Pseudogap Mediated by Quantum-Size Effects in Lead Islands

Scanning tunneling spectroscopy measurements of Pb islands on Si(111) at high energy resolution reveal a novel pseudogap, or a pseudopeak in special cases, around the Fermi level in addition to the usual quantum well states. These gap or peak features persist to temperatures as high as $\sim 80\mathrm{K}$ and are uniquely related to the quantum well nanostructure of the Pb islands. A systematic analysis indicates that electron-phonon scattering is responsible for the observed electronic structure.

Figure 1

(a) A $dI/dV$ tunneling spectrum taken at 10 K on a 19 ML Pb island grown on Si(111) from the point marked $\times$ in the included topographic image. $E\mathrm{\text{−}}{E}_F$ is the electron energy relative to the Fermi level. The tip height is set by $V=-2\mathrm{V}$ and $I=1.0\mathrm{nA}$. (b) A detailed view of the tunneling spectrum near the Fermi level showing a pseudogap. The tip height is set by $V=-80\mathrm{mV}$ and $I=0.5\mathrm{nA}$. The convex background is caused by the overlapping tails of the two QWS peaks at $-0.30$ and $+0.35\mathrm{eV}$. For comparison, the $dI/dV$ curves taken from a thick Au(111) film ($\sim 150\mathrm{nm}$), a single crystal Pb(111), and a 19 ML Pb island on Cu(111) are also displayed; these curves are shifted vertically for clarity.

Figure 2

(a) A topographic image of an island with a crater in the middle, exposing multiple thicknesses ranging from 12 to 19 ML. (b) Experimental $dI/dV$ tunneling spectra for various terrace thicknesses. The curves are shifted vertically for clarity. Also shown, for comparison, are theoretical tunneling probabilities. (c) Detailed view of the tunneling spectra near the Fermi level. (d) Calculated tunneling probabilities for comparison.

Figure 3

(a) Topographic images of three islands of different sizes. (b) Tunneling spectra at three temperatures from these islands at a thickness of 19 ML. (c) Calculated tunneling probabilities of a 19 ML film at the same three temperatures. The curves at 15 and 50 K are shifted vertically for clarity.

Figure 4

(a) Temperature dependent $dI/dV$ curves on two large 19 ML Pb islands with a size over $1\mu \mathrm{m}$. Bulk Pb has a superconducting transition temperature of 7.2 K. (b) Temperature dependent $dI/dV$ curves taken from an underdoped Bi2212 with a superconducting transition temperature of 84 K (taken from 19, 28). There is a strong similarity between the two cases.