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The 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 of 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 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 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.