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Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking

The existence of electronic symmetry breaking in the underdoped cuprates, and its disappearance with increased hole-density $p$, are now widely reported. However, the relationship between this transition and the momentum space ($\vec{k}$-space) electronic structure underpinning the superconductivity has not been established. Here we visualize the $\vec{Q}$=0 (intra-unit-cell) and $\vec{Q}\neq$0 (density wave) broken-symmetry states simultaneously with the coherent $\vec{k}$-space topology, for Bi$_2$Sr$_2$CaCu$_2$O$_{8+d}$ samples spanning the phase diagram 0.06$\leq p \leq$0.23. We show that the electronic symmetry breaking tendencies weaken with increasing $p$ and disappear close to $p_c$=0.19. Concomitantly, the coherent $\vec{k}$-space topology undergoes an abrupt transition, from arcs to closed contours, at the same $p_c$. These data reveal that the $\vec{k}$-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.