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The Hall coefficient R_H of the cuprate superconductor YBa2Cu3Oy was measuredin magnetic fields up to 60 T for a hole concentration p from 0.078 to 0.152,in the underdoped regime. In fields large enough to suppress superconductivity,R_H(T) is seen to go from positive at high temperature to negative at lowtemperature, for p > 0.08. This change of sign is attributed to the emergenceof an electron pocket in the Fermi surface at low temperature. At p < 0.08, thenormal-state R_H(T) remains positive at all temperatures, increasingmonotonically as T \to 0. We attribute the change of behaviour across p = 0.08to a Lifshitz transition, namely a change in Fermi-surface topology occurringat a critical concentration p_L = 0.08, where the electron pocket vanishes. Theloss of the high-mobility electron pocket across p_L coincides with a ten-folddrop in the conductivity at low temperature, revealed in measurements of theelectrical resistivity $\rho$ at high fields, showing that the so-calledmetal-insulator crossover of cuprates is in fact driven by a Lifshitztransition. It also coincides with a jump in the in-plane anisotropy of $\rho$,showing that without its electron pocket the Fermi surface must have strongtwo-fold in-plane anisotropy. These findings are consistent with aFermi-surface reconstruction caused by a unidirectional spin-density wave orstripe order.

Lifshitz critical point in the cuprate superconductor YBa2Cu3Oy from high-field Hall effect measurements