Disorder-induced suppression of superconductivity in the $\mathrm{Si}\left(111\right)-(\sqrt{7}\times \sqrt{3})$-In surface: Scanning tunneling microscopy study

The critical effect of disorder on the two-dimensional (2D) surface superconductor $\mathrm{Si}\left(111\right)-(\sqrt{7}\times \sqrt{3})$-In is clarified by comparing two regions with different degrees of disorder. Low-temperature scanning tunneling microscopy measurements reveal that superconductivity is retained in the less disordered region, judging from the characteristic differential conductance $(dI/dV)$ spectra and from the formation of vortices under magnetic fields. In striking contrast, the absence of those features in the highly disordered region shows that superconductivity is strongly suppressed there. Analysis of observed zero-bias anomalies in $dI/dV$ spectra allows us to estimate the reduction in the transition temperature $T_{\mathrm{c}}$, which explains the fate of superconductivity in each region.

Figure 1

(a) STM image of a $500\text{nm}\times 500$ nm region on the surface (set point: 10 pA at $+50$ mV). (b) STM images of a $20\text{nm}\times 20$ nm region on a flat region (set point: 50 pA at $+500$ mV). Note that the void defects in this image appear as white dots in (a) and in Fig. 2 because of insufficient spatial resolutions in the latter images. (c) STM images of a $20\text{nm}\times 20$ nm region on a rough region (set point: 50 pA at $+500$ mV). The arrows indicate the holes where In films did not grow. The parallelograms in (b) and (c) represent $\sqrt{7}\times \sqrt{3}$ unit cells. (d), (e) Fourier transforms of the STM images (b) and (c), respectively. The circles indicate spots corresponding to the $\sqrt{7}\times \sqrt{3}$ periodicity. (f) Line profiles measured along the solid lines in the STM image (a).

Figure 2

(a) Series of tunneling spectra measured in a zero magnetic field at 15 points, indicated in the STM image in (b). The curves are shifted from each other by 4 nS for clarity (set point: 400 pA at $+20$ mV; bias modulation: 200 $\mu {\mathrm{V}}_{\mathrm{rms}}$ at 610 Hz). (b) STM image of a $50\text{nm}\times 200$ nm region including a boundary between a flat region and a rough region (set point: 10 pA at $+50$ mV). The white dots in the flat region correspond to the void defects in Fig. 1. (c) Representative tunneling spectrum of the flat region. The dashed curve is the result of fitting by the Dynes formula (set point: 400 pA at $+20$ mV; bias modulation: 50 $\mu {\mathrm{V}}_{\mathrm{rms}}$ at 610 Hz). (d) Semilogarithmic plot of the tunneling spectra at points $A$ and $D$. The solid (dotted) curves represent the data on the positive (negative) biases. The black solid lines are the results of fitting by Eq. (1).

Figure 3

(a)–(d) ZBC images in magnetic fields of $B_{\mathrm{ext}}=0.08$, 0.12, 0.18, and 0.24 T. The field of view is the same as that of Fig. 1. Vortex cores are imaged as bright spots in the flat region (set point: 200 pA at $+20$ mV; bias modulation: 200 $\mu {\mathrm{V}}_{\mathrm{rms}}$ at 610 Hz). (e) Average ZBC plotted as a function of distance $d$ from the boundary of the flat region. To plot these curves, ZBC was averaged over all the points with a given value of $d$, where the sign of $d$ is defined to be positive (negative) for the flat (rough) region. (f) Line profile of the ZBC image along the line $P-Q$ across a vortex core in (a).