The field-induced superconductor-insulator transition (SIT) in disordered thin films is a typical example of a quantum phase transition (QPT) [1]. The SIT results from the requirement that in two dimensions electrons should be localized at zero temperature (T = 0), otherwise condense. The quantum criticality of SIT has been demonstrated by a scaling analysis of the resistance. Meanwhile, in some two-dimensional systems, such as amorphous films [2], Josephson junction arrays [2], and recently-developed highly crystalline films [3], an emergence of the anomalous metallic state between the superconducting and insulating phases has been reported. The QPT picture for SIT is not applicable to the superconductor-metal-insulator transition (SMIT) [2], whose origin has not been fully revealed from resistance measurements. Therefore, it is necessary to uncover the role of quantum fluctuations and critical behavior associated with the SMIT.

In this study [4], we performed thermoelectric Nernst measurements down to 0.1 K, which sensitively detect fluctuations of the superconducting order parameter [5]. We studied a 12 nm-thick amorphous MoxGe1-x thin film, which shows the field-induced SMIT. Over the whole field range, amplitude fluctuations and phase fluctuations (vortex liquid) of the order parameter are clearly detected. As T → 0, the field range where the vortex-liquid signals are observable shrinks but remains finite within the metallic state, indicating that the metallic state stems from a quantum vortex liquid (QVL). Moreover, the transport entropy of vortices in the QVL phase decays slowly at T →0, which evokes the behavior of a quantum critical point. These results suggest that the metallic state results from broadening of the quantum critical point of SIT.

 [1] A. M. Goldman and N. Marcovi´c, Physics Today 51, 39 (1998).
[2] A. Kapitulnik, S. A. Kivelson, and B. Spivak, Rev. Mod. Phys. 91, 011002 (2019).
[3] Y. Saito, Y. Kasahara, J. Ye, Y. Iwasa, and T. Nojima, Science 350, 409 (2015).
[4] K. Ienaga, T. Hayashi, Y. Tamoto, S. Kaneko, and S. Okuma (submitted).
[5] K. Behnia and H. Aubin, Rep. Prog. Phys. 79, 046502 (2016).

Keywords: two-dimensional superconductor, quantum critical point, thermoelectric measurement