Local control of parity and charge in nanoscale superconducting lead islands

Small superconducting islands can exhibit charge quantization, where Coulomb interactions compete with Cooper pairing. Using scanning tunneling spectroscopy, we probe this interplay by measuring the charging energy ($E_C$) and the pairing energy ($\Delta$) of individual nano-islands. Below a critical island size, where $E_C > \Delta$, we observe a crossover between even and odd parity ground states. By applying controlled voltage pulses, we continuously tune the island's electrostatic potential and map the full charge-parity landscape. These results demonstrate tunable superconducting ground states, offering a potential platform for qubit design and control.