Squeezed Abrikosov-Josephson Vortex in Atomic-Layer Pb Superconductors Formed on Vicinal Si(111) Substrates

Unlike bulk counterparts, two-dimensional (2D) superconductors are sensitive to disorder. Here, we investigated superconductivity of Pb atomic layers formed on vicinal substrates to reveal how surface steps with an interval shorter than the coherence length $\xi$ affect it. Electrical transport showed reduced critical temperature and enhanced critical magnetic field. Scanning tunneling microscopy exhibited vortices elongated along the steps, that is, Abrikosov-Josephson vortices squeezed normal to the steps due to the reduced $\xi$. These results demonstrate that steps work as disorder and vicinal substrates provide a unique platform to manipulate the degree of disorder on 2D superconductors.

Figure 1

(a),(b) temperature dependence of sheet resistance measured on the SIC samples formed (a) on a flat and (b) on a 1.1°-tilted vicinal substrates under out-of-plane magnetic fields. (c) temperature dependence of the upper critical magnetic field $B_{\mathrm{c}2}$. Black and blue squares indicate $B_{\mathrm{c}2}$ determined by the UD scaling theory (below 150 mT) on the flat and vicinal samples, respectively. The dashed curves are the WHH fitting curves. The stars mark $B_{\mathrm{c}2}$ measured by STM at 0.36 K.

Figure 2

(a),(g) STM images taken on (a) flat and (g) 1.1°-tilted vicinal SIC samples, respectively. (b)–(f), (h)–(l) ZBC maps under various magnetic fields taken on the same area as (a),(g), respectively. The tip height was stabilized with $V_S=10\mathrm{mV}$, $I_T=200\mathrm{pA}$.

Figure 3

(a) Evolution of ZBC as a function of the magnetic field taken on the flat (black triangle) and the vicinal (blue square) samples. The ZBC values are normalized by the spatially averaged ZBC taken under 400 mT. The solid line indicates a linear fit of ZBC before reaching the saturation and the dashed horizontal line indicates the saturated ZBC. (b) ZBC profiles across the vortex center taken on the flat substrate (black triangles) and the vicinal samples; red circles and blue squares indicate profiles taken along and perpendicular to the steps, respectively. Red (blue) lines are the profiles taken on the vortices of the flat sample multiplied by $0.78\pm 0.03$ in height and by $1.56\pm 0.27$ ($0.76\pm 0.08$) along the horizontal axis. Insets show the averaged vortices taken on the flat and vicinal samples.

Figure 4

(a) terrace width dependence of the critical magnetic field. The solid curve is a fitting with Eq. (5) in the main text. The inset shows a schematic of the arrayed resistors to model the vicinal SIC samples. (b) terrace width dependence of the suppressed DOS at the vortex center. The solid curve is a fitting given as $t^{4{\xi }_{\perp }/w}$.