Influence of Nanosize Hole Defects and their Geometric Arrangements on the Superfluid Density in Atomically Thin Single Crystals of Indium Superconductor

Using Indium $\sqrt{7}\times \sqrt{3}$ on Si(111) as an atomically thin superconductor platform, and by systematically controlling the density of nanohole defects (nanometer size voids), we reveal the impacts of defect density and defect geometric arrangements on superconductivity at macroscopic and microscopic length scales. When nanohole defects are uniformly dispersed in the atomic layer, the superfluid density monotonically decreases as a function of defect density (from 0.7% to 5% of the surface area) with minor change in the transition temperature $T_C$, measured both microscopically and macroscopically. With a slight increase in the defect density from 5% to 6%, these point defects are organized into defect chains that enclose individual two-dimensional patches. This new geometric arrangement of defects dramatically impacts the superconductivity, leading to the total disappearance of macroscopic superfluid density and the collapse of the microscopic superconducting gap. This study sheds new light on the understanding of how local defects and their geometric arrangements impact superconductivity in the two-dimensional limit.

Figure 1

Schematic illustration of methodology. (a) Indium adatoms on Si(111) and reconstruction into the $\sqrt{7}\times \sqrt{3}$ phase. (b) Microscopic probe of scanning tunneling microscope. Both the probe apex and the tunneling region are in nm scale. (c) Macroscopic probe of the double-coil mutual inductance system. Both the probe coil size and the sample size are in mm scale.

Figure 2

Temperature dependent superfluid density. (a)–(d) Topography of indium $\sqrt{7}\times \sqrt{3}$ samples with varying defect densities. The top right insets show their corresponding atomic images where the scale bar is 1 nm. (e)–(f) Topographic image of hole and island defects. (g) Temperature dependent superfluid density for sample No. 1 to No. 4. The two-fluid model fitting is used for sample No. 1 and No. 2 to extrapolate the SFD at 0 K. The blue dashed line is the universal BKT line. (h) The temperature dependent ${\sigma }_1$ for sample No. 1 to No. 4.

Figure 3

Temperature dependent quasiparticle excitation spectrum. (a),(b) STM image taken on sample No. 2 and No. 3. (c),(d) Temperature dependent tunneling spectra on the pristine area of sample No. 2 and No. 3 using superconducting Nb and Pb tips, respectively. Spectra acquisition positions for 2.3 K are marked on (a) and (b) with the corresponding color. Spectra at other temperatures are also taken at a similar area, more than 10 nm away from the hole defects. Curves are offset for clarity. The black dashed line is a guide to show the temperature dependent $|{\mathrm{\Delta }}_1-{\mathrm{\Delta }}_2|$ tunneling peak position. (e),(f) BCS gap fitting for sample No. 2 and No. 3, respectively. The inset in (e) shows a typical fitted result of a tunneling spectrum using superconducting Nb tip at 2.58 K. (g) A summary of critical temperatures $T_{C,SFD}$ and $T_{C,BCS}$ as a function of hole defect density. Data points for sample No. 1 and No. 2 are laterally offset to avoid overlapping, both are at 0.7% hole defect concentrations. (h) A summary of SFD at 2.3 K for samples of different hole defect density. Horizontal error bars represent statistical standard deviations of hole defect density.

Figure 4

Uniformity of superconducting gap distribution. (a),(c) STM image taken on sample No. 2 and No. 3. (b),(d) The spatial dependence of superconducting gap spectra along the white dashed arrow in (a) and (c), respectively. The position independent $\pm |{\mathrm{\Delta }}_1+{\mathrm{\Delta }}_2|$ (bright yellow) peak energies show that the gap is spatially uniform. (e) Topography on sample No. 3 showing step edge defects and hole defects. (f) Spectra taken on position I to III as labeled in (e). Inside the window marked by the red dashed line, duplicate curves which are amplified by a factor of 7 are also plotted to better show the tunneling peak feature at $\pm |{\mathrm{\Delta }}_1-{\mathrm{\Delta }}_2|$. Curves are offset for clarity and the horizontal black bars mark the zero for each curve.