Figure 1

(a) Tricrystal geometry. The polar plots represent the pairing wave functions, with the red lobe phases shifted by $\pi$ relative to the blue. (b) Schematic of the pickup loop area of the SQUID susceptometer sensor used. (c),(d),(e) are SQUID microscope images of the tricrystal point of a ${\mathrm{Y}}_{0.7}{\mathrm{C}\mathrm{a}}_{0.3}{\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ film on a ${\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ tricrystal with the geometry of (a). All SSM images in this Letter were taken at 4.2 K. The dashed lines indicate grain boundaries. (c) illustrates the inversion of a $N_{\varphi }=-1/2$ vortex at the tricrystal point (top image). [(c), middle image] a 5 mA pulse of current is passed through the susceptometer field coil to invert a $-1/2$ vortex [(c), top image] to a $+1/2$ vortex, creating also a $N_{\varphi }=-1$ Josephson vortex in the horizontal grain boundary. [(c), bottom image] the $-1$ Josephson vortex is dragged from the tricrystal point by moving the sensor parallel to the grain boundary while applying a current of 4 mA. $\Delta {\varphi }_s$ is the net variation in flux through the SQUID pickup loop. (f) Shows the integration of the total flux (in units of ${\varphi }_0$) of the $N_{\varphi }=+1/2$ state [(d), red dots], the $-1/2$ state [(e), blue dots], and a nearby $N_{\varphi }=+1$ integer vortex (green dots) over a circular area $A_{\mathrm{i}\mathrm{n}\mathrm{t}}$ centered at the tricrystal point. The blue line in (f) is the $N_{\varphi }=-1/2$ data multiplied by $-1$, demonstrating double degeneracy. The red line in (f) is the $N_{\varphi }=+1/2$ data multiplied by $2$.Reuse & Permissions

Figure 2

SQUID microscope images, taken with an $8\mu \mathrm{m}$ square pickup loop, of the tricrystal point region for an underdoped ($T_c=28.5\mathrm{K}$, $\mathrm{\text{thickness}}=310\mathrm{n}\mathrm{m}$) La-214 film epitaxially grown by laser ablation. (a) Difference image $[{\varphi }_s(+20\mathrm{n}\mathrm{T})-{\varphi }_s(-20\mathrm{n}\mathrm{T})]/2$ (to cancel out stray fields) for images taken with the sample cooled in $\pm 20\mathrm{n}\mathrm{T}$ fields, resulting in $N_{\varphi }=\pm 1/2$ Josephson vortices at the tricrystal point. The sum image $[{\varphi }_s(+20\mathrm{n}\mathrm{T})+{\varphi }_s(-20\mathrm{n}\mathrm{T})]/2$ (b) shows that the flux from the $N_{\varphi }=\pm 1/2$ vortices cancel out within a few percent. (c) Cross sections through the data of (a), and fits using the Josephson penetration depths ${\Lambda }_J$ along the two grain boundaries as fitting parameters, assuming the vortex at the tricrystal point has ${\varphi }_0/2$ of magnetic flux. The best fit value, allowing the total flux at the tricrystal point to vary, was $\varphi =(0.585\pm 0.1){\varphi }_0$.Reuse & Permissions

Figure 3

SQUID microscope images for tricrystal samples with optimally, underdoped, and overdoped ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ 300 nm thick films epitaxially grown by RF sputtering on a ${\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ substrate with the geometry of Fig. 1a. The images were taken with a $4\mu \mathrm{m}$ octagonal pickup loop (optimal) and a $7.5\mu \mathrm{m}$ square pickup loop (overdoped and underdoped). Full scale variation in ${\varphi }_s$ was $0.4{\varphi }_0$, $0.18{\varphi }_0$, and $0.21{\varphi }_0$, respectively. The lines are cross sections of the image data through the tricrystal point along the directions indicated.Reuse & Permissions

Figure 4

Plots of $4.2\mathrm{K}/T_{c,\max }$ vs $p$, the calculated doping holes per ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ layer, calculated from the ratio $T_c/T_{c,\max }$ using Eq. (1) (solid line), for the samples reported in this Letter, with $p_c=0.16$, and $T_{c,\max }=90$, 90, 38, and 82 K for optimally doped ${\mathrm{Y}\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ (yellow dot), ${\mathrm{Y}}_{0.7}{\mathrm{C}\mathrm{a}}_{0.3}{\mathrm{B}\mathrm{a}}_2{\mathrm{C}\mathrm{u}}_3{\mathrm{O}}_{7-\delta }$ (green dot), ${\mathrm{L}\mathrm{a}}_{1.85}{\mathrm{S}\mathrm{r}}_{0.15}{\mathrm{C}\mathrm{u}\mathrm{O}}_y$ (red dots), and ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_2{\mathrm{C}\mathrm{a}\mathrm{C}\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ (blue dots), respectively.Reuse & Permissions