Broadened quantum critical ground state in a disordered superconducting thin film

A superconductor-insulator transition (SIT) in two dimensions is a prototypical quantum phase transition (QPT) with a clear quantum critical point (QCP) at zero temperature (T = 0). The SIT is induced by a field B and observed in disordered thin films. In some of weakly disordered or crystalline thin films, however, an anomalous metallic (AM) ground state emerges over a wide B range between the superconducting and insulating phases. It remains a fundamental open question how the QPT picture of the SIT is modified when the AM state appears. Here we present measurements of the Nernst effect N, which has great sensitivity to the fluctuations of the superconducting order parameter. From a thorough contour map of N in the B-T plane, we found a thermal-to-quantum crossover line of the superconducting fluctuations, a so-called ghost-temperature line associated with the QPT, as well as a ghost-field line associated with a thermal transition. The QCP is identified as a T = 0 intercept of the ghost-temperature line inside the AM state, which verifies that the AM state is a broadened critical state of the SIT.