Two energy gaps in the tunneling-conductance spectra of the superconducting clathrate ${\text{Ba}}_8{\text{Si}}_{46}$

We have studied the quasiparticle excitation spectrum of the superconductor ${\text{Ba}}_8{\text{Si}}_{46}$ by local tunneling spectroscopy. Using high-energy resolution achieved in superconductor-insulator-superconductor junctions we observed tunneling conductance spectra of a nonconventional shape revealing two distinct energy gaps, ${\Delta }_L=1.3\pm 0.1\text{meV}$ and ${\Delta }_S=0.9\pm 0.2\text{meV}$. The analysis of tunneling data identified ${\Delta }_L$ as the leading superconducting gap in the bulk material. A smaller and more dispersive gap ${\Delta }_S$ is interpreted as induced either in reciprocal space, via the quasiparticle interband scattering from the leading superconducting band, or in real space, by the proximity effect to a normal layer at the surface.

Figure 1

(Color online) Two typical SIN tunneling conductance spectra obtained with a ${\text{Ba}}_8{\text{Si}}_{46}$ tips and Au sample [red (gray) and blue (black) dots] at 2.3 K. Solid lines: best fits using Schopol & Scharnberg-McMillan equations [Eq. (5)] with ${\Delta }_1^0=0.08\text{meV}$, ${\Gamma }_{12}=10\text{meV}$, ${\Delta }_2^0=1.2\text{meV}$, ${\Gamma }_{21}=1.49\text{meV}$ for the red (gray) curve and ${\Delta }_1^0=0.05\text{meV}$, ${\Gamma }_{12}=11\text{meV}$, ${\Delta }_2^0=1.33\text{meV}$, ${\Gamma }_{21}=1.31\text{meV}$ for the blue (black) curve. Inset: schematic drawing of the experimental geometry.

Figure 2

(Color online) ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{NbSe}}_2$ SIS spectra at $T=2.3\text{K}$. The spectra reveal two distinct energy gaps in ${\text{Ba}}_8{\text{Si}}_{46}$ (showed with arrows): ${\Delta }_S\approx 0.8\text{meV}$ for the blue (black) curve and ${\Delta }_L\approx 1.4\text{meV}$ for the red (gray) curve. Above: vortex lattice in ${\text{NbSe}}_2$ at $B=0.165\text{T}$ revealed with a ${\text{Ba}}_8{\text{Si}}_{46}$ tip at several biases (from left to right) $-2.0$, $-0.9$, $+1.0$, and $+1.9\text{mV}$ showing the contrast inversion characteristic of SIS junctions (Ref. 21).

Figure 3

(Color online) A typical ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{Ba}}_8{\text{Si}}_{46}$ SIS tunneling conductance spectrum [circled blue (black) curve]. A pure BCS fit, red (gray) line, clearly fails to reproduce the dips and the broadened quasiparticle peaks (pointed with arrows).

Figure 4

(Color online) Partial DOSs in the band 1 in (a) and 2 in (b) calculated within the McMillan model with ${\Delta }_1^0=0$, ${\Delta }_2^0=1.3\text{meV}$, ${\Gamma }_1=0.5$, 1, 2, 5, and 15 meV and ${\Gamma }_2={\Gamma }_1/10$. (c) Evolution of the excitation gap and apparent gaps ${\Delta }_L$, ${\Delta }_S$ with the scattering rate ${\Gamma }_1$, corresponding to (a) and (b). In (c), simulated conductance spectra at 2.3 K are shown for a SIS junction with both electrodes exhibiting the DOS of the small gap band shown in (a). The plot (d) shows the evolution of the excitation gap and the peak-to-peak gaps ${\Delta }_S$ and ${\Delta }_L$ in the small gap and large gap band, as a function of the coupling ${\Gamma }_1$.

Figure 5

(Color online) Typical ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{NbSe}}_2$ SIS tunneling conductance spectra [red (gray) triangles and blue (black) circles] observed at $T=2.2\text{K}$. Solid lines: best SIS fits with Schopol & Scharnberg-McMillan equations [Eq. (5)] with the following parameters: for the red (gray) curve: ${\Delta }_1^0=0.0\text{meV}$, ${\Gamma }_{12}=2.2\text{meV}$, ${\Delta }_2^0=1.1\text{meV}$, and ${\Gamma }_{21}=0.17\text{meV}$, and for the blue (black) curve ${\Delta }_1^0=0.07\text{meV}$, ${\Gamma }_{12}=3.54\text{meV}$, ${\Delta }_2^0=1.34\text{meV}$, and ${\Gamma }_{21}=0.26\text{meV}$. The DOS of ${\text{NbSe}}_2$ used for the fits was taken from Ref. 29.

Figure 6

(Color online) Typical ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{Ba}}_8{\text{Si}}_{46}$ SIS tunneling conductance spectra [red (gray) triangles and blue (black) circles] observed at $T=2.2\text{K}$. In some junctions a negative tunneling conductance is measured at the dip positions (arrows). Solid lines: best SIS fits with Schopol & Scharnberg-McMillan model obtained with the following parameters: for the red (gray) curve ${\Delta }_1^0=0.0\text{meV}$, ${\Gamma }_{12}=2.6\text{meV}$, ${\Delta }_2^0=1.1\text{meV}$, and ${\Gamma }_{21}=0.18\text{meV}$; and for the blue (black) curve ${\Delta }_1^0=0.0\text{meV}$, ${\Gamma }_{12}=3.7\text{meV}$, ${\Delta }_2^0=1.23\text{meV}$, and ${\Gamma }_{21}=0.40\text{meV}$.

Figure 7

(Color online) (a) Temperature dependence of the ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{Ba}}_8{\text{Si}}_{46}$ SIS spectra in black and their fits in red (gray) using Schopol & Scharnberg-McMillan model. The spectra are shifted for clarity. In (b) temperature dependence of the peak-to-peak gap extracted from ${\text{Ba}}_8{\text{Si}}_{46}$ vs ${\text{Ba}}_8{\text{Si}}_{46}$ SIS spectra.

Figure 8

(Color online) Scatter plot of the fit parameters ${\Gamma }_2$ vs ${\Gamma }_1$. Red (gray) line: linear dependence ${\Gamma }_2={\Gamma }_1/10$.