Closing the superconducting gap in small Pb nanoislands with high magnetic fields

Superconducting properties change in confined geometries. Here we study the effects of strong confinement in nanosized Pb islands on Si(111) $7\times 7$. Small hexagonal islands with diameters less than 50 nm and a uniform height of seven atomic layers are formed by depositing Pb at low temperature and annealing at 300 K. We measure the tunneling spectra of individual Pb nanoislands using a low-temperature scanning tunneling microscope operated at 0.6 K and follow the narrowing of the superconducting gap as a function of magnetic field. We find the critical magnetic field, at which the superconducting gap vanishes, reaches several Tesla, which represents a greater than 50-fold enhancement compared to the bulk value. By independently measuring the size of the superconducting gap, and the critical magnetic field that quenches superconductivity for a range of nanoislands, we can correlate these two fundamental parameters and estimate the maximal achievable critical field for 7 ML Pb nanoislands to be 7 T.

Figure 1

Constant current STM topographies of nanosized Pb islands. (a) The Si(111) $7\times 7$ surface is covered with a Pb wetting layer on which the hexagonal Pb-islands are grown $(V=0.1$ V, $I=70$ pA). The visible atomic steps and flat terraces result from the underlying Si surface. (b) Zoom-in to wetting layer $(V=0.01$ V, $I=150$ pA). The wetting layer exhibits some residual structure of the Si(111) $7\times 7$ substrate but otherwise appears disordered. (c) Constant current topography of the Si(111) $7\times 7$ surface prior to Pb evaporation $(V=-2.2$ V, $I=100$ pA). (d) The top surface of a typical Pb island. The impact of the mostly disordered wetting layer is observable $(V=0.1$ V, $I=2.5$ nA). (e) Zoom-in showing the hexagonal crystalline structure of the top surface of a Pb island $(V=-1.2$ mV, $I=1$ nA).

Figure 2

(a) The superconducting gap in spectra of the differential conductance $\left(dI/dV\right)$ taken at different magnetic fields on a Pb island with diameter $d=22$ nm as a function of bias voltage. Spectra acquired at different magnetic fields are shifted vertically for clarity. Each bar indicates the zero conductance at the corresponding magnetic field. The $dI/dV$ spectra are averaged over different positions on the island which is indicated by different colors. At zero field a fit according to the Dynes formula is performed (blue dotted line), ${\mathrm{\Delta }}_0=(1.03\pm 0.01)$ meV. In the further analysis the $dI/dV$ spectra of different positions are averaged and normalized to the averaged background conductance ${\sigma }_b$. (b) The averaged $dI/dV$ spectra show the closing of the superconducting gap and are plotted color coded as a function of bias voltage and magnetic field and with a logarithmic color scale. The gray area indicates magnetic fields at which no data was recorded. The black crosses mark the position of the bias voltage width $V_e$ at which the normalized conductance dropped to $1/e$ of the background conductance. The evolution of the superconducting gap (green line) is fitted to $V_e$ using equation (1). For this island, a critical field of $B_c=(3.5\pm 0.1)$ T was found.

Figure 3

(a)–(h) Color-coded $dI/dV$ spectra for islands with different diameters $d$ from 55 nm to 10 nm as a function of bias voltage and magnetic field. The data was treated and plotted in the same fashion as demonstrated in Fig. 2. (i) The fitted critical fields $B_c$ as a function of the diameter $d$ of the islands showing that $B_c$ increases as $d$ decreases. The highest observed critical field is $(5.2\pm 0.4)$ T. The trend of the critical field is fitted by two different functions $A_2/d$ (green line) and $A_1/(d_0+d)$ (red line).

Figure 4

(a) The fitted superconducting gap size ${\mathrm{\Delta }}_0$ at zero magnetic field for different Pb islands as a function of the inverse island diameter $1/d$. Dark green crosses correspond to islands for which critical fields were determined in Fig. 3. Light green crosses note additional islands. The measurements indicate a linear dependence of the gap with the inverse island diameter $1/d$. The red line is a linear fit to ${\mathrm{\Delta }}_0={\mathrm{\Delta }}_{\infty }-m/d$. The error bars are the estimated standard deviations of the fitting parameters. (b) Critical field $B_c$ plotted against the extracted zero-field gap ${\mathrm{\Delta }}_0$ for the islands shown in Fig. 3 (dark green crosses). This correlation of $B_c$ with ${\mathrm{\Delta }}_0$ reveals a curvature, which is also noticeable in the combination of the $A_1/(d_0+d)$ fit of the critical field $B_c\left(d\right)$ and the $m/d$ fit of the zero field gap ${\mathrm{\Delta }}_0\left(d\right)$ (blue curve). The observed behavior suggests that in the limit of vanishing superconductivity a maximal critical field of $6.7_{-1.5}^{+1.8}$ T is reached.