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

The current-voltage characteristics measured in the insulating state terminating the superconducting phase in disordered superconductors exhibit sharp threshold voltages, where the current abruptly changes by as much as 5 orders of magnitude. We analyze the current-voltage characteristics of an amorphous indium oxide film in the field-tuned insulating state, and show that they are consistent with a bistability of the electron temperature, and with a significant overheating of the electron system above the lattice temperature. An analysis of these current jumps indicates that, in the insulating state, the electrons are thermally decoupled from the phonon bath.

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the “superinsulating” phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T < 0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator.

The superconductor-insulator transition (SIT) is an accessible quantum phase transition 1,2 that is observed in a number of systems and can be driven by various experimental means 3-9 . A central outstanding issue regards the physical nature of the insulating phase terminating superconductivity 10 . Theoretical advances led to the proposition that this insulator is a new state of matter, termed a superinsulator 11,12 , because its properties can be inferred from the superconductor by invoking duality symmetry 13 . Here we report on the observation of duality symmetry near the magnetic-field-driven SIT in amorphous indium oxide. However, we show that the symmetry is broken by the emergence of the strong insulating state at low temperature.For the magnetic-field-driven SIT (B-SIT) in disordered films, the concept of vortex-charge duality was investigated in ref. 14, using the dirty boson model. In the superconductor, Cooper pairs are condensed into a superfluid at low temperature (T ) values leading to a zero resistivity (ρ) state, with vortices as bosonic excitations introducing dissipation and causing finite ρ. According to the duality concept, in the insulating state, vortices are condensed in a collective mode with zero conductivity (σ ), and the Cooper pairs are the bosonic excitation contributing to a finite σ .The vortex-charge duality has also been applied to the analysis of Josephson junction arrays 15,16 , which are often used as a model system for the SIT in disordered films 11,12,17 . In these systems the insulating state is commonly ascribed to a Coulomb blockade of superconducting islands. Duality is also applied to many other systems, for example, boson duality in two-dimensional electron gases 18 . Recently, evidence for the vortex-charge duality near a SIT was found in LaAlO 3 /SrTiO 3 interfaces 13 .Here, we experimentally investigate the duality symmetry across the B-SIT. We apply a duality transformation relating states within the superconductor to states in the B-driven insulator. We observe vortex-charge duality symmetry that holds up to one order of magnitude in B, T and ρ. The new aspect of this work is that we find systematic deviations from duality symmetry that originate in the B-induced magnetoresistance (ρ(B)) peak 5 . These deviations are qualitatively different at low and high T , as will be shown in detail below.In Fig. 1 we present ρ(B) isotherms obtained from sample RAM005b, which is superconducting at B = 0 with T c = 1.3 K. For all T values where reliable Ohmic data could be collected ρ increases with B until it reaches a T -dependent peak at B peak between 8.5-9.7 T. We restrict ourselves to T > 0.15 K because in the insulating phase, at T < 0.15 K, severe bi-stability of the electron T develops 19 , resulting in strongly nonlinear I -V , that prevented reliable measurements of ρ.The isotherms exhibit a weakly T -dependent crossing point close to h/(2e) 2 , where h is Planck's constant and 2e is the charge