Berezinskii-Kosterlitz-Thouless transition and anomalous metallic phase in a hybrid Josephson junction array

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a semiconductor-superconductor two-dimensional Josephson junction array. Tuned by an electrostatic top gate, the system exhibits separate superconducting (S), anomalous metal (M*), and insulating (I) phases, bordered by separatrices of the temperature-dependent sheet resistance ${R}_{s}$. We find that the gate-dependent BKT transition temperature falls to zero at the S-M* boundary, suggesting incomplete vortex-antivortex pairing in the M* phase. In the S phase, ${R}_{s}$ is roughly proportional to the perpendicular magnetic field at the BKT transition, as expected, while in the M* phase, ${R}_{s}$ deviates from its zero-field value as a power law in the field with exponent close to 1/2 at low temperature. An in-plane magnetic field eliminates the M* phase, leaving a small scaling exponent at the S-I boundary, which we interpret as a remnant of the incipient M* phase.