Quantum criticality inside the field-induced metallic state in an amorphous superconducting thin film

The field-induced superconductor-insulator transition (SIT) in disordered thin films is a typical example of a quantum phase transition. The quantum criticality of SIT has been demonstrated by a scaling analysis of resistance[1], and quite recently by thermoelectric Nernst signals[2]. Meanwhile, the picture for the superconductor-metal-insulator transition (SMIT) observed in some two-dimensional systems[3] has not been revealed from resistance measurements. To uncover the critical behavior associated with the SMIT, we conducted Nernst measurements in an amorphous Mo_xGe_1-x thin film down to 0.1 K[4]. We detected amplitude fluctuations and phase fluctuations (vortex liquid) of the order parameter over the whole field range. The vortex-liquid signals remain toward 0 K within a field range of the anomalous metallic state, indicating a quantum vortex liquid. The transport entropy of vortices in the quantum vortex liquid evokes the quantum critical behavior, suggesting that the metallic state results from broadening of the quantum critical point of SIT.
[1] A. M. Goldman and N. Marcović, Phys. Today 51, 39 (1998).
[2] A. Roy et al., Phys. Rev. Lett. 121, 047003 (2018).
[3] A. Kapitulnik et al., Rev. Mod. Phys. 91, 011002 (2019).
[4] K. Ienaga et al., submitted to Phys. Rev. Lett.