Ultimate Vortex Confinement Studied by Scanning Tunneling Spectroscopy

We report a detailed scanning tunneling microscopy study of a superconductor in a strong vortex confinement regime. This is achieved in a thin nanoisland of Pb having a size $d$ about 3 times the coherence length, and a thickness $h$ such that $h\ll d\ll \lambda$, where $\lambda$ is the London penetration depth. In this geometry the magnetic field evolution of local tunneling spectra reveals only two superconducting configurations to exist: zero and single vorticity. The normal state is reached at ${\mu }_0{H}_c=0.46\mathrm{T}$, about 6 times the critical field of bulk Pb, with no higher order vorticity observed. Basing on our STS data, we discuss the role of local supercurrents in both configurations.

Figure 1

Constant current topographic STM images of Pb islands on Si(111) surface taken on a large scale (a) and on a local scale (b) showing the island selected for the study. Locations $C$ and $E$ correspond, respectively, to the island center and edge.

Figure 2

(a) Characteristic local tunneling conductance spectrum $dI/dV(V)$ (set point $I_0=750\mathrm{pA}$, $V_0=-4.5\mathrm{mV}$) of the island at ${\mu }_{0}H=0\mathrm{T}$ (circles); best fit using standard BCS DOS with $\Delta =1.12\mathrm{meV}$, $T=4.3\mathrm{K}$ (red or gray line). (b) In nonzero magnetic field the tunneling spectra become spatially inhomogeneous: the color-coded ZBC map of the island (here at ${\mu }_{0}H=180\mathrm{mT}$) shows the radial distribution of ZBC values with higher ZBC observed close to the island border.

Figure 3

(a) Color-coded diagram of ZBC values vs magnetic field taken over a line crossing the island center [solid line in Fig. 1b]. The abrupt transition from $L=0$ state to $L=1$ takes place at ${\mu }_0{H}_0=235\mathrm{mT}$. (b) ZBC profiles: at 0 mT, in $L=0$ configuration at 190 mT, just before the transition to $L=1$ (233 mT), just after the transition to $L=1$ (237 mT), in the normal state at 500 mT. (c) Evolution of the ZBC in the magnetic field in locations $C$ (blue or dark gray circles) and in $E$ (black circles).

Figure 4

Evolution of the local tunneling $dI/dV(V)$ spectra (set point $I_0=750\mathrm{pA}$, $V_0=-4.5\mathrm{mV}$) in the magnetic field. (a) In the island center, at the location $C$ [see Fig. 1b]; (b) At the sample border, location $E$. Each data set is presented as 2D and 3D plots for clarity.

Figure 5

Tentative picture of the superfluid velocity $v_s$ distribution over the island (gray disc) at low fields (a), at $H_0$ just after transition into $L=1$ state (b), at $H_{\min }$ (c), and at $H_{\min }<H<H_c$ (d). Black arrows represent Meissner screening currents, red or gray arrows—vortex-generated currents. Dashed line contour delimits the surface penetrated by the flux quantum ${\varphi }_0$. The blue or medium gray circle $\pi {\xi }_{\mathrm{eff}}^2$ centered near the sample border shows the superconducting wave packet extension [13].