A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite temperature counterparts, their dynamic and static critical behaviors are intimately intertwined.We show that considerable insight is gained by considering the path integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite temperature behavior, which turns out to be described by the theory of finite size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations.We illustrate these ideas using Josephson junction arrays and with a set of recent experiments on phase transitions in systems exhibiting the quantum Hall effect. CONTENTS

We present the results of an experimental study of superconducting, disordered, thin films of amorphous indium oxide. These films can be driven from the superconducting phase to a reentrant insulating state by the application of a perpendicular magnetic field (B). We find that the high-B insulator exhibits activated transport with a characteristic temperature, TI. TI has a maximum value (TpI) that is close to the superconducting transition temperature (Tc) at B=0, suggesting a possible relation between the conduction mechanisms in the superconducting and insulating phases. Tp(I) and Tc display opposite dependences on the disorder strength.

International audienceThe most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a pronounced transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behaviour proceeds through the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address this question by studying the local superconducting gap of a highly disordered amorphous superconductor by means of scanning tunnelling spectroscopy. Our measurements reveal that, in the vicinity of the superconductor-insulator transition, the coherence peaks in the one-particle density of states disappear whereas the superconducting gap remains intact, indicating the presence of localized Cooper pairs. Our results provide the first direct evidence that the superconductor-insulator transition in some homogeneously disordered materials is driven by Cooper-pair localization

A hundred years after discovery of superconductivity, one fundamental prediction of the theory, the coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect: whilst the latter is a coherent transfer of charges between superconducting contacts 2,3 , the former is a

We report on a zero magnetic field transport study of a two-dimensional, variable-density, hole system in GaAs. As the density is varied we observe, for the first time in GaAsbased materials, a crossover from an insulating behavior at low-density, to a metallic-like behavior at high-density, where the metallic behavior is characterized by a large drop in the resistivity as the temperature is lowered. These results are in agreement with recent experiments on Si-based twodimensional systems by Kravchenko et al.[1] and others [2][3][4][5]. We show that, in the metallic region, the resistivity is dominated by an exponential temperature-dependence with a characteristic temperature which is proportional to the hole density, and appear to reach a constant value at lower temperatures. 71.30.+hThe study of the transport properties of twodimensional electron systems (2DES's) revealed numerous unique features associated with their reduced dimensionality. A central question is whether a metal-insulator transition (MIT) can occur in two-dimensions (2D). Using scaling arguments Abrahams et al. [6] stated that non-interacting electrons in 2D systems are localized at zero temperature (T ) for any level of disorder, and a MIT is not expected to occur at zero magnetic-field (B). This work motivated several experimental studies which investigated the T dependence of the resistivity (ρ) of low-mobility 2DES in Si metal-oxide semiconductor filedeffect transistors (MOSFET's) [7,8] and in In 2 O 3−x films [9]. The resistivity was found to increase with decreasing T , and its T -dependence changed from weak to strong as the density of the 2DES was lowered, or the disorder increased. These experiments seemed to confirm the theoretical notion that no metallic phase exists in 2D.However, several recent studies presented evidence to the contrary. In these studies 2DES's in Si MOSFET's [1,2] and Si/SiGe heterostructure [3][4][5] were used, and the resistivity was measured as a function of T for various carrier-densities. These studies demonstrated a clear crossover from metallic to insulating behavior at low T . Further, in the metallic region, the resistivity was shown to decrease with decreasing T by as much as a factor of eight, while in the insulating region the resistivity increases sharply with decreasing T . The authors of refs.[1] took these results as evidence for the existence of a MIT in 2D, and several theoretical works have tried to associate them with modified scaling [10] or raised the possibility of superconductivity [11,12]. The disagreement between these new results and earlier ones are generally attributed to the higher mobility in these samples (reaching a value as high as 75, 000 cm 2 /V ·s) and to the high effective mass of electrons in Si (m = 0.19m 0 ) which, according to the authors, combine to accentuate the effect of carrier-carrier interactions. It was therefore suggested [13] that due to the heavy mass of holes in GaAs (0.6m 0 , 0.38m 0 ) [14,15] and the superior quality of molecular beam epitaxy (MBE) growth, a ...