Large-scale modulation in the superconducting properties of thin films due to domains in the $\mathrm{SrTi}{\mathrm{O}}_3$ substrate

Scanning superconducting quantum interference device measurements reveal large-scale modulations of the superfluid density and the critical temperature in superconducting Nb, NbN, and underdoped $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ films deposited on $\mathrm{SrTi}{\mathrm{O}}_3$ (STO). We show that these modulations are a result of the STO domains and domain walls, forming below the 105 K structural phase transition of STO. We found that the flow of normal current, measured above the superconducting transition, is also modulated over the same domain structure, suggesting a modified carrier density. In clean STO, domain walls remain mobile down to low temperatures. Modulated superconductivity over mobile channels offers the opportunity to locally control superconducting properties and better understand the relations between superconductivity and the local structure.

Figure 1

Modulated superfluid density in superconducting films grown on STO. (a) Sketch of the three domain boundary orientations in STO after the structural phase transition. The 45° domain boundary (left) is between two domains with unit cells elongated in-plane, while the 0° (middle) and 90° (right) are due to lengthening out-of-plane. (b) A sketch of polycrystalline Nb on STO. Domain boundaries are represented by red lines in the STO. (c) Left: The way SQUID susceptometer detects the diamagnetic response of a superconducting sample. We induce current in the field coil (green loop), which generates the flow of supercurrents in the sample (green dashed line). The supercurrents counter the applied magnetic field. The pickup loop (purple) captures the overall field, which is less than the applied field. Right: SQUID magnetometer detects current distribution in the sample by mapping the magnetic fields generated by the current flow (black arrow). (d) Map of the diamagnetic response of sample 5 (Table 1), showing stripy modulation of the superconductivity (SC) corresponding to the 0° and 90° domains of STO. Inset: A diagram of the susceptibility signal $S$ as a function of the distance between the SQUID sensor and the sample. The reading of the front minus the rear pickup loops increases as the sensor approaches the SC. After reaching the touchdown (TD) point, the susceptibility signal remains constant. The full susceptibility signal $S_{\mathrm{total}}$ is the difference between the susceptibility signal at the TD point and far from the sample. (e) Magnetic (copper-colored) and susceptibility images, taken simultaneously, of sample 3 (Table 1) at two different locations showing vortices aligned in lines corresponding to stripes of modulation in the diamagnetic response. Black and white objects are vortices of opposite polarity. Vortex density was controlled by an external magnetic field or by driving currents during cooldown. The stripy modulations are not the only factor determining the position of vortices, thus not all the vortices are aligned with the stripes. Each vortex carries one flux quantum, ${\mathrm{\Phi }}_0$. The keyhole shape of the vortices is a result of a convolution between the magnetic field lines from the vortex (circular) and the point spread function of the SQUID (circle with leads).

Figure 2

New configuration of stripes with reduced superfluid density appears after recooling the sample through 105 K. (a) Susceptibility image showing stripy modulations in sample 3, corresponding to the 0° and 90° STO domains. The stripes of reduced diamagnetic response appear in an area of stronger signal. This suggests that the reduced signal occurs on domain walls. (b) The same area imaged after heating the sample to 140 K, above the structural transition temperature, and cooling it back to 4.2 K. The configuration of modulations changed, showing now only 0° domains. The black spots are defects of local reduction in the superfluid density, or bumps that elevate the SQUID and lower its signal. They can be used for comparing between the two images. Scale bar is 50 µm. (c) Two areas in sample 5 showing that the configuration of stripes did not change after cycling the temperature around 15 K, above the superconducting transition temperature. The stripe configuration changed after cycling around 140 K. Scale bars are 50 µm.

Figure 3

Temperature evolution of the superfluid density. (a) The full susceptibility signal $S_{\mathrm{total}}$ as a function of temperature. $T{c}_{\mathrm{H}}=8.5\mathrm{K}$. Inset: Susceptibility maps of the same area in sample 4 (Table 1) at three different temperatures corresponding to the colored points. The amplitude of the modulation increased with temperature, while above the critical temperature, the signal is not diamagnetic and does not depend on location. The dashed line marks the location of the cross section used in Fig. 4. Values span over 2, 26, and $0.22{\mathrm{\Phi }}_0/\mathrm{A}$ (top to bottom). These ranges of values are also marked in panel a by a colored rectangle on the right-hand side. All scale bars are 50 µm. (b) Susceptibility as a function of height. As the sensor approaches the sample, the diamagnetic response becomes stronger (below $T\mathrm{c})$. The diamagnetic response near the surface is stronger at lower temperatures, because the penetration depth is smaller. $S_{\mathrm{total}}$ is defined as the difference between the susceptibility signal at the TD point and the signal far from the sample. Above $T{c}_{\mathrm{H}}$, there is no difference between the two locations. Colors correspond to the colored points in panel a.

Figure 4

Modulation of the diamagnetic signal as a function of temperature. (a) Linecuts of susceptibility taken from the area indicated in Fig. 3 at different temperatures corresponding to the colors in Fig. 3. The modulation of the diamagnetic signal increased with temperature, disappearing above $T{c}_{\mathrm{H}}$. $\mathrm{\Delta }S$ is defined as the amplitude of the modulation. (b) $S_{\mathrm{total}}$ (black empty circles) plotted with $\mathrm{\Delta }S$ (red circles) as a function of temperature in units of $T/T{c}_{\mathrm{H}}$. $\mathrm{\Delta }S$ hardly changes with temperature until close to $T{c}_{\mathrm{H}}$, where it increases rapidly till it almost merges with $S_{\mathrm{total}}$. (c) The relative modulation signal $\mathrm{\Delta }S/S_{\mathrm{total}}$ plotted as a function of temperature in units of $T/T{c}_{\mathrm{H}}$. The two extreme values of the critical temperature, the highest ${Tc}_{\mathrm{H}}$ and the lowest ${Tc}_{\mathrm{L}}$, are marked with dashed lines. Inset: $S_{\mathrm{total}}$ signal as a function of temperature, measured on (cyan) and off (black) a stripe that showed reduced diamagnetic response. The darker stripes have lower $T\mathrm{c},T{c}_{\mathrm{L}}$; $T{c}_{\mathrm{L}}/T{c}_{\mathrm{H}}=0.99$. (d) Zoom on the region close to $T{c}_{\mathrm{H}}$ in panel b. $\mathrm{\Delta }S$ increases and then decreases, overlapping $S_{\mathrm{total}}$ only at $T/T{c}_{\mathrm{H}}=1$.

Figure 5

The flow of normal current is also modulated, even above $T\mathrm{c}$. (a)–(c) Susceptibility (left, gray) and flux response to current (right) measured simultaneously on sample 4. (a) $T=9.97\mathrm{K}$, above $T{c}_{\mathrm{H}}$. Stripy pattern is visible in the current response map, indicating that the normal current is modulated. The amplitude of the modulation, $\mathrm{\Delta }M$, is $4.2\mathrm{m}{\mathrm{\Phi }}_0/\mathrm{A}$. In contrast, no modulation, or any diamagnetic response, is detectable in the susceptibility map. (b) $T=8.34\mathrm{K}$, below $T{c}_{\mathrm{H}}$. Stripy modulations are visible in both susceptibility and current response maps. The modulation observed in the current response, $\mathrm{\Delta }M=9.4\mathrm{m}{\mathrm{\Phi }}_0/\mathrm{A}$, is 224% stronger than the modulation observed above $T{c}_{\mathrm{H}}$. (c) $T=4.22\mathrm{K}$. Weak stripy modulations in both susceptibility and current response. $\mathrm{\Delta }M=1.1\mathrm{m}{\mathrm{\Phi }}_0/\mathrm{A}$. (d) The modulation of the current response, $\mathrm{\Delta }M$, as a function of temperature. $\mathrm{\Delta }M$ is increased as we approach $T{c}_{\mathrm{H}}$ and drops immediately after to a nonzero value. Colored dots correspond to the images shown in panel (a)–(c). $\mathrm{\Delta }M$ was extracted from the cross section marked in panel b.