| Popis: |
Superconductivity has been at the heart of research into quantum phenomena since its discovery over a century ago. More recently efforts have been made to understand the nature of the quantum phase transition (QPT) that separates the superconducting and insulating phases in certain 2D materials at zero temperature. This superconductor-insulator transition (SIT) has been theoretically and experimentally proven to be driven by quantum fluctuations of the superconducting phase instead of the breakup of Cooper pairs. In this thesis we present a study of quantum fluctuations across the SIT and how they can be imaged in both theoretical simulations and experimental measurements. We begin with an overview of the field from a historical perspective, describing the development of the theory of SITs driven by experiments on thin films. We present the Josephson junction array (JJA) model as a paradigm to investigate the quantum phase fluctuation-driven SIT using quantum Monte Carlo (QMC) techniques.We explore the manifestation of quantum fluctuations across the SIT in three different local measurements: the diamagnetic susceptibility χ(r), two-particle density of states P(r, ω), and compressibility κ(r), revealed through their local maps and calculated via QMC. χ(r) probes the system’s ability to generate diamagnetic currents and its local map displays growing fluctuations upon increasing both temperature the quantum tuning parameter g. Remarkably, however, these fluctuations persist well below Tc as the SIT is approached, indicating the quantum nature of these fluctuations. We compare our results to SQUID susceptometry measurements performed on thin-film NbTiN and find good qualitative agreement. The map of κ(r) paints a similar picture when tuned via g, but in contrast to χ(r), we find a fundamental difference in its evolution with temperature, providing a complementary local probe to χ(r). P(r, ω), obtained using Maximum Entropy analytic continuation of imaginary time QMC data, shows strongly diminished zero-energy spectral weight in nearly-insulating islands, correlating with regions of suppressed κ(r). We discuss the experimental implications of our results for scanning Josephson spectroscopy, compressibility, and scanning SQUID measurements, the first time these quantities have been discussed together in the context of quantum fluctuations. |
