93-0183.