Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.
We discuss the boundary critical behaviors of two-dimensional (2D) quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the one-dimensional boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: (i) the quantum phase transition between a 2D
Z2 topological order and an ordered phase with spontaneous symmetry breaking; (ii) the continuous quantum phase transition between metal and a particular type of Mott insulator [
U(1) spin liquid]. In particular, we obtain the critical exponents and scaling laws of these exotic quantum phase transitions when the systems are probed from the boundary in proposed experimental setup. These critical exponents obtained are significantly different from those one would see through bulk measurements. This theoretical study could be relevant to many purely 2D systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.