Flow diagram of the metal-insulator transition in two dimensions

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems challenged the veracity of one of the most influential conjectures in the physics of disordered electrons, which states that `in two dimensions, there is no true metallic behaviour'; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory (Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this diagram is accurately described by the renormalization group theory without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a value in remarkable agreement with the one predicted by the theory.Comment: as publishe

Coherent quantum phase slip

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 dual to the Josephson effect: whilst the latter is a coherent transfer of charges between superconducting contacts, the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations of incoherent phase slip, the CQPS has been only a subject of theoretical study. Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors in the vicinity of the superconductor-insulator transition (SIT). Here we report the first direct observation of the CQPS in a strongly disordered indium-oxide (InOx) superconducting wire inserted in a loop, which is manifested by the superposition of the quantum states with different number of fluxes. Similarly to the Josephson effect, our observation is expected to lead to novel applications in superconducting electronics and quantum metrology.Comment: 14 pages, 3 figure

Single and two-particle energy gaps across the disorder-driven superconductor-insulator transition

The competition between superconductivity and localization raises profound questions in condensed matter physics. In spite of decades of research, the mechanism of the superconductor-insulator transition (SIT) and the nature of the insulator are not understood. We use quantum Monte Carlo simulations that treat, on an equal footing, inhomogeneous amplitude variations and phase fluctuations, a major advance over previous theories. We gain new microscopic insights and make testable predictions for local spectroscopic probes. The energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT, despite a robust single-particle gap.Comment: 7 pages, 5 figures (plus supplement with 4 pages, 5 figures

Localization of preformed Cooper pairs in disordered superconductors

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

Fermi liquids and Luttinger liquids

In these lecture notes, the basic physics of Fermi liquids and Luttinger liquids is presented. Fermi liquids are discussed both from a phenomenological viewpoint, in relation to microscopic approaches, and as renormalization group fixed points. Luttinger liquids are introduced using the bosonization formalism, and their essential differences with Fermi liquids are pointed out. Applications to transport effects, the effect of disorder, quantum spin chains, and spin ladders, both insulating and metallic, are given