Creating nanostructured superconductors on demand by local current annealing

Superconductivity results from a Bose condensate of Cooper-paired electrons with a macroscopic quantum wave function. Dramatic effects can occur when the region of the condensate is shaped and confined to the nanometer scale. Recent progress in nanostructured superconductors has revealed a route to topological superconductivity, with possible applications in quantum computing. However, challenges remain in controlling the shape and size of specific superconducting materials. Here, we report a method to create nanostructured superconductors by partial crystallization of the half-Heusler material, YPtBi. Superconducting islands, with diameters in the range of 100 nm, were reproducibly created by local current annealing of disordered YPtBi in the tunneling junction of a scanning tunneling microscope. We characterize the superconducting island properties by scanning tunneling spectroscopic measurements to determine the gap energy, critical temperature and field, coherence length, and vortex formations. These results show unique properties of a confined superconductor and demonstrate that this method holds promise to create tailored superconductors for a wide variety of nanometer scale applications.

Figure 1

Creating YPtBi superconducting nanostructured islands by local current annealing. (a) $C{1}_b$ crystal structure of YPtBi: Y (purple), Pt (gray), Bi (green). (b) Illustration of the process of creating superconducting islands by passing a current pulse with the STM probe tip held fixed within $\approx 1\mathrm{nm}$ of an amorphous YPtBi layer. (c) Three-dimensional rendered STM topographic image $(200\mathrm{nm}\times 200\mathrm{nm})$ of a created superconducting island [see red box in (d)]. (d) SEM image showing seven different superconducting nanostructures created by local current annealing with the STM probe tip. The island in the lower left corner, outlined by the red box, is used for the superconducting property measurements shown in Figs. 2, 3, 4, 5, 6. (e) TEM cross section of the superconducting island in the bottom center of (d) highlighted by the orange line. The cross-sectional image shows $\approx 50$-nm-thick amorphous layer covering the entire surface of the YPtBi crystal. The white arrow indicates the boundary between the amorphous layer and underlying crystal. The superconducting nanostructure created by local current annealing is outlined by the white oval. Most of the nanostructures are characterized by a dimple in the center of the structure. (f) High-resolution TEM image of the boundary region separating the underlying YPtBi crystal and the region of the created nanostructure. TEM analysis shows that the superconducting nanostructure contains more crystalline domains than the surrounding amorphous regions, which were not subject to local current annealing.

Figure 2

Tunneling spectroscopy of a superconducting nanostructured island. (a) Comparison of tunneling spectra on the pristine cleaved surface and nanostructured island for a large sample bias range of $\pm 100\mathrm{mV}$. Over this range of tunneling bias the pristine cleaved surface and nanostructure appear similar. (b) With a smaller bias range of $\pm 10\mathrm{mV}$, the nanostructured island displays a superconducting gap at very low bias. (c) and (d) Differential tunneling conductance spectra (blue dots) over $\pm 1\mathrm{mV}$ sample bias measured over the center and perimeter of the nanostructured island in Fig. 1, respectively. Note in both cases the spectra are not fully gapped and show some conductance within the gap. The solid red lines are fits to the modified BCS Maki theory [33, 34] yielding the following parameters: island center, ${\mathrm{\Delta }}_0=\left(222\pm 1\right)\mu \mathrm{eV},\zeta =0.019\pm 0.001,T_{\mathrm{eff}}=150\mathrm{mK}$; island perimeter, ${\mathrm{\Delta }}_0=\left(198\pm 1\right)\mu \mathrm{eV},\zeta =0.029\pm 0.002,T_{\mathrm{eff}}=150\mathrm{mK}$ [40].

Figure 3

Proximity effect across a nanostructured superconducting island. (a) STM topographic image, $190\mathrm{nm}\times 300\mathrm{nm}$, of the superconducting island. The height scale from dark to bright is 9.5 nm. (b) $dI/dV$ line scan as a function of position through the center of the island along the green line in (a). The $dI/dV$ is normalized and shown in a color scale. The blue area denotes larger gap values, $\mathrm{\Delta }$. (c) Schematic of the superconducting order parameter profile across a conventional normal-superconducting junction. (d) The ZBC profile from the normalized $dI/dV(V_{\mathrm{b}}=0\mathrm{V})$ (blue symbols) from the bottom boundary region of the island. Note the ZBC is plotted with the high value (small gap) pointing down to be a measure of the superconducting order parameter. The red line is an exponential fit yielding a decay length ${\xi }_{\mathrm{N}}=\left(20\pm 2\right)\mathrm{nm}$ [40]. (e) The ZBC profile from the normalized $dI/dV(V_{\mathrm{b}}=0\mathrm{V})$ (blue symbols), and the STM topographic height (orange symbols) across the superconducting island. The red dashed lines denote the positions of the island boundaries. (f) The ZBC profile from the normalized $dI/dV(V_{\mathrm{b}}=0\mathrm{V})$ (blue symbols) from the top boundary region of the island. The red line is an exponential fit yielding a decay length ${\xi }_{\mathrm{N}}=\left(20\pm 2\right)\mathrm{nm}$ [40]. Note in (d)–(f) the ZBC is plotted with the large values (small gap) pointing down to be a measure of the superconducting order parameter. The error bars are the standard error of the mean values.

Figure 4

Superconducting properties of a nanostructured island. (a) Temperature-dependent tunneling spectra showing the transition from the superconducting to normal state measured in the center of the island in Fig. 1. (b) The superconducting gap, $\mathrm{\Delta }$ (symbols), as a function of temperature determined from fitting the spectra in (a) to BCS theory. The uncertainties are smaller than the symbol size. The solid line is a fit to BCS theory yielding ${\mathrm{\Delta }}_0=\left(221\pm 3\right)\mu \mathrm{eV}$ and $T_C=\left(1.37\pm 0.02\right)\mathrm{K}$ [40]. (c) Magnetic field–dependent tunneling spectra showing the transition to the normal state. (d) The superconducting gap, Δ (symbols), as a function of magnetic field determined from fitting the spectra in (d) to BCS theory. The uncertainties are smaller than the symbol size. From the absence of a superconductor gap, the upper critical field is estimated to be center $B_{C2}\approx 2.25\mathrm{T}$.

Figure 5

Sequential addition of vortices in a nanostructured superconducting island. (a) STM topographic image, $200\mathrm{nm}\times 200\mathrm{nm}$, of the superconducting island. (b)–(p) Corresponding Fermi-level $dI/dV(V_{\mathrm{b}}=0)$ maps showing superconducting (red) and normal (blue) regions of the island as vortices (small blue disks) sequentially populate the nanostructure as the magnetic field is increased. The vortices are seen to distribute along the perimeter of the island and avoid the center. Image size for (b)–(m) is $200\mathrm{nm}\times 200\mathrm{nm}$. Maps (n)–(p) are zoomed in, $100\mathrm{nm}\times 100\mathrm{nm}$, to focus on the center region at higher fields.

Figure 6

Vorticity versus normalized magnetic flux for a nanostructured superconducting island. The number of vortices in the superconducting island from Fig. 5 (blue symbols), $L$, is plotted versus the normalized magnetic flux (bottom axis) and magnetic field (top axis). The normalized magnetic flux, ${\mathrm{\Phi }}_{\mathrm{d}}/{\mathrm{\Phi }}_0=B\pi {\left(D/2\right)}^2$, where $D$ is the diameter of the island, and ${\mathrm{\Phi }}_0$ is the flux quantum. The solid line represents the condition $L={\mathrm{\Phi }}_{\mathrm{d}}/{\mathrm{\Phi }}_0$. The blue solid lines are a linear fit from $L=0$ to 4, and $L=5$ to 8. The change in slope shows the rate of vortex addition to the island decreases by a factor of 2 after four vortices are added to the island. The initial slope corresponds to one vortex added for an increment of magnetic field of 0.0625 T, changing to a field increase of 0.125 T per added vortex after $L=4$. The uncertainty in the normalized flux is derived from the uncertainty in the island area, which was determined from the STM topographic profile in Fig. 3 [57].

Figure 7

Optical alignment of STM probe tip onto the cleaved YPtBi crystal.

Figure 8

STM imaging of the cleaved YPtBi surface. (a) Large area, $50\mathrm{nm}\times 50\mathrm{nm}$, STM topographic image of the cleaved surface. Height scale is 1.7 nm from dark to bright. (b) Zoomed-in STM image, $20\mathrm{nm}\times 20\mathrm{nm}$, from the blue boxed region in (a). The inset shows an atomic resolution image, $5\mathrm{nm}\times 5\mathrm{nm}$, of several of the clusters, which make up the cleaved surface. The height scale is 1.1 nm for (b), and 0.3 nm for the inset.

Figure 9

Al thin-film tunneling spectrum (blue circles). Tunneling $dI/dV$ spectrum from a 100-nm-thick Al film measured at $\approx 10\mathrm{mK}$ (red line). Modified BCS Maki calculation with parameters $\mathrm{\Delta }=\left(178\pm 0.2\right)\mu \mathrm{V},\zeta =0.019\pm 0.001$, and $T_{\mathrm{eff}}=(160\pm 5)\mathrm{mK}$ [40].

Figure 10

Sample preparation for TEM measurements. (a) Pt markers written near nanostructures for reference. (b) Carbon and tungsten deposited to protect surface during ion milling. (c) Wedge-shaped sample is cut out to minimize disturbance to nanostructures. (d) Lift-out of sample. (e) Mounting and thinning of sample on TEM holder. (f) Cross-sectional TEM sample.

Figure 11

TEM measurements of a YPtBi nanostructure. (a) Annular dark-field STEM cross-sectional image of one of the superconducting nanostructures shown in Fig. 1. The white arrow indicates the boundary between the amorphous layer and underlying crystal. (b) Cross-sectional image from the red boxed region in (a), showing the underlying crystal structure of YPtBi and the amorphous overlayer. (c) Cross-sectional image from the blue boxed region in (a), inside the nanostructure. The image shows small crystallites, which give rise to the peaks in the Fourier transform image in (d).

Figure 12

Electrical characterization of bulk YPtBi crystals. (a) Temperature-dependent resistance shows the bulk superconductivity transition. (b) Upper critical field versus temperature. The upper critical field was defined at $90\%R_{\mathrm{N}}$, where $R_{\mathrm{N}}$ is the normal state resistance. Error bars indicate field step size. (c) Temperature-dependent resistance under different magnetic fields. (d) Magnetoresistance at different temperatures.