Vortex core spectroscopy links pseudogap and Lifshitz critical point in a cuprate superconductor

Understanding how superconductivity competes with other electronic phases in cuprates requires direct access to the hidden non-superconducting low temperature phase, for which Abrikosov vortices provide a unique local probe. We map the doping- and field-dependent evolution of vortex-core states in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ across a broad doping range spanning the Fermi-surface Lifshitz transition. High-resolution scanning tunneling spectroscopy reveals a striking transformation of the vortex-core spectrum from unconventional, pseudogap-like signatures at moderate doping to more BCS-like behavior beyond a critical doping $p^{\ast }\approx 0.21$. This crossover aligns with the pseudogap endpoint and the onset of Fermi-surface reconstruction, indicating a direct link between pseudogap physics and vortex electronic structure. Our findings highlight the vortex core as a sensitive local probe of the cuprate ground state.