Experimental Demonstration of a Two-Band Superconducting State for Lead Using Scanning Tunneling Spectroscopy

The type I superconductor lead (Pb) has been theoretically predicted to be a two-band superconductor. We use scanning tunneling spectroscopy (STS) to resolve two superconducting gaps with an energy difference of $150\mu \mathrm{eV}$. Tunneling into Pb(111), Pb(110), and Pb(100) crystals reveals a strong dependence of the two coherence peak intensities on the crystal orientation. We show that this is the result of a selective tunneling into the two bands at the energy of the two coherence peaks. This is further sustained by the observation of signatures of the Fermi sheets in differential conductance maps around subsurface defects. A modification of the density of states of the two bands by adatoms on the surface confirms the different orbital character of each of the two subbands.

Figure 1

$dI/dV(V)$ spectra on clean terraces of Pb(111), (100), and (110) single crystal surfaces. The superconducting gap around $E_F$ is framed by QPRs at $\approx \pm 2.7\mathrm{mV}$, consisting of two peaks separated by $\approx 150\mu \mathrm{eV}$. The energy of the peaks is given as the sum of the pairing energy of the tip (${\mathrm{\Delta }}_{\text{tip}}$) and the sample (${\mathrm{\Delta }}_{\mathrm{s}1}$ and ${\mathrm{\Delta }}_{\mathrm{s}2}$, respectively). The insets show the corresponding top views on the two FSs of a Pb single crystal. 3D models from [28]. Lock-in modulation amplitude was $15{\mu \mathrm{V}}_{\text{rms}}$ at 912 Hz.

Figure 2

(a)–(d) Subsurface Ne inclusion. High-resolution topography (a) on an atomically flat Pb(100) terrace (set point: 5 mV, 250 pA). Constant-height $dI/dV$ maps at 5 mV (b), 2.64 mV (c), and 2.76 mV (d) ($25{\mu \mathrm{V}}_{\text{rms}}$, 912 Hz, set point: 5 mV, 500 pA). In the duplicated maps, prominent scattering signatures are highlighted as a guide for the eye. A quantum well state between the impurity and the surface leads to the higher conductance in the center of all maps. Note that the topography in (a) combines features visible in (c) and (d) because all states up to the applied bias—i.e., both Fermi sheets—contribute to the tunneling current. (e)–(h) 3D models of the two FSs of Pb from Ref. [28]. The curvature of the FS is color coded onto the 3D model in (e) and (f), which are oriented according to the crystalline directions in (a)–(d). Dark blue and dark red correspond to low and high curvature, respectively. Black lines in (e) and (f) mark the boundaries of the first Brillouin zone.

Figure 3

Pb adatom on Pb(100). (a) $dI/dV(V)$ spectrum on clean Pb(100) (top) and on a Pb adatom (bottom). (b) Intensity ratio $R$ of QPR1 vs QPR2 and apparent height across a Pb adatom, as sketched in the inset. $R$ is determined by numerical deconvolution of the spectra, as discussed in the Supplemental Material [24].