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There is a heated debate on the Josephson effect in twistedBi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes. Recent experimental results suggest thepresence of either anomalously isotropic pairing or exotic $d$+i$d$-wavepairing, in addition to the commonly believed $d$-wave one. Here, we addressthis controversy by fabricating ultraclean junctions with uncompromisedcrystalline quality and stoichiometry at the junction interfaces. In theoptimally doped regime, we obtain prominent Josephson coupling (2-4 mV) inmultiple junctions with the twist angle of 45$^\circ$, in sharp contrast to arecent report that shows two orders of magnitude suppression around 45$^\circ$from the value at 0$^\circ$. We further extend this study to the previouslyunexplored overdoped regime and observe pronounced Josephson tunneling at45$^\circ$ together with Josephson diode effect up to 50 K. Our work helpsestablish the persistent presence of an isotropic pairing component across theentire superconducting phase diagram.

Persistent Josephson tunneling between Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ flakes twisted by 45$^\circ$ across the superconducting dome