Figure 1

(a) Schematic layout of the investigated SQUIDs. Four grain boundaries are crossing the “$\pi$ design”; grain boundary 4 has a nominal misorientation of 0° and for that reason it is not an active one. All of the other three are 30° [001]-tilt symmetric grain boundaries rotated by 120° with respect to one another, each of them creating a Josephson junction. A single grain boundary is crossing the “0 design.” The current $I$ and voltage $U$ leads are indicated; also shown are the lobes of a potential $d_{x^2-y^2}$ order parameter. (b) Enlarged optical microscope image of the “tetracrystal point” showing the ${\mathrm{L}\mathrm{a}}_{2-x}{\mathrm{C}\mathrm{e}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_{4-y}$ crystal orientations (the orientation of the $a$ and $b$ vectors) on each of the four crystals (white crystallites a few microns long oriented perpendicular to each other within each of the four crystals are clearly visible).Reuse & Permissions

Figure 2

Current-voltage characteristics measured at 4.2 K of the “$\pi$ design” for an applied field $B_{\mathrm{o}\mathrm{f}\mathrm{f}\mathrm{s}\mathrm{e}\mathrm{t}}$ that cancels out the background residual field in the shielded cryostat and consequently minimizes the critical current, and for the smallest magnetic field that causes a maximum of the critical current.Reuse & Permissions

Figure 3

Dependencies of the critical current $I_c$ on applied magnetic field (a) of the “0 design” and (b) of the “$\pi$ design” at 4.2 K.Reuse & Permissions

Figure 4

Calculated critical current versus applied flux per junction for a standard SQUID and a $\pi$-SQUID. $I_{\max }$ is defined as $\max (j_{c1},j_{c2})(2w+h)d$.Reuse & Permissions